DAGM-2M conditional volatility (with skewness)

Description

Obtains the conditional volatility of the DAGM with two MIDAS variables. For details, see Amendola et al. (2019).

Usage

DAGM_2M_cond_vol(param, daily_ret, mv_m_1, mv_m_2, K_1, K_2, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

start_val<-c(0.01,0.80,0.05,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(DAGM_2M_cond_vol(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

DAGM-2M conditional volatility (no skewness)

Description

Obtains the conditional volatility of the DAGM with two MIDAS variables. For details, see Amendola et al. (2019).

Usage

DAGM_2M_cond_vol_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

start_val<-c(0.01,0.80,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(DAGM_2M_cond_vol_no_skew(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

DAGM-2M log-likelihood (with skewness)

Description

Obtains the log-likelihood of the DAGM with two MIDAS variables, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_2M_loglik(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(0.01,0.80,0.05,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
sum(DAGM_2M_loglik(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24,distribution="norm"))

DAGM-2M log-likelihood (without skewness)

Description

Obtains the log-likelihood of the DAGM with two MIDAS variables, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_2M_loglik_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(0.01,0.80,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
sum(DAGM_2M_loglik_no_skew(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24,distribution="norm"))

DAGM-2M (daily) long-run volatility (with skewness)

Description

Obtains the long-run volatility of the DAGM with two MIDAS variables. For details, see Amendola et al. (2019).

Usage

DAGM_2M_long_run(param, daily_ret, mv_m_1, mv_m_2, K_1, K_2, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the long-run volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

start_val<-c(0.01,0.80,0.05,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(DAGM_2M_long_run(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

DAGM-2M (daily) long-run volatility (no skewness)

Description

Obtains the long-run volatility of the DAGM with two MIDAS variables. For details, see Amendola et al. (2019).

Usage

DAGM_2M_long_run_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is an "xts" object representing the long-run volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

start_val<-c(0.01,0.80,0.2,0.1,1.1,0.4,1.1,0.5,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(DAGM_2M_long_run_no_skew(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

DAGM-X conditional volatility (with skewness)

Description

Obtains the conditional volatility for the DAGM-X, with an asymmetric term linked to past negative returns. For details, see Amendola et al. (2019).

Usage

DAGM_X_cond_vol(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# estimated volatility 
est_val<-c(0.01,0.80,0.05,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
vol<-DAGM_X_cond_vol(est_val,r_t,X,mv_m,K=12)
head(vol)

DAGM-X conditional volatility (no skewness)

Description

Obtains the conditional volatility for the DAGM-X. For details, see Amendola et al. (2019).

Usage

DAGM_X_cond_vol_no_skew(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# estimated volatility 
est_val<-c(0.01,0.80,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
vol<-DAGM_X_cond_vol_no_skew(est_val,r_t,X,mv_m,K=12)
head(vol)

DAGM-X log-likelihood (with skewness)

Description

Obtains the log-likelihood of the DAGM-X, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_X_loglik(param, daily_ret, X, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(0.01,0.80,0.05,0.05,0,0,1.1,0,1.1)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(DAGM_X_loglik(start_val,r_t,X,mv_m,K=12,distribution="norm"))

DAGM-X log-likelihood (no skewness)

Description

Obtains the log-likelihood of the DAGM-X, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_X_loglik_no_skew(
  param,
  daily_ret,
  X,
  mv_m,
  K,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(0.01,0.80,0.05,0,0,1.1,0,1.1)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(DAGM_X_loglik_no_skew(start_val,r_t,X,mv_m,K=12,distribution="norm"))

DAGM-X (daily) long-run volatility (with skewness)

Description

Obtains the daily long-run volatility for the DAGM-X, with an asymmetric term linked to past negative returns. For details, see Amendola et al. (2019).

Usage

DAGM_X_long_run_vol(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

est_val<-c(0.01,0.80,0.05,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(DAGM_X_long_run_vol(est_val,r_t,X,mv_m,K=12))

DAGM-X (daily) long-run volatility (no skewness)

Description

Obtains the daily long-run volatility for the DAGM-X. For details, see Amendola et al. (2019).

Usage

DAGM_X_long_run_vol_no_skew(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

est_val<-c(0.01,0.80,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(DAGM_X_long_run_vol_no_skew(est_val,r_t,X,mv_m,K=12))

DAGM conditional volatility (with skewness)

Description

Obtains the conditional volatility for the DAGM, with an asymmetric term linked to past negative returns. For details, see Amendola et al. (2019).

Usage

DAGM_cond_vol(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# estimated volatility 
est_val<-c(0.01,0.80,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
vol<-DAGM_cond_vol(est_val,r_t,mv_m,K=12)
head(vol)

DAGM conditional volatility (no skewness)

Description

Obtains the conditional volatility for the DAGM. For details, see Amendola et al. (2019).

Usage

DAGM_cond_vol_no_skew(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# est_val<-c(0.01,0.80,0,0.1,1.1,-0.3,1.1)
# r_t<-sp500['/2010']
# mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
# head(DAGM_cond_vol_no_skew(est_val,r_t,mv_m,K=12))

DAGM log-likelihood (with skewness)

Description

Obtains the log-likelihood of the DAGM, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_loglik(param, daily_ret, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(0.01,0.80,0.05,0,0,1.1,0,1.1)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(DAGM_loglik(start_val,r_t,mv_m,K=12,distribution="norm"))

DAGM log-likelihood (without skewness)

Description

Obtains the log-likelihood of the DAGM, without the asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Amendola et al. (2019).

