Mixed Data Sampling Regression

Description

Package for estimating, testing and forecasting MIDAS regression.

Details

Methods and tools for mixed frequency time series data analysis. Allows estimation, model selection and forecasting for MIDAS regressions.

Author(s)

Virmantas Kvedaras virmantas.kvedaras@mif.vu.lt, Vaidotas Zemlys (maintainer) zemlys@gmail.com

See Also

Useful links:

• http://mpiktas.github.io/midasr/

• Report bugs at https://github.com/mpiktas/midasr/issues

Combine lws_table objects

Description

Combines lws_table objects

Usage

## S3 method for class 'lws_table'
... + check = TRUE

Arguments

Details

The lws_table objects have similar structure to table, i.e. it is a list with 3 elements which are the lists with the same number of elements. The base function c would cbind such tables. This function rbinds them.

Value

lws_table object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

nlmn <- expand_weights_lags("nealmon",0,c(4,8),1,start=list(nealmon=rep(0,3)))
nbt <- expand_weights_lags("nbeta",0,c(4,8),1,start=list(nbeta=rep(0,4)))

nlmn+nbt

US quartely seasonaly adjusted consumer price index

Description

US quarterly CPI from 1960Q1 to 2017Q3s. Seasonaly adjusted, Index 2015=1

Format

A data.frame object.

Source

FRED

US weekly effective federal funds rate.

Description

US weekly effective federal funds rate from 1954-07-07 to 2017-12-13

Format

A data.frame object.

Source

FRED

United States total employment non-farms payroll, monthly, seasonally adjusted.

Description

United States total employment non-farms payroll, monthly, seasonally adjusted. Retrieved from FRED, symbol "PAYEMS" at 2014-04-25.

Format

A ts object.

Source

FRED, Federal Reserve Economic Data, from the Federal Reserve Bank of St. Louis

Examples

## Do not run:
## library(quantmod)
## USpayems <- ts(getSymbols("PAYEMS",src="FRED",auto.assign=FALSE),start=c(1939,1),frequency=12)

United States gross domestic product, quarterly, seasonaly adjusted annual rate.

Description

United States gross domestic product, quarterly, seasonaly adjusted annual rate. Retrieved from FRED, symbol "GDP" at 2014-04-25.

Format

A ts object.

Source

FRED, Federal Reserve Economic Data, from the Federal Reserve Bank of St. Louis

Examples

## Do not run:
## library(quantmod)
## USqgdp <- ts(getSymbols("GDP",src="FRED",auto.assign=FALSE),start=c(1947,1),frequency=4)

US annual gross domestic product in billions of chained 2005 dollars

Description

The annual gross domestic product in billions of chained 2005 dollars for US from 1948 to 2011. This data is kept for historical purposes, newer data is in 2012 chained dollars.

Format

A ts object.

Source

U.S. Department of Commerce, Bureau of Economic Analysis

US monthly unemployment rate

Description

The monthly unemployment rate for United States from 1948 to 2011.

Format

A ts object.

Source

FRED

Andreou, Ghysels, Kourtellos LM test

Description

Perform the test whether hyperparameters of normalized exponential Almon lag weights are zero

Usage

agk.test(x)

Arguments

Value

a htest object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Andreou E., Ghysels E., Kourtellos A. Regression models with mixed sampling frequencies Journal of Econometrics 158 (2010) 246-261

Examples

##' ##Load data
data("USunempr")
data("USrealgdp")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
t <- 1:length(y)

mr <- midas_r(y~t+fmls(x,11,12,nealmon),start=list(x=c(0,0,0)))

agk.test(mr)

Almon polynomial MIDAS weights specification

Description

Calculate Almon polynomial MIDAS weights

Usage

almonp(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Gradient function for Almon polynomial MIDAS weights

Description

Calculate gradient for Almon polynomial MIDAS weights specification

Usage

almonp_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Vaidotas Zemlys

Weight and lag selection table for aggregates based MIDAS regression model

Description

Create weight and lag selection table for the aggregates based MIDAS regression model

Usage

amidas_table(
  formula,
  data,
  weights,
  wstart,
  type,
  start = NULL,
  from,
  to,
  IC = c("AIC", "BIC"),
  test = c("hAh_test"),
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

This function estimates models sequentialy increasing the midas lag from kmin to kmax and varying the weights of the last term of the given formula

This function estimates models sequentially increasing the midas lag from kmin to kmax and varying the weights of the last term of the given formula

Value

a midas_r_ic_table object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)

tb <- amidas_table(y~trend+fmls(x,12,12,nealmon),
                   data=list(y=y,x=x,trend=trend),
                   weights=c("nealmon"),wstart=list(nealmon=c(0,0,0)),
                   start=list(trend=1),type=c("A"),
                   from=0,to=c(1,2))

Weights for aggregates based MIDAS regressions

Description

Produces weights for aggregates based MIDAS regression

Usage

amweights(p, d, m, weight = nealmon, type = c("A", "B", "C"))

Arguments

Details

Suppose a weight function w(\beta,\theta) satisfies the following equation:

w(\beta,\theta)=\beta g(\theta)

The following combinations are defined, corresponding to structure types A, B and C respectively:

(w(\beta_1,\theta_1),...,w(\beta_k,\theta_k))

(w(\beta_1,\theta),...,w(\beta_k,\theta))

\beta(w(1,\theta),...,w(1,\theta)),

where k is the number of low frequency lags, i.e. d/m. If the latter value is not whole number, the error is produced.