Usage

DAGM_loglik_no_skew(param, daily_ret, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.80,gamma_1=0.05,m=0,theta_pos=0,w2_pos=1.1,theta_neg=0,w2_neg=1.1)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(DAGM_loglik(start_val,r_t,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(0.01,0.80,0.05,0,0,1.1,0,1.1,5)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(DAGM_loglik(start_val,r_t,mv_m,K=12,distribution="std"))

DAGM (daily) long-run volatility (with skewness)

Description

Obtains the daily long-run volatility for the DAGM, with an asymmetric term linked to past negative returns. For details, see Amendola et al. (2019).

Usage

DAGM_long_run_vol(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

est_val<-c(0.01,0.80,0.05,0,0.1,1.1,-0.3,1.1)
r_t<-sp500['/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(DAGM_long_run_vol(est_val,r_t,mv_m,K=12))

DAGM (daily) long-run volatility (no skewness)

Description

Obtains the daily long-run volatility for the DAGM. For details, see Amendola et al. (2019).

Usage

DAGM_long_run_vol_no_skew(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the long-run volatility.

References

Amendola A, Candila V, Gallo GM (2019). “On the asymmetric impact of macro–variables on volatility.” Economic Modelling, 76, 135–152. doi:10.1016/j.econmod.2018.07.025.

See Also

mv_into_mat.

Examples

# est_val<-c(0.01,0.80,0,0.1,1.1,-0.3,1.1)
# r_t<-sp500['/2010']
# mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
# head(DAGM_long_run_vol_no_skew(est_val,r_t,mv_m,K=12))

GARCH-MIDAS-2M conditional volatility (with skewness)

Description

Obtains the conditional volatility of the GARCH-MIDAS with two low-frequency variables, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_cond_vol(param, daily_ret, mv_m_1, mv_m_2, K_1, K_2, lag_fun = "Beta")

Arguments

Value

The resulting vector is the conditional volatility for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(GM_2M_cond_vol(est_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

GARCH-MIDAS-2M conditional volatility (without skewness)

Description

Obtains the conditional volatility of the GARCH-MIDAS with two low-frequency variables. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_cond_vol_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the conditional volatility for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(GM_2M_cond_vol_no_skew(est_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

GARCH-MIDAS-2M log-likelihood (with skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS with two low-frequency variables, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_loglik(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
sum(GM_2M_loglik(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24,distribution="norm"))

GARCH-MIDAS-2M log-likelihood (without skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS with two low-frequency variables, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_loglik_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
sum(GM_2M_loglik_no_skew(start_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24,distribution="norm"))

GARCH-MIDAS-2M long-run volatility (with skewness)

Description

Obtains the long-run volatility of the GARCH-MIDAS with two low-frequency variables, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_long_run_vol(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the long-run volatility for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(GM_2M_long_run_vol(est_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

GARCH-MIDAS-2M long-run volatility (without skewness)

Description

Obtains the long-run volatility of the GARCH-MIDAS with two low-frequency variables. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_2M_long_run_vol_no_skew(
  param,
  daily_ret,
  mv_m_1,
  mv_m_2,
  K_1,
  K_2,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the long-run volatility for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
est_val<-c(alpha=0.01,beta=0.8,m=0,theta_1=0.1,w2_1=2,theta_2=0.1,w2_2=2)
r_t<-sp500['2005/2010']
mv_m_1<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
mv_m_2<-mv_into_mat(r_t,diff(indpro),K=24,"monthly")
head(GM_2M_long_run_vol_no_skew(est_val,r_t,mv_m_1,mv_m_2,K_1=12,K_2=24))

GARCH-MIDAS-X conditional volatility (with skewness)

Description

Obtains the estimated conditional volatility for the GARCH-MIDAS-X model, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_cond_vol(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# estimated volatility
est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,z=0.1,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_X_cond_vol(est_val,r_t,X,mv_m,K=12))

GARCH-MIDAS-X conditional volatility (without skewness)

Description

Obtains the estimated conditional volatility for the GARCH-MIDAS-X model, without the skewness parameter in the short–run. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_cond_vol_no_skew(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,z=0.1,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_X_cond_vol_no_skew(est_val,r_t,X,mv_m,K=12))

GARCH-MIDAS-X log-likelihood (with skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS-X, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_loglik(param, daily_ret, X, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,z=0.1,m=0,theta=0.1,w2=2)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_X_loglik(start_val,r_t,X=X,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,z=0.1,m=0,theta=0.1,w2=2,shape=5)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_X_loglik(start_val,r_t,X=X,mv_m,K=12,distribution="std"))

GARCH-MIDAS-X log-likelihood (no skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS-X, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_loglik_no_skew(
  param,
  daily_ret,
  X,
  mv_m,
  K,
  distribution,
  lag_fun = "Beta"
)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,z=0.1,m=0,theta=0.1,w2=2)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_X_loglik_no_skew(start_val,r_t,X,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,z=0.1,m=0,theta=0.1,w2=2,shape=5)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,indpro,K=12,"monthly")
sum(GM_X_loglik_no_skew(start_val,r_t,X,mv_m,K=12,distribution="std"))

GARCH-MIDAS-X (daily) long-run (with skewness)

Description

Obtains the estimated daily long-run volatility for the GARCH-MIDAS-X model, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_long_run_vol(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# estimated volatility
est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,z=0.1,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_X_long_run_vol(est_val,r_t,X,mv_m,K=12))

GARCH-MIDAS-X (daily) long-run volatility (without skewness)

Description

Obtains the daily long-run volatility for the GARCH-MIDAS-X model, without the skewness parameter in the short–run. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_X_long_run_vol_no_skew(param, daily_ret, X, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,z=0.1,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
X<-rv5['/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_X_long_run_vol_no_skew(est_val,r_t,X,mv_m,K=12))

GARCH-MIDAS conditional volatility (with skewness)

Description

Obtains the estimated conditional volatility for the GARCH-MIDAS model, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_cond_vol(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# estimated volatility
est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_cond_vol(est_val,r_t,mv_m,K=12))

GARCH-MIDAS conditional volatility (without skewness)

Description

Obtains the estimated conditional volatility for the GARCH-MIDAS model, without the skewness parameter in the short–run. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_cond_vol_no_skew(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_cond_vol_no_skew(est_val,r_t,mv_m,K=12))

GARCH-MIDAS log-likelihood (with skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_loglik(param, daily_ret, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=0,theta=0.1,w2=2)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_loglik(start_val,r_t,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=0,theta=0.1,w2=2,shape=5)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_loglik(start_val,r_t,mv_m,K=12,distribution="std"))

GARCH-MIDAS log-likelihood (no skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS, according to two errors' conditional distributions: Normal and Student-t. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_loglik_no_skew(param, daily_ret, mv_m, K, distribution, lag_fun = "Beta")

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,m=0,theta=0.1,w2=2)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_loglik_no_skew(start_val,r_t,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,m=0,theta=0.1,w2=2,shape=5)
r_t<-sp500['2005/2010']
mv_m<-mv_into_mat(r_t,indpro,K=12,"monthly")
sum(GM_loglik_no_skew(start_val,r_t,mv_m,K=12,distribution="std"))

GARCH-MIDAS (daily) long-run (with skewness)

Description

Obtains the estimated daily long-run volatility for the GARCH-MIDAS model, with an asymmetric term linked to past negative returns. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_long_run_vol(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

# estimated volatility
est_val<-c(alpha=0.01,beta=0.8,gamma=0.05,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_long_run_vol(est_val,r_t,mv_m,K=12))

GARCH-MIDAS (daily) long-run volatility (without skewness)

Description

Obtains the daily long-run volatility for the GARCH-MIDAS model, without the skewness parameter in the short-run.. For details, see Engle et al. (2013) and Conrad and Loch (2015).

Usage

GM_long_run_vol_no_skew(param, daily_ret, mv_m, K, lag_fun = "Beta")

Arguments

Value

The resulting vector is an "xts" object representing the conditional volatility.

References

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.01,beta=0.8,m=2,theta=0.1,w2=2)
r_t<-sp500['/2010']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
head(GM_long_run_vol_no_skew(est_val,r_t,mv_m,K=12))

Information Criteria

Description

Returns the Akaike and Bayesian information criteria.

Usage

Inf_criteria(est)

Arguments

Value

The resulting vector represents the AIC and BIC criteria.

Loss functions

Description

Returns the MSE and QLIKE.

Usage

LF_f(vol_est, vol_proxy)

Arguments

Value

The resulting vector represents the MSE and QLIKE averages.

MEM-MIDAS-X log-likelihood (with skewness parameter)

Description

Obtains the log-likelihood of the MEM-MIDAS-X, with an asymmetric term linked to past negative returns and an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_loglik(param, x, daily_ret, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

start_val<-c(alpha=0.10,beta=0.8,gamma=0.1,m=0,theta=-0.16,w2=5,delta=0.1)
r_t<-sp500['2010']
real<-(rv5['2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_X_loglik(start_val,real,r_t,mv_m,K=12,z=vix['2010']))

MEM-MIDAS-X log-likelihood (no skewness parameter)

Description

Obtains the log-likelihood of the MEM-MIDAS-X, with an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_loglik_no_skew(param, x, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

start_val<-c(alpha=0.10,beta=0.8,m=0,theta=-0.16,w2=5,delta=0.1)
real<-(rv5['2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_X_loglik_no_skew(start_val,real,mv_m,K=12,z=vix['2010']))

MEM-MIDAS-X long-run one-step-ahead predictions (with skewness parameter)

Description

Predicts the long-run term of the dependent variable, usually the realized volatility, for the MEM-MIDAS-X, with an asymmetric term linked to past negative returns and an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_lr_pred(param, x, daily_ret, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

MEM-MIDAS-X long-run one-step-ahead predictions (no skewness parameter)

Description

Predicts the long-run term of the dependent variable, usually the realized volatility, for the MEM-MIDAS-X, with an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_lr_pred_no_skew(param, x, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

MEM-MIDAS-X one-step-ahead predictions (with skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the MEM-MIDAS-X, with an asymmetric term linked to past negative returns and an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_pred(param, x, daily_ret, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

MEM-MIDAS-X one-step-ahead predictions (no skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the MEM-MIDAS-X, with an additional X part (for instance, the VIX).

Usage

MEM_MIDAS_X_pred_no_skew(param, x, mv_m, K, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

MEM-MIDAS log-likelihood (with skewness parameter)

Description

Obtains the log-likelihood of the MEM-MIDAS, with an asymmetric term linked to past negative returns.

Usage

MEM_MIDAS_loglik(param, x, daily_ret, mv_m, K)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

start_val<-c(alpha=0.10,beta=0.8,gamma=0.1,m=0,theta=-0.16,w2=5)
r_t<-sp500['/2010']
real<-(rv5['/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_loglik(start_val,real,r_t,mv_m,K=12))

MEM-MIDAS log-likelihood (no skewness parameter)

Description

Obtains the log-likelihood of the MEM-MIDAS.