The starting values p should be supplied then as follows:

(\beta_1,\theta_1,...,\beta_k,\theta_k)

(\beta_1,...,\beta_k,\theta)

(\beta,\theta)

Value

a vector of weights

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Average forecasts of MIDAS models

Description

Average MIDAS model forecasts using specified weighting scheme. Produce in-sample and out-of-sample accuracy measures.

Usage

average_forecast(
  modlist,
  data,
  insample,
  outsample,
  type = c("fixed", "recursive", "rolling"),
  fweights = c("EW", "BICW", "MSFE", "DMSFE"),
  measures = c("MSE", "MAPE", "MASE"),
  show_progress = TRUE
)

Arguments

Details

Given the data, split it to in-sample and out-of-sample data. Then given the list of models, reestimate each model with in-sample data and produce out-of-sample forecast. Given the forecasts average them with the specified weighting scheme. Then calculate the accuracy measures for individual and average forecasts.

The forecasts can be produced in 3 ways. The "fixed" forecast uses model estimated with in-sample data. The "rolling" forecast reestimates model each time by increasing the in-sample by one low frequency observation and dropping the first low frequency observation. These reestimated models then are used to produce out-of-sample forecasts. The "recursive" forecast differs from "rolling" that it does not drop observations from the beginning of data.

Value

a list containing forecasts and tables of accuracy measures

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

set.seed(1001)
## Number of low-frequency observations
n<-250
## Linear trend and higher-frequency explanatory variables (e.g. quarterly and monthly)
trend<-c(1:n)
x<-rnorm(4*n)
z<-rnorm(12*n)
## Exponential Almon polynomial constraint-consistent coefficients
fn.x <- nealmon(p=c(1,-0.5),d=8)
fn.z <- nealmon(p=c(2,0.5,-0.1),d=17)
## Simulated low-frequency series (e.g. yearly)
y<-2+0.1*trend+mls(x,0:7,4)%*%fn.x+mls(z,0:16,12)%*%fn.z+rnorm(n)
mod1 <- midas_r(y ~ trend + mls(x, 4:14, 4, nealmon) + mls(z, 12:22, 12, nealmon),
                start=list(x=c(10,1,-0.1),z=c(2,-0.1)))
mod2 <- midas_r(y ~ trend + mls(x, 4:20, 4, nealmon) + mls(z, 12:25, 12, nealmon),
                start=list(x=c(10,1,-0.1),z=c(2,-0.1)))

##Calculate average forecasts
avgf <- average_forecast(list(mod1,mod2),
                        data=list(y=y,x=x,z=z,trend=trend),
                        insample=1:200,outsample=201:250,
                        type="fixed",
                        measures=c("MSE","MAPE","MASE"),
                        fweights=c("EW","BICW","MSFE","DMSFE"))

Check data for MIDAS regression

Description

Given mixed frequency data check whether higher frequency data can be converted to the lowest frequency.

Usage

check_mixfreq(data)

Arguments

Details

The number of observations in higher frequency data elements should have a common divisor with the number of observations in response variable. It is always assumed that the response variable is of the lowest frequency.

Value

a boolean TRUE, if mixed frequency data is conformable, FALSE if it is not.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Extract coefficients of MIDAS regression

Description

Extracts various coefficients of MIDAS regression

Usage

## S3 method for class 'midas_nlpr'
coef(object, type = c("plain", "midas", "nlpr"), term_names = NULL, ...)

Arguments

Details

MIDAS regression has two sets of cofficients. The first set is the coefficients associated with the parameters of weight functions associated with MIDAS regression terms. These are the coefficients of the NLS problem associated with MIDAS regression. The second is the coefficients of the linear model, i.e the values of weight functions of terms, or so called MIDAS coefficients. By default the function returns the first set of the coefficients.

Value

a vector with coefficients

Author(s)

Vaidotas Zemlys

Extract coefficients of MIDAS regression

Description

Extracts various coefficients of MIDAS regression

Usage

## S3 method for class 'midas_r'
coef(object, midas = FALSE, term_names = NULL, ...)

Arguments

Details

MIDAS regression has two sets of cofficients. The first set is the coefficients associated with the parameters of weight functions associated with MIDAS regression terms. These are the coefficients of the NLS problem associated with MIDAS regression. The second is the coefficients of the linear model, i.e the values of weight functions of terms, or so called MIDAS coefficients. By default the function returns the first set of the coefficients.