Usage

MEM_MIDAS_loglik_no_skew(param, x, mv_m, K)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

start_val<-c(alpha=0.10,beta=0.8,m=0,theta=-0.16,w2=5)
real<-(rv5['/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_loglik_no_skew(start_val,real,mv_m,K=12))

MEM-MIDAS long-run one-step-ahead predictions (with skewness parameter)

Description

Predicts the long-run term of the dependent variable, usually the realized volatility, for the MEM-MIDAS, with an asymmetric term linked to past negative returns.

Usage

MEM_MIDAS_lr_pred(param, x, daily_ret, mv_m, K)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.10,beta=0.8,gamma=0.1,m=0,theta=-0.16,w2=5)
r_t<-sp500['/2010']
real<-(rv5['/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
est_vol<-MEM_MIDAS_pred(est_val,real,r_t,mv_m,K=12)
head(est_vol)

MEM-MIDAS long-run one-step-ahead predictions (no skewness parameter)

Description

Predicts the long-run term of the dependent variable, usually the realized volatility, for the MEM-MIDAS.

Usage

MEM_MIDAS_lr_pred_no_skew(param, x, mv_m, K)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.10,beta=0.8,m=0,theta=-0.16,w2=5)
real<-(rv5['/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_lr_pred_no_skew(est_val,real,mv_m,K=12))

MEM-MIDAS one-step-ahead predictions (with skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the MEM-MIDAS, with an asymmetric term linked to past negative returns.

Usage

MEM_MIDAS_pred(param, x, daily_ret, mv_m, K)

Arguments

Value

The resulting vector is the one-step-ahead prediction for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.10,beta=0.8,gamma=0.1,m=0,theta=-0.16,w2=5)
r_t<-sp500['/2010']
real<-rv5['/2010']^0.5 # realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
est_vol<-MEM_MIDAS_pred(est_val,real,r_t,mv_m,K=12)
head(est_vol)

MEM-MIDAS one-step-ahead predictions (no skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the MEM-MIDAS.

Usage

MEM_MIDAS_pred_no_skew(param, x, mv_m, K)

Arguments

Value

The resulting vector is the one-step-ahead prediction for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

See Also

mv_into_mat.

Examples

est_val<-c(alpha=0.10,beta=0.8,m=0,theta=-0.16,w2=5)
real<-(rv5['/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
sum(MEM_MIDAS_pred_no_skew(est_val,real,mv_m,K=12))

Standard errors for the Quasi Maximum Likelihood estimator of the MEM-based models

Description

Obtains the standard errors for the Quasi Maximum Likelihood (QML) estimator.

Usage

MEM_QMLE_sd(est, x, x_pred)

Arguments

Value

The resulting vector represents the QML standard errors.

MEM-X log-likelihood (with skewness parameter)

Description

Obtains the log-likelihood of the base MEM, with an asymmetric term linked to past negative returns and an additional X part (for instance, the VIX).

Usage

MEM_X_loglik(param, x, daily_ret, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

start_val<-c(alpha=0.10,beta=0.8,gamma=0.05,delta=0.01)
real<-(rv5['2009/2010'])^0.5		# realized volatility
r_t<-sp500['2009/2010']
z<-vix['2009/2010']
sum(MEM_X_loglik(start_val,real,r_t,z))

MEM-X log-likelihood (no skewness parameter)

Description

Obtains the log-likelihood of the base MEM, with an additional X part (for instance, the VIX).

Usage

MEM_X_loglik_no_skew(param, x, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Examples

start_val<-c(alpha=0.10,beta=0.8,delta=0.01)
real<-(rv5['2009/2010'])^0.5		# realized volatility
z<-vix['2009/2010']
sum(MEM_X_loglik_no_skew(start_val,real,z))

MEM-X one-step-ahead predictions (with skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the base MEM, with an asymmetric term linked to past negative returns and an additional X part (for instance, the VIX).

Usage

MEM_X_pred(param, x, daily_ret, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

MEM-X one-step-ahead predictions (no skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the base MEM, with an additional X part (for instance, the VIX).

Usage

MEM_X_pred_no_skew(param, x, z)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

MEM log-likelihood (with skewness parameter)

Description

Obtains the log-likelihood of the base MEM, with an asymmetric term linked to past negative returns. For details, see Engle and Gallo (2006).

Usage

MEM_loglik(param, x, daily_ret)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Engle RF, Gallo GM (2006). “A Multiple Indicators Model for Volatility Using Intra-Daily Data.” Journal of Econometrics, 131, 3–27. doi:10.1016/j.jeconom.2005.01.018.

Examples

start_val<-c(alpha=0.10,beta=0.8,gamma=0.05)
real<-(rv5['/2010'])^0.5		# realized volatility
r_t<-sp500['/2010']
sum(MEM_loglik(start_val,real,r_t))

MEM log-likelihood (no skewness parameter)

Description

Obtains the log-likelihood of the base MEM. For details, see Engle and Gallo (2006).

Usage

MEM_loglik_no_skew(param, x)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Engle RF, Gallo GM (2006). “A Multiple Indicators Model for Volatility Using Intra-Daily Data.” Journal of Econometrics, 131, 3–27. doi:10.1016/j.jeconom.2005.01.018.

Examples

start_val<-c(alpha=0.10,beta=0.8)
real<-(rv5['/2010'])^0.5		# realized volatility
sum(MEM_loglik_no_skew(start_val,real))

MEM one-step-ahead predictions (with skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the base MEM, with an asymmetric term linked to past negative returns. For details, see Engle and Gallo (2006).

Usage

MEM_pred(param, x, daily_ret)

Arguments

Value

The resulting vector is the one-step-ahead prediction for each i,t.

References

Engle RF, Gallo GM (2006). “A Multiple Indicators Model for Volatility Using Intra-Daily Data.” Journal of Econometrics, 131, 3–27. doi:10.1016/j.jeconom.2005.01.018.

Examples

est_val<-c(alpha=0.10,beta=0.8,gamma=0.05)
real<-(rv5['/2010'])^0.5		# realized volatility
r_t<-sp500['/2010']
head(MEM_pred(est_val,real,r_t))

MEM one-step-ahead predictions (no skewness parameter)

Description

Predicts the dependent variable, usually the realized volatility, for the base MEM. For details, see Engle and Gallo (2006).

Usage

MEM_pred_no_skew(param, x)

Arguments

Value

The resulting vector is the log-likelihood value for each i,t.

References

Engle RF, Gallo GM (2006). “A Multiple Indicators Model for Volatility Using Intra-Daily Data.” Journal of Econometrics, 131, 3–27. doi:10.1016/j.jeconom.2005.01.018.

Examples

est_val<-c(alpha=0.10,beta=0.8)
real<-(rv5['/2010'])^0.5		# realized volatility
head(MEM_pred_no_skew(est_val,real))

Standard errors for the Quasi Maximum Likelihood estimator of the GARCH-MIDAS-based models

Description

Obtains the standard errors for the Quasi Maximum Likelihood (QML) estimator.

Usage

QMLE_sd(est)

Arguments

Value

The resulting vector represents the QML standard errors.

Beta function

Description

Represents a tool able to accommodate various lag structures for the additional MIDAS variable observed each "low-frequency" period t. It can have a monotonically increasing, decreasing weighting scheme or a hump-shaped weighting scheme. The Beta function is:

\delta_k(\omega)=\frac{(k/K)^{\omega_1-1} (1-k/K)^{\omega_2-1}}{\sum_{j=1}^K (j/K)^{\omega_1-1}(1-j/K)^{\omega_2-1}}.

For additional details, see Ghysels et al. (2007).

Usage

beta_function(k, K, w1, w2)

Arguments

Value

The weights associated to each lag k, with k=1,\cdots,K.

References

Ghysels E, Sinko A, Valkanov R (2007). “MIDAS regressions: Further results and new directions.” Econometric Reviews, 26(1), 53–90. doi:10.1080/07474930600972467.

Examples

# suppose to have four lags: 
# K<-4 
# w1<-1	# by setting w1=1, only a monotonically decreasing weighting scheme is allowed
	#(more recent observations weigh more)
# w2<-5
beta_function(1:4,K=4,w1=1,w2=5)

Exponential Almon Lag

Description

Represents a tool able to accommodate various lag structures for the additional MIDAS variable observed each "low-frequency" period t. It can have a monotonically increasing, decreasing weighting scheme or a hump-shaped weighting scheme. As in Ghysels et al. (2007), here the function form uses only two parameters:

\delta_k(\omega_1, \omega_2) = \frac{exp(\omega_{1}k + \omega_2 k^2)}{\sum_{k=1}^K exp(\omega_1 k + \omega_2 k^2)}.

For additional details, see Almon (1965) and Ghysels et al. (2007).

Usage

exp_almon(k, K, w1, w2)

Arguments

Value

The weights associated to each lag k, with k=1,\cdots,K.

References

Almon S (1965). “The distributed lag between capital appropriations and expenditures.” Econometrica: Journal of the Econometric Society, 178–196. doi:10.2307/1911894.

Ghysels E, Sinko A, Valkanov R (2007). “MIDAS regressions: Further results and new directions.” Econometric Reviews, 26(1), 53–90. doi:10.1080/07474930600972467.

Examples

# suppose to have four lags: 
# K<-4 # Note: the number of lags to consider
# w1<-1	
# w2<- -0.5 # by setting w2<0, the monotonically decreasing weighting scheme is used
exp_almon(1:4,K=4,w1=0.1,w2=-0.5)

Monthly U.S. Industrial Production

Description

Monthly data on the U.S. Industrial Production index (IP, index 2012=100, seasonally adjusted) collected from the Federal Reserve Economic Data (FRED) archive. The IP has been used as MIDAS term in different contributions (see, for instance, Engle et al. (2013), Conrad and Loch (2015), and Amendola et al. (2017)).

Usage

data(indpro)

Format

An object of class "xts".

Source

Archive of the Federal Reserve Economic Data (FRED)

References

Amendola A, Candila V, Scognamillo A (2017). “On the influence of US monetary policy on crude oil price volatility.” Empirical Economics, 52(1), 155–178. doi:10.1007/s00181-016-1069-5.

Conrad C, Loch K (2015). “Anticipating Long-Term Stock Market Volatility.” Journal of Applied Econometrics, 30(7), 1090–1114. doi:10.1002/jae.2404.

Engle RF, Ghysels E, Sohn B (2013). “Stock market volatility and macroeconomic fundamentals.” Review of Economics and Statistics, 95(3), 776–797. doi:10.1162/REST_a_00300.

Examples

head(indpro)
summary(indpro)
plot(indpro)

Multi–step–ahead predictions of the GARCH–MIDAS–based models with and without the '–X' part.

Description

Calculates the multi–step–ahead predictions for the GARCH–MIDAS and DAGM models, according to the procedure suggested by Amendola et al. (2021).