Value

a vector with coefficients

Author(s)

Vaidotas Zemlys

Examples

#Simulate MIDAS regression
n<-250
trend<-c(1:n)
x<-rnorm(4*n)
z<-rnorm(12*n)
fn.x <- nealmon(p=c(1,-0.5),d=8)
fn.z <- nealmon(p=c(2,0.5,-0.1),d=17)
y<-2+0.1*trend+mls(x,0:7,4)%*%fn.x+mls(z,0:16,12)%*%fn.z+rnorm(n)
eqr<-midas_r(y ~ trend + mls(x, 0:7, 4, nealmon) +
             mls(z, 0:16, 12, nealmon),
             start = list(x = c(1, -0.5), z = c(2, 0.5, -0.1)))

coef(eqr)
coef(eqr, term_names = "x")
coef(eqr, midas = TRUE)
coef(eqr, midas = TRUE, term_names = "x")

Extract coefficients of MIDAS regression

Description

Extracts various coefficients of MIDAS regression

Usage

## S3 method for class 'midas_sp'
coef(object, type = c("plain", "midas", "bw"), term_names = NULL, ...)

Arguments

Details

MIDAS regression has two sets of cofficients. The first set is the coefficients associated with the parameters of weight functions associated with MIDAS regression terms. These are the coefficients of the NLS problem associated with MIDAS regression. The second is the coefficients of the linear model, i.e the values of weight functions of terms, or so called MIDAS coefficients. By default the function returns the first set of the coefficients.

Value

a vector with coefficients

Author(s)

Vaidotas Zemlys

Check whether non-linear least squares restricted MIDAS regression problem has converged

Description

Computes the gradient and hessian of the optimisation function of restricted MIDAS regression and checks whether the conditions of local optimum are met. Numerical estimates are used.

Usage

deriv_tests(x, tol = 1e-06)

## S3 method for class 'midas_r'
deriv_tests(x, tol = 1e-06)

Arguments

Value

a list with gradient, hessian of optimisation function and convergence message

Author(s)

Vaidotas Zemlys

See Also

midas_r

Non-linear parametric MIDAS regression model deviance

Description

Returns the deviance of a fitted MIDAS regression object

Usage

## S3 method for class 'midas_nlpr'
deviance(object, ...)

Arguments

Value

The sum of squared residuals

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

MIDAS regression model deviance

Description

Returns the deviance of a fitted MIDAS regression object

Usage

## S3 method for class 'midas_r'
deviance(object, ...)

Arguments

Value

The sum of squared residuals

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Semi-parametric MIDAS regression model deviance

Description

Returns the deviance of a fitted MIDAS regression object

Usage

## S3 method for class 'midas_sp'
deviance(object, ...)

Arguments

Value

The sum of squared residuals

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

MIDAS lag structure for unit root processes

Description

Prepares MIDAS lag structure for unit root processes

Usage

dmls(x, k, m, ...)

Arguments

Value

a matrix containing the first differences and the lag k+1.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Create table of weights, lags and starting values for Ghysels weight schema

Description

Create table of weights, lags and starting values for Ghysels weight schema, see amweights

Usage

expand_amidas(weight, type = c("A", "B", "C"), from = 0, to, m, start)

Arguments

Details

Given weight function creates lags starting from kmin to kmax and replicates starting values for each low frequency lag.

Value

a lws_table object, a list with elements weights, lags and starts

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

expand_amidas("nealmon","A",0,c(1,2),12,c(0,0,0))

Create table of weights, lags and starting values

Description

Creates table of weights, lags and starting values

Usage

expand_weights_lags(weights, from = 0, to, m = 1, start)

Arguments

Details

For each weight function creates lags starting from kmin to kmax. This is a convenience function for easier work with the function midas_r_ic_table.

Value

a lws_table object, a list with elements weights, lags and starts.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

expand_weights_lags(c("nealmon","nbeta"),0,c(4,8),1,start=list(nealmon=rep(0,3),nbeta=rep(0,4)))
nlmn <- expand_weights_lags("nealmon",0,c(4,8),1,start=list(nealmon=rep(0,3)))
nbt <- expand_weights_lags("nbeta",0,c(4,8),1,start=list(nbeta=rep(0,4)))

nlmn+nbt

Extract coefficients and GOF measures from MIDAS regression object

Description

Extract coefficients and GOF measures from MIDAS regression object

Usage

extract.midas_r(
  model,
  include.rsquared = TRUE,
  include.nobs = TRUE,
  include.rmse = TRUE,
  ...
)

Arguments

Value

texreg object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Fitted values for non-linear parametric MIDAS regression model

Description

Returns the fitted values of a fitted non-linear parametric MIDAS regression object

Usage

## S3 method for class 'midas_nlpr'
fitted(object, ...)

Arguments

Value

the vector of fitted values

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Fitted values for semi-parametric MIDAS regression model

Description

Returns the fitted values of a fitted semi-parametric MIDAS regression object

Usage

## S3 method for class 'midas_sp'
fitted(object, ...)

Arguments

Value

the vector of fitted values

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Full MIDAS lag structure

Description

Create a matrix of MIDAS lags, including contemporaneous lag up to selected order.

Usage

fmls(x, k, m, ...)

Arguments

Details

This is a convenience function, it calls link{mls} to perform actual calculations.

Value

a matrix containing the lags

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

See Also

mls

Forecast MIDAS regression

Description

Forecasts MIDAS regression given the future values of regressors. For dynamic models (with lagged response variable) there is an option to calculate dynamic forecast, when forecasted values of response variable are substituted into the lags of response variable.

Usage

## S3 method for class 'midas_r'
forecast(
  object,
  newdata = NULL,
  se = FALSE,
  level = c(80, 95),
  fan = FALSE,
  npaths = 999,
  method = c("static", "dynamic"),
  insample = get_estimation_sample(object),
  show_progress = TRUE,
  add_ts_info = FALSE,
  ...
)

Arguments

Details

Given future values of regressors this function combines the historical values used in the fitting the MIDAS regression model and calculates the forecasts.