Usage

multi_step_ahead_pred(est, h, X = NULL)

Arguments

Details

The multi–step–ahead procedure calculates the volatility predictions keeping fixed the information set at the last observation available and projecting forward the forecasts. The procedure calculates the volatility predictions conditionally to the parameters estimated in the in-sample period. Therefore, the estimation object (through the ugmfit function) has to be provided. For additional details, see Eq. (20) in Amendola et al. (2021).

Value

The multi-step-ahead predictions, for the following h days, starting from the last day of the chosen in-sample period adopted in the 'est' object.

References

Amendola A, Candila V, Gallo GM (2021). “Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model.” Economic and Statistics. doi:10.1016/j.ecosta.2020.11.001.

Examples

r_t<-sp500['2008']
X<-(rv5['2008'])^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly") 
fit<-ugmfit(model="GMX",skew="YES",distribution="norm",r_t,mv_m,K=12,X=X)
### ten days predictions
multi_step_ahead_pred(fit,h=10,X)

MIDAS variable matrix transformation

Description

Implements the transformation of the MIDAS variable into a matrix, whose dimension is (K+1) \times N, where K is the number of lagged realizations to consider and N is the length of the variable x.

Usage

mv_into_mat(x, mv, K, type)

Arguments

Value

The resulting matrix has as many rows as the number of lagged realizations (plus one) of the MIDAS variable to consider, and as many columns as the length of x.

Examples

require(xts)
# weekly frequency
# obtain weekly MIDAS variable after daily aggregation
RV_weekly_sum<-apply.weekly(rv5^0.5,sum) #realized volatility
# then allocate correctly the information
RV_weekly<-as.xts(coredata(RV_weekly_sum),seq(as.Date("2000-01-10"), 
by = "week", length.out = length(RV_weekly_sum)))
# use mv_into_mat 
mv_into_mat(sp500['2002/2003-12-26'],diff(RV_weekly['/2003-12']),K=4,type="weekly")

# monthly frequency
r_t<-sp500['2005/2010']
mv_into_mat(r_t,diff(indpro),K=12,type="monthly")

# quarterly frequency
RV_quarterly_sum<-apply.quarterly(rv5,sum)
RV_quarterly<-as.xts(coredata(RV_quarterly_sum),seq(as.Date("2000-04-01"), 
by = "quarter", length.out = length(RV_quarterly_sum)))
mv_into_mat(sp500['2004/2010'],diff(RV_quarterly),K=10,type="quarterly")

# yearly frequency
RV_yearly_sum<-apply.yearly(rv5,sum)
RV_yearly<-as.xts(coredata(RV_yearly_sum),seq(as.Date("2001-01-01"), 
by = "year", length.out = length(RV_yearly_sum)))
mv_into_mat(sp500['2006/2010'],diff(RV_yearly),K=2,type="yearly")

Print method for 'rumidas' class

Description

Print method for 'rumidas' class

Usage

## S3 method for class 'rumidas'
print(x, ...)

Arguments

S&P 500 realized variance at 5-minutes

Description

Daily data on the realized variance of the S&P 500 collected from the realized library of the Oxford-Man Institute (Heber et al. 2009). The realized variance has been calculated using intradaily intervals of five minutes (Andersen and Bollerslev 1998).

Usage

data(rv5)

Format

An object of class "xts".

Source

Realized library of the Oxford-Man Institute

References

Andersen TG, Bollerslev T (1998). “Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts.” International Economic Review, 39, 885–905. doi:10.2307/2527343.

Heber G, Lunde A, Shephard N, Sheppard K (2009). “OMI's realised library, version 0.1.” Oxford–Man Institute, University of Oxford.

Examples

head(rv5)
summary(rv5)
plot(rv5)

S&P 500 daily log-returns

Description

Daily data on S&P 500 collected from the realized library of the Oxford-Man Institute (Heber et al. 2009).

Usage

data(sp500)

Format

An object of class "xts".

Source

Realized library of the Oxford-Man Institute

References

Heber G, Lunde A, Shephard N, Sheppard K (2009). “OMI's realised library, version 0.1.” Oxford–Man Institute, University of Oxford.

Examples

head(sp500)
summary(sp500)
plot(sp500)

Summation function for the multi-step-ahead predictions of the GARCH–MIDAS models with the '–X' part.

Description

For details, see Eq. (20) of Amendola et al. (2021).

Usage

sum_X_f(COEF, DELTA, H)

Arguments

Value

The vector of the summation for each H.

References

Amendola A, Candila V, Gallo GM (2021). “Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model.” Economic and Statistics. doi:10.1016/j.ecosta.2020.11.001.

Summary method for 'rumidas' class

Description

Summary method for 'rumidas' class

Usage

## S3 method for class 'rumidas'
summary(object, ...)

Arguments

Examples

r_t<-sp500['2003/2010']
real<-(rv5['2003/2010'])^0.5		# realized volatility
fit<-umemfit(model="MEM",skew="NO",x=real)
summary.rumidas(fit)

Methods for obtaining (and evaluating) a variety of GARCH-MIDAS-based models

Description

Estimates several GARCH-MIDAS-based models, according to two errors' conditional distributions: Normal and Student-t, and the presence of asymmetric terms in the short- and long-run components.

Usage

ugmfit(
  model,
  skew,
  distribution,
  daily_ret,
  mv_m,
  mv_m_2 = NULL,
  K,
  K_2 = NULL,
  lag_fun = "Beta",
  X = NULL,
  out_of_sample = NULL,
  vol_proxy = NULL,
  R = 100
)

Arguments

Details

Function ugmfit implements the estimation and evaluation of the GARCH–MIDAS–based models, with and without the asymmetric term linked to negative lagged daily returns, according to two distributions for the error term. The general framework assumes that:

r_{i,t}= \sqrt{\tau_t \times g_{i,t} } \epsilon_{i,t},

where

• r_{i,t} is the daily return for the i-th day (i = 1, \ldots, N_t) of the period t (for example, a week, a month or a quarter; t = 1 , \ldots, T);

• \tau_{t} is the long-run component, varying each period t;

• g_{i,t} is the short–run term, varying each day i of the period t;

• \epsilon_{i,t} is an iid error term which has a zero mean and unit variance.

The short–run component of the GARCH–MIDAS (parameter "model" set to "GM"), DAGM (parameter "model" set to "DAGM"), and DAGM with two MIDAS variables (parameter "model" set to "DAGM2M") models is as follows. When the parameter "skew" is present (set to "YES"):

g_{i,t} = \left(1-\alpha-\gamma/2-\beta\right) + \left(\alpha + \gamma \cdot I_{\left(r_{i-1,t} < 0 \right)}\right) \frac{\left(r_{i-1,t}\right)^2}{\tau_t} + \beta g_{i-1,t},

where I_{(\cdot)} is an indicator function. The short–run component of the GARCH–MIDAS–X (parameter "model" set to "GMX") and DAGM–X (parameter "model" set to "DAGMX"), when the parameter "skew" is set to "YES", is:

g_{i,t} = \left(1-\alpha-\gamma/2-\beta\right) + \left(\alpha + \gamma \cdot I_{\left(r_{i-1,t} < 0 \right)}\right) \frac{\left(r_{i-1,t}\right)^2}{\tau_t} + \beta g_{i-1,t} + z \cdot \left(X_{i-1,t}- E(X_{i-1,t})\right).

When, for the models GARCH–MIDAS, GARCH–MIDAS–X, DAGM, and DAGM–X, the parameter "skew" is set to "NO", parameter \gamma disappears. For details on the GARCH–MIDAS–X and DAGM–X models, see Amendola et al. (2021). The long-run component of the GARCH-MIDAS and GARCH–MIDAS–X models is:

\tau_{t} = \exp \left\{ m + \theta \sum_{j=1}^K \delta_{j}(\omega) X_{t-j}\right\},

where X_{t} is the MIDAS term and \delta_{j}(\omega) is the chosen weighting function, which can be the Beta (beta_function) or Exponential Almon lag (exp_almon) functions. The long-run component of the DAGM and DAGM–X models is:

\tau_t = \exp \left(m + \theta^{+} \sum_{k=1}^K \delta_k(\omega)^{+} X_{t-k} I_{\left( X_{t-k} \geq 0 \right)} + \theta^{-} \sum_{k=1}^K \delta_k(\omega)^{-} X_{t-k} I_{\left( X_{t-k} < 0 \right)} \right).

Value

ugmfit returns an object of class 'rumidas'. The function summary.rumidas can be used to print a summary of the results. Moreover, an object of class 'rumidas' is a list containing the following components:

• model: The model used for the estimation.

• rob_coef_mat: The matrix of estimated coefficients, with the QML standard errors. For details, see: Bollerslev and Wooldridge (1992).

• obs: The number of daily observations used for the (in-sample) estimation.

• period: The period of the in-sample estimation.

• loglik: The value of the log-likelihood at the maximum.

• inf_criteria: The AIC and BIC information criteria.

• loss_in_s: The in-sample MSE and QLIKE averages, calculated considering the distance with respect to the volatility proxy (if provided) or the squared daily returns.

• est_in_s: The one-step-ahead volatility, for the in-sample period, that is: \sqrt{\hat{\tau}_t \times \hat{g}_{i,t} }.

• est_lr_in_s: The one-step-ahead long-run volatility, for the in-sample period.

• loss_oos: The out-of-sample MSE and QLIKE averages, calculated considering the distance with respect to the volatility proxy (if provided) or the squared daily returns.

• est_oos: The one-step-ahead volatility, for the out-of-sample period, that is: \sqrt{\hat{\tau}_t \times \hat{g}_{i,t} }.

• est_lr_oos: The one-step-ahead long-run volatility, for the out-of-sample period.

References

Amendola A, Candila V, Gallo GM (2021). “Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model.” Economic and Statistics. doi:10.1016/j.ecosta.2020.11.001.

Bollerslev T, Wooldridge JM (1992). “Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances.” Econometric Reviews, 11, 143–172. doi:10.1080/07474939208800229.

See Also

mv_into_mat.

Examples

# estimate a GARH-MIDAS model, without the skewness parameter
r_t<-sp500['2008']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly") 
fit<-ugmfit(model="GM",skew="NO",distribution="norm",r_t,mv_m,K=12)
fit
summary.rumidas(fit)
names(fit)

# to see the estimated coefficients with the QML standard errors:
fit$rob_coef_mat

# estimate a DAGM model, with the skewness parameter, 
# including the volatility proxy (realized variance), and
# leaving the last 100 observations for the out-of-sample evaluation
r_t<-sp500['2002/2020']
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly") 
fit_2<-ugmfit(model="DAGM",skew="YES",distribution="norm",r_t,
mv_m,K=12,vol_proxy=rv5['2002/2020'],out_of_sample=100)
fit_2
summary.rumidas(fit_2)
# estimate a GM-X model, without the skewness parameter
r_t<-sp500['2010/2013']
X<-vix['2010/2013'] 
mv_m<-mv_into_mat(r_t,diff(indpro),K=36,"monthly") 
fit_3<-ugmfit(model="GMX",skew="NO",distribution="norm",r_t,mv_m,K=36,X=X)
summary.rumidas(fit_3)