Value

an object of class "forecast", a list containing following elements:

The methods print, summary and plot from package forecast can be used on the object.

Author(s)

Vaidotas Zemlys

Examples

data("USrealgdp")
data("USunempr")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr), start = 1949)
trend <- 1:length(y)

##24 high frequency lags of x included
mr <- midas_r(y ~ trend + fmls(x, 23, 12, nealmon), start = list(x = rep(0, 3)))

##Forecast horizon
h <- 3
##Declining unemployment
xn <- rep(-0.1, 12*h)
##New trend values
trendn <- length(y) + 1:h

##Static forecasts combining historic and new high frequency data
forecast(mr, list(trend = trendn, x = xn), method = "static")

##Dynamic AR* model
mr.dyn <- midas_r(y ~ trend + mls(y, 1:2, 1, "*")
                   + fmls(x, 11, 12, nealmon),
                  start = list(x = rep(0, 3)))

forecast(mr.dyn, list(trend = trendn, x = xn), method = "dynamic")

##Use print, summary and plot methods from package forecast

fmr <- forecast(mr, list(trend = trendn, x = xn), method = "static")
fmr
summary(fmr)
plot(fmr)

Generalized exponential MIDAS coefficients

Description

Calculates the MIDAS coefficients for generalized exponential MIDAS lag specification

Usage

genexp(p, d, m)

Arguments

Details

Generalized exponential MIDAS lag specification is a generalization of exponential Almon lag. It is defined as a product of first order polynomial with exponent of the second order polynomial. This spefication was used by V. Kvedaras and V. Zemlys (2012).

Value

a vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Kvedaras V., Zemlys, V. Testing the functional constraints on parameters in regressions with variables of different frequency Economics Letters 116 (2012) 250-254

Gradient of generalized exponential MIDAS coefficient generating function

Description

Calculates the gradient of generalized exponential MIDAS lag specification

Usage

genexp_gradient(p, d, m)

Arguments

Details

Generalized exponential MIDAS lag specification is a generalization of exponential Almon lag. It is defined as a product of first order polynomial with exponent of the second order polynomial. This spefication was used by V. Kvedaras and V. Zemlys (2012).

Value

a vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Kvedaras V., Zemlys, V. Testing the functional constraints on parameters in regressions with variables of different frequency Economics Letters 116 (2012) 250-254

Get the data which was used to etimate MIDAS regression

Description

Gets the data which was used to estimate MIDAS regression

Usage

get_estimation_sample(object)

Arguments

Details

A helper function.

Value

a named list with mixed frequency data

Author(s)

Vaidotas Zemlys

Normalized Gompertz probability density function MIDAS weights specification

Description

Calculate MIDAS weights according to normalized Gompertz probability density function specification

Usage

gompertzp(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Gradient function for normalized Gompertz probability density function MIDAS weights specification

Description

Calculate gradient function for normalized Gompertz probability density function specification of MIDAS weights.

Usage

gompertzp_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Test restrictions on coefficients of MIDAS regression

Description

Perform a test whether the restriction on MIDAS regression coefficients holds.

Usage

hAh_test(x)

Arguments

Details

Given MIDAS regression:

y_t=\sum_{j=0}^k\sum_{i=0}^{m-1}\theta_{jm+i} x_{(t-j)m-i}+u_t

test the null hypothesis that the following restriction holds:

\theta_h=g(h,\lambda),

where h=0,...,(k+1)m.

Value

a htest object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Kvedaras V., Zemlys, V. Testing the functional constraints on parameters in regressions with variables of different frequency Economics Letters 116 (2012) 250-254

See Also

hAhr_test

Examples

##The parameter function
theta_h0 <- function(p, dk, ...) {
   i <- (1:dk-1)
   (p[1] + p[2]*i)*exp(p[3]*i + p[4]*i^2)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,0.1,-0.1,-0.001),4*12)

##Plot the coefficients
plot(theta0)

##Generate the predictor variable
set.seed(13)

xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))
##Fit restricted model
mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1,list(y=y,x=x),
              start=list(x=c(-0.1,0.1,-0.1,-0.001)))

##Perform test (the expected result should be the acceptance of null)

hAh_test(mr)

##Fit using gradient function

##The gradient function
theta_h0_gradient<-function(p, dk,...) {
   i <- (1:dk-1)
   a <- exp(p[3]*i + p[4]*i^2)
   cbind(a, a*i, a*i*(p[1]+p[2]*i), a*i^2*(p[1]+p[2]*i))
}

mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1,list(y=y,x=x),
              start=list(x=c(-0.1,0.1,-0.1,-0.001)),
              weight_gradients=list())

##The test will use an user supplied gradient of weight function. See the
##help of midas_r on how to supply the gradient.

hAh_test(mr)

Test restrictions on coefficients of MIDAS regression using robust version of the test

Description

Perform a test whether the restriction on MIDAS regression coefficients holds.

Usage

hAhr_test(x, PHI = vcovHAC(x$unrestricted, sandwich = FALSE))

Arguments

Details

Given MIDAS regression:

y_t=\sum_{j=0}^k\sum_{i=0}^{m-1}\theta_{jm+i} x_{(t-j)m-i}+u_t

test the null hypothesis that the following restriction holds:

\theta_h=g(h,\lambda),

where h=0,...,(k+1)m.

Value

a htest object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Kvedaras V., Zemlys, V. The statistical content and empirical testing of the MIDAS restrictions

See Also

hAh_test

Examples

##The parameter function
theta_h0 <- function(p, dk, ...) {
   i <- (1:dk-1)
   (p[1] + p[2]*i)*exp(p[3]*i + p[4]*i^2)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,0.1,-0.1,-0.001),4*12)

##Plot the coefficients
plot(theta0)

##Generate the predictor variable
set.seed(13)

xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))
##Fit restricted model
mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1,
              list(y=y,x=x),
              start=list(x=c(-0.1,0.1,-0.1,-0.001)))

##The gradient function
theta_h0_gradient <-function(p, dk,...) {
   i <- (1:dk-1)
   a <- exp(p[3]*i + p[4]*i^2)
   cbind(a, a*i, a*i*(p[1]+p[2]*i), a*i^2*(p[1]+p[2]*i))
}

##Perform test (the expected result should be the acceptance of null)

hAhr_test(mr)

mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1,
              list(y=y,x=x),
              start=list(x=c(-0.1,0.1,-0.1,-0.001)),
              weight_gradients=list())

##Use exact gradient. Note the
hAhr_test(mr)

HAR(3)-RV model MIDAS weights specification

Description

HAR(3)-RV model MIDAS weights specification

Usage

harstep(p, d, m)

Arguments

Details

MIDAS weights for Heterogeneous Autoregressive model of Realized Volatilty (HAR-RV). It is assumed that month has 20 days.

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Corsi, F., A Simple Approximate Long-Memory Model of Realized Volatility, Journal of Financial Econometrics Vol. 7 No. 2 (2009) 174-196

Gradient function for HAR(3)-RV model MIDAS weights specification

Description

Gradient function for HAR(3)-RV model MIDAS weights specification

Usage

harstep_gradient(p, d, m)

Arguments

Details

MIDAS weights for Heterogeneous Autoregressive model of Realized Volatilty (HAR-RV). It is assumed that month has 20 days.

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Corsi, F., A Simple Approximate Long-Memory Model of Realized Volatility, Journal of Financial Econometrics Vol. 7 No. 2 (2009) 174-196

Create a high frequency lag selection table for MIDAS regression model

Description

Creates a high frequency lag selection table for MIDAS regression model with given information criteria and minimum and maximum lags.

Usage

hf_lags_table(
  formula,
  data,
  start,
  from,
  to,
  IC = c("AIC", "BIC"),
  test = c("hAh_test"),
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

This function estimates models sequentially increasing the midas lag from kmin to kmax of the last term of the given formula

Value

a midas_r_iclagtab object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)

mlr <- hf_lags_table(y ~ trend + fmls(x, 12, 12,nealmon),
                     start = list(x=rep(0,3)),
                     data = list(y = y, x = x, trend = trend),
                     from=c(x=0),to=list(x=c(4,4)))
mlr

Restricted MIDAS regression with I(1) regressors

Description

Estimate restricted MIDAS regression using non-linear least squares, when the regressor is I(1)

Usage

imidas_r(
  formula,
  data,
  start,
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

Given MIDAS regression:

y_t=\sum_{j=0}^k\sum_{i=0}^{m-1}\theta_{jm+i} x_{(t-j)m-i}+\mathbf{z_t}\beta+u_t

estimate the parameters of the restriction

\theta_h=g(h,\lambda),

where h=0,...,(k+1)m, together with coefficients \beta corresponding to additional low frequency regressors.

It is assumed that x is a I(1) process, hence the special transformation is made. After the transformation midas_r is used for estimation.

MIDAS regression involves times series with different frequencies.

The restriction function must return the restricted coefficients of the MIDAS regression.

Value

a midas_r object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

See Also

midas_r.midas_r

Examples

theta.h0 <- function(p, dk) {
  i <- (1:dk-1)/100
  pol <- p[3]*i + p[4]*i^2
 (p[1] + p[2]*i)*exp(pol)
}

theta0 <- theta.h0(c(-0.1,10,-10,-10),4*12)

xx <- ts(cumsum(rnorm(600*12)), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))

imr <- imidas_r(y~fmls(x,4*12-1,12,theta.h0)-1,start=list(x=c(-0.1,10,-10,-10)))

Normalized log-Cauchy probability density function MIDAS weights specification

Description

Calculate MIDAS weights according to normalized log-Cauchy probability density function specification

Usage

lcauchyp(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Gradient function for normalized log-Cauchy probability density function MIDAS weights specification

Description

Calculate gradient function for normalized log-Cauchy probability density function specification of MIDAS weights.

Usage

lcauchyp_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Create a low frequency lag selection table for MIDAS regression model

Description

Creates a low frequency lag selection table for MIDAS regression model with given information criteria and minimum and maximum lags.