Methods for obtaining (and evaluating) a variety of MEM(-MIDAS)-based models

Description

Estimates several MEM and MEM-MIDAS-based models. For details, see Amendola et al. (2024)

Usage

umemfit(
  model,
  skew,
  x,
  daily_ret = NULL,
  mv_m = NULL,
  K = NULL,
  z = NULL,
  out_of_sample = NULL,
  R = 100
)

Arguments

Details

Function umemfit implements the estimation and evaluation of the MEM, MEM-MIDAS MEM-X and MEM-MIDAS-X models, with and without the asymmetric term linked to negative lagged daily returns. The general framework assumes that:

x_{i,t}= \mu_{i,t}\epsilon_{i,t} = \tau_{t} \xi_{i,t} \epsilon_{i,t},

where

• x_{i,t} is a time series coming from a non-negative discrete time process for the i-th day (i = 1, \ldots, N_t) of the period t (for example, a week, a month or a quarter; t = 1 , \ldots, T);

• \tau_{t} is the long-run component, determining the average level of the conditional mean, varying each period t;

• \xi_{i,t} is a factor centered around one, labelled as the short–run term, which plays the role of dumping or amplifying \tau_{i,t};

• \epsilon_{i,t} is an iid error term which, conditionally on the information set, has a unit mean, an unknown variance, and a probability density function defined over a non-negative support.

The short–run component of the MEM-MIDAS-X is:

\xi_{i,t}=(1-\alpha-\gamma/2-\beta) + \left(\alpha + \gamma \cdot {I}_{\left(r_{i-1,t} < 0 \right)}\right) \frac{x_{i-1,t}}{\tau_t} + \beta \xi_{i-1,t} + \delta \left(Z_{i-1,t}-E(Z)\right),

where I_{(\cdot)} is an indicator function, r_{i,t} is the daily return of the day i of the period t and Z is an additional X term (for instance, the VIX). When the X part is absent, then the parameter \delta cancels. The long-run component of the MEM-MIDAS and MEM-MIDAS-X is:

\tau_{t} = \exp \left\{ m + \theta \sum_{k=1}^K \delta_{k}(\omega) X_{t-k}\right\},

where X_{t} is the MIDAS term. When the "skew" parameter is set to "NO", \gamma disappears. The MEM and MEM-X models do not have the long- and short-run components. Therefore, they directly evolve according to \mu_{i,t}. When the "skew" and X parameters are present, the MEM-X is:

\mu_{i,t}= \left(1-\alpha - \gamma / 2 - \beta \right)\mu + (\alpha + \gamma I_{\left(r_{i-1,t} < 0 \right)}) x_{i-1,t} + \beta \mu_{i-1,t}+\delta \left(Z_{i-1,t}-E(Z)\right),

where \mu=E(x_{i,t}). When the "skew" parameter is set to "NO", in the previous equation \gamma cancels. Finally, when the additional X part is not present, then we have the MEM model, where \delta disappears.

Value

umemfit returns an object of class 'rumidas'. The function summary.rumidas can be used to print a summary of the results. Moreover, an object of class 'rumidas' is a list containing the following components:

• model: The model used for the estimation.

• rob_coef_mat: The matrix of estimated coefficients, with the QML standard errors.

• obs: The number of daily observations used for the (in-sample) estimation.

• period: The period of the in-sample estimation.

• loglik: The value of the log-likelihood at the maximum.

• inf_criteria: The AIC and BIC information criteria.

• loss_in_s: The in-sample MSE and QLIKE averages, calculated considering the distance with respect to the dependent variable.

• est_in_s: The in-sample predicted dependent variable.

• est_lr_in_s: The in-sample predicted long-run component (if present) of the dependent variable.

• loss_oos: The out-of-sample MSE and QLIKE averages, calculated considering the distance with respect to the dependent variable.

• est_oos: The out-of-sample predicted dependent variable.

• est_lr_oos: The out-of-sample predicted long-run component (if present) of the dependent variable.

References

Amendola A, Candila V, Cipollini F, Gallo GM (2024). “Doubly multiplicative error models with long-and short-run components.” Socio-Economic Planning Sciences, 91, 101764. doi:10.1016/j.seps.2023.101764.

See Also

mv_into_mat.

Examples

# estimate the base MEM, without the asymmetric term linked to negative lagged returns
real<-(rv5['2003/2010'])^0.5		# realized volatility
fit<-umemfit(model="MEM",skew="NO",x=real)
fit
summary.rumidas(fit)
# to see the estimated coefficients with the QML standard errors:
fit$rob_coef_mat

# All the other elements of fit are:
names(fit)

# estimate the MEM-MIDAS, with the asymmetric term linked to negative lagged returns,
# leaving the last 200 observations for the out-of-sample analysis
r_t<-sp500['2003/2010']
real<-(rv5['2003/2010'])^0.5		# realized volatility
mv_m<-mv_into_mat(real,diff(indpro),K=12,"monthly")
fit_2<-umemfit(model="MEMMIDAS",skew="YES",x=real,daily_ret=r_t,mv_m=mv_m,K=12,out_of_sample=200)
fit_2
summary.rumidas(fit_2)
# to see the estimated coefficients with the QML standard errors:
fit_2$rob_coef_mat

VIX daily data

Description

Daily data on VIX collected from Yahoo Finance site. The VIX data have been de-annualized and multiplied by 100^{-1}.

Usage

data(vix)

Format

An object of class "xts".

Source

Yahoo Finance

Examples

head(vix)
summary(vix)
plot(vix)