Usage

lf_lags_table(
  formula,
  data,
  start,
  from,
  to,
  IC = c("AIC", "BIC"),
  test = c("hAh_test"),
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

This function estimates models sequentially increasing the midas lag from kmin to kmax of the last term of the given formula

Value

a midas_r_ic_table object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)

mlr <- lf_lags_table(y~trend+fmls(x,12,12,nealmon),
                     start=list(x=rep(0,3)),
                     from=c(x=0),to=list(x=c(3,4)))
mlr

Compute LSTR term for high frequency variable

Description

Compute LSTR term for high frequency variable

Usage

lstr(X, theta, beta, sd_x = sd(c(X), na.rm = TRUE))

Arguments

Value

a vector

Simulate simple autoregressive MIDAS model

Description

Given the predictor variable, the weights and autoregressive coefficients, simulate MIDAS regression response variable.

Usage

midas_auto_sim(
  n,
  alpha,
  x,
  theta,
  rand_gen = rnorm,
  innov = rand_gen(n, ...),
  n_start = NA,
  ...
)

Arguments

Value

a ts object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

theta_h0 <- function(p, dk) {
  i <- (1:dk-1)/100
  pol <- p[3]*i + p[4]*i^2
  (p[1] + p[2]*i)*exp(pol)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,10,-10,-10),4*12)

##Generate the predictor variable
xx <- ts(arima.sim(model = list(ar = 0.6), 1000 * 12), frequency = 12)

y <- midas_auto_sim(500, 0.5, xx, theta0, n_start = 200)
x <- window(xx, start=start(y))
midas_r(y ~ mls(y, 1, 1) + fmls(x, 4*12-1, 12, theta_h0), start = list(x = c(-0.1, 10, -10, -10)))

LSTR (Logistic Smooth TRansition) MIDAS regression

Description

Function for fitting LSTR MIDAS regression without the formula interface

Usage

midas_lstr_plain(
  y,
  X,
  z = NULL,
  weight,
  start_lstr,
  start_x,
  start_z = NULL,
  method = c("Nelder-Mead"),
  ...
)

Arguments

Value

an object similar to midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Simulate LSTR MIDAS regression model

Description

Simulate LSTR MIDAS regression model

Usage

midas_lstr_sim(
  n,
  m,
  theta,
  intercept,
  plstr,
  ar.x,
  ar.y,
  rand.gen = rnorm,
  n.start = NA,
  ...
)

Arguments

Value

a list

Examples

nnbeta <- function(p, k) nbeta(c(1, p), k)

dgp <- midas_lstr_sim(250,
  m = 12, theta = nnbeta(c(2, 4), 24),
  intercept = c(1), plstr = c(1.5, 1, log(1), 1),
  ar.x = 0.9, ar.y = 0.5, n.start = 100
)

z <- cbind(1, mls(dgp$y, 1:2, 1))
colnames(z) <- c("Intercept", "y1", "y2")
X <- mls(dgp$x, 0:23, 12)

lstr_mod <- midas_lstr_plain(dgp$y, X, z, nnbeta,
  start_lstr = c(1.5, 1, 1, 1),
  start_x = c(2, 4), start_z = c(1, 0.5, 0)
)

coef(lstr_mod)

MMM (Mean-Min-Max) MIDAS regression

Description

Function for fitting MMM MIDAS regression without the formula interface

Usage

midas_mmm_plain(
  y,
  X,
  z = NULL,
  weight,
  start_mmm,
  start_x,
  start_z = NULL,
  method = c("Nelder-Mead"),
  ...
)

Arguments

Value

an object similar to midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Simulate MMM MIDAS regression model

Description

Simulate MMM MIDAS regression model

Usage

midas_mmm_sim(
  n,
  m,
  theta,
  intercept,
  pmmm,
  ar.x,
  ar.y,
  rand.gen = rnorm,
  n.start = NA,
  ...
)

Arguments

Value

a list

Examples

nnbeta <- function(p, k) nbeta(c(1, p), k)

dgp <- midas_mmm_sim(250,
  m = 12, theta = nnbeta(c(2, 4), 24),
  intercept = c(1), pmmm = c(1.5, 1),
  ar.x = 0.9, ar.y = 0.5, n.start = 100
)

z <- cbind(1, mls(dgp$y, 1:2, 1))
colnames(z) <- c("Intercept", "y1", "y2")
X <- mls(dgp$x, 0:23, 12)

mmm_mod <- midas_mmm_plain(dgp$y, X, z, nnbeta,
  start_mmm = c(1.5, 1),
  start_x = c(2, 4), start_z = c(1, 0.5, 0)
)

coef(mmm_mod)

Non-linear parametric MIDAS regression

Description

Estimate restricted MIDAS regression using non-linear least squares.

Usage

midas_nlpr(formula, data, start, Ofunction = "optim", ...)

Arguments

Details

Given MIDAS regression:

y_t = \sum_{j=1}^p\alpha_jy_{t-j} +\sum_{i=0}^{k}\sum_{j=0}^{l_i}\beta_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

estimate the parameters of the restriction

\beta_j^{(i)}=g^{(i)}(j,\lambda).

Such model is a generalisation of so called ADL-MIDAS regression. It is not required that all the coefficients should be restricted, i.e the function g^{(i)} might be an identity function. Model with no restrictions is called U-MIDAS model. The regressors x_\tau^{(i)} must be of higher (or of the same) frequency as the dependent variable y_t.

Value

a midas_r object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Fit restricted MIDAS regression

Description

Workhorse function for fitting restricted MIDAS regression

Usage

midas_nlpr.fit(x)

Arguments

Value

midas_r object

Author(s)

Vaidotas Zemlys

MIDAS Partialy linear non-parametric regression

Description

Function for fitting PL MIDAS regression without the formula interface

Usage

midas_pl_plain(
  y,
  X,
  z,
  p.ar = NULL,
  weight,
  degree = 1,
  start_bws,
  start_x,
  start_ar = NULL,
  method = c("Nelder-Mead"),
  ...
)

Arguments

Value

an object similar to midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Simulate PL MIDAS regression model

Description

Simulate PL MIDAS regression model

Usage

midas_pl_sim(
  n,
  m,
  theta,
  gfun,
  ar.x,
  ar.y,
  rand.gen = rnorm,
  n.start = NA,
  ...
)

Arguments

Value

a list

Examples

nnbeta <- function(p, k) nbeta(c(1, p), k)

dgp <- midas_pl_sim(250,
  m = 12, theta = nnbeta(c(2, 4), 24),
  gfun = function(x) 0.25 * x^3,
  ar.x = 0.9, ar.y = 0.5, n.start = 100
)

Restricted MIDAS quantile regression

Description

Estimate restricted MIDAS quantile regression using nonlinear quantile regression

Usage

midas_qr(
  formula,
  data,
  tau = 0.5,
  start,
  Ofunction = "nlrq",
  weight_gradients = NULL,
  guess_start = TRUE,
  ...
)

Arguments

Value

a midas_r object which is the list with the following elements:

Author(s)

Vaidotas Zemlys-Balevicius

Examples

##Take the same example as in midas_r

theta_h0 <- function(p, dk, ...) {
   i <- (1:dk-1)/100
   pol <- p[3]*i + p[4]*i^2
   (p[1] + p[2]*i)*exp(pol)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,10,-10,-10),4*12)

##Plot the coefficients
plot(theta0)

##Generate the predictor variable
xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))

##Fit quantile regression. All the coefficients except intercept should be constant.
##Intercept coefficient should correspond to quantile function of regression errors.
mr <- midas_qr(y~fmls(x,4*12-1,12,theta_h0), tau = c(0.1, 0.5, 0.9),
              list(y=y,x=x),
              start=list(x=c(-0.1,10,-10,-10)))

mr

Restricted MIDAS regression

Description

Estimate restricted MIDAS regression using non-linear least squares.

Usage

midas_r(
  formula,
  data,
  start,
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

Given MIDAS regression:

y_t = \sum_{j=1}^p\alpha_jy_{t-j} +\sum_{i=0}^{k}\sum_{j=0}^{l_i}\beta_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

estimate the parameters of the restriction

\beta_j^{(i)}=g^{(i)}(j,\lambda).

Such model is a generalisation of so called ADL-MIDAS regression. It is not required that all the coefficients should be restricted, i.e the function g^{(i)} might be an identity function. Model with no restrictions is called U-MIDAS model. The regressors x_\tau^{(i)} must be of higher (or of the same) frequency as the dependent variable y_t.

MIDAS-AR* (a model with a common factor, see (Clements and Galvao, 2008)) can be estimated by specifying additional argument, see an example.

The restriction function must return the restricted coefficients of the MIDAS regression.

Value

a midas_r object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Clements, M. and Galvao, A., Macroeconomic Forecasting With Mixed-Frequency Data: Forecasting Output Growth in the United States, Journal of Business and Economic Statistics, Vol.26 (No.4), (2008) 546-554

Examples

##The parameter function
theta_h0 <- function(p, dk, ...) {
   i <- (1:dk-1)/100
   pol <- p[3]*i + p[4]*i^2
   (p[1] + p[2]*i)*exp(pol)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,10,-10,-10),4*12)

##Plot the coefficients
plot(theta0)

##Generate the predictor variable
xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))

##Fit restricted model
mr <- midas_r(y~fmls(x,4*12-1,12,theta_h0)-1,
              list(y=y,x=x),
              start=list(x=c(-0.1,10,-10,-10)))

##Include intercept and trend in regression
mr_it <- midas_r(y~fmls(x,4*12-1,12,theta_h0)+trend,
                 list(data.frame(y=y,trend=1:500),x=x),
                 start=list(x=c(-0.1,10,-10,-10)))

data("USrealgdp")
data("USunempr")

y.ar <- diff(log(USrealgdp))
xx <- window(diff(USunempr), start = 1949)
trend <- 1:length(y.ar)

##Fit AR(1) model
mr_ar <- midas_r(y.ar ~ trend + mls(y.ar, 1, 1) +
                 fmls(xx, 11, 12, nealmon),
                 start = list(xx = rep(0, 3)))

##First order MIDAS-AR* restricted model
mr_arstar <-  midas_r(y.ar ~ trend + mls(y.ar, 1, 1, "*")
                     + fmls(xx, 11, 12, nealmon),
                     start = list(xx = rep(0, 3)))

Fit restricted MIDAS regression

Description

Workhorse function for fitting restricted MIDAS regression

Usage

midas_r.fit(x)

Arguments

Value

midas_r object

Author(s)

Vaidotas Zemlys

Create a weight and lag selection table for MIDAS regression model

Description

Creates a weight and lag selection table for MIDAS regression model with given information criteria and minimum and maximum lags.

Usage

midas_r_ic_table(
  formula,
  data = NULL,
  start = NULL,
  table,
  IC = c("AIC", "BIC"),
  test = c("hAh_test"),
  Ofunction = "optim",
  weight_gradients = NULL,
  show_progress = TRUE,
  ...
)

Arguments

Details

This function estimates models sequentially increasing the midas lag from kmin to kmax and varying the weights of the last term of the given formula

Value

a midas_r_ic_table object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)


mwlr <- midas_r_ic_table(y~trend+fmls(x,12,12,nealmon),
                   table=list(x=list(weights=
                   as.list(c("nealmon","nealmon","nbeta")),
                   lags=list(0:4,0:5,0:6),
                   starts=list(rep(0,3),rep(0,3,),c(1,1,1,0)))))

mwlr

Estimate non-parametric MIDAS regression

Description

Estimates non-parametric MIDAS regression

Usage

midas_r_np(formula, data, lambda = NULL)

Arguments

Details

Estimates non-parametric MIDAS regression accodring Breitung et al.

Value

a midas_r_np object

Author(s)

Vaidotas Zemlys

References

Breitung J, Roling C, Elengikal S (2013). Forecasting inflation rates using daily data: A nonparametric MIDAS approach Working paper, URL http://www.ect.uni-bonn.de/mitarbeiter/joerg-breitung/npmidas.

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)
midas_r_np(y~trend+fmls(x,12,12))

Restricted MIDAS regression

Description

Function for fitting MIDAS regression without the formula interface

Usage

midas_r_plain(
  y,
  X,
  z = NULL,
  weight,
  grw = NULL,
  startx,
  startz = NULL,
  method = c("Nelder-Mead", "BFGS"),
  ...
)

Arguments

Value

an object similar to midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)

X<-fmls(x,11,12)

midas_r_plain(y,X,trend,weight=nealmon,startx=c(0,0,0))

MIDAS Single index regression

Description

Function for fitting SI MIDAS regression without the formula interface

Usage

midas_si_plain(
  y,
  X,
  p.ar = NULL,
  weight,
  degree = 1,
  start_bws,
  start_x,
  start_ar = NULL,
  method = "Nelder-Mead",
  ...
)

Arguments

Value

an object similar to midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Simulate SI MIDAS regression model

Description

Simulate SI MIDAS regression model

Usage

midas_si_sim(
  n,
  m,
  theta,
  gfun,
  ar.x,
  ar.y,
  rand.gen = rnorm,
  n.start = NA,
  ...
)

Arguments

Value

a list

Examples

nnbeta <- function(p, k) nbeta(c(1, p), k)

dgp <- midas_si_sim(250,
  m = 12, theta = nnbeta(c(2, 4), 24),
  gfun = function(x) 0.03 * x^3,
  ar.x = 0.9, ar.y = 0.5, n.start = 100
)

Simulate simple MIDAS regression response variable

Description

Given the predictor variable and the coefficients simulate MIDAS regression response variable.

Usage

midas_sim(n, x, theta, rand_gen = rnorm, innov = rand_gen(n, ...), ...)

Arguments

Details

MIDAS regression with one predictor variable has the following form:

y_t=\sum_{j=0}^{h}\theta_jx_{tm-j}+u_t,

where m is the frequency ratio and h is the number of high frequency lags included in the regression.

MIDAS regression involves times series with different frequencies. In R the frequency property is set when creating time series objects ts. Hence the frequency ratio m which figures in MIDAS regression is calculated from frequency property of time series objects supplied.

Value

a ts object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

##The parameter function
theta_h0 <- function(p, dk) {
   i <- (1:dk-1)/100
   pol <- p[3]*i + p[4]*i^2
   (p[1] + p[2]*i)*exp(pol)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,10,-10,-10),4*12)

##Plot the coefficients
plot(theta0)

##Generate the predictor variable, leave 4 low frequency lags of data for burn-in.
xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))
midas_r(y ~ mls(y, 1, 1) + fmls(x, 4*12-1, 12, theta_h0), start = list(x = c(-0.1, 10, -10, -10)))

Semi-parametric MIDAS regression

Description

Estimate semi-parametric MIDAS regression using non-linear least squares.

Usage

midas_sp(formula, data, bws, start, degree = 1, Ofunction = "optim", ...)

Arguments

Details

Given MIDAS regression:

y_t = \sum_{j=1}^p\alpha_jy_{t-j} +\sum_{i=0}^{k}\sum_{j=0}^{l_i}\beta_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

estimate the parameters of the restriction

\beta_j^{(i)}=g^{(i)}(j,\lambda).

Such model is a generalisation of so called ADL-MIDAS regression. It is not required that all the coefficients should be restricted, i.e the function g^{(i)} might be an identity function. The regressors x_\tau^{(i)} must be of higher (or of the same) frequency as the dependent variable y_t.

Value

a midas_sp object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys-Balevičius

Estimate unrestricted MIDAS regression

Description

Estimate unrestricted MIDAS regression using OLS. This function is a wrapper for lm.

Usage

midas_u(formula, data, ...)

Arguments

Details

MIDAS regression has the following form:

y_t = \sum_{j=1}^p\alpha_jy_{t-j} +\sum_{i=0}^{k}\sum_{j=0}^{l_i}\beta_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

where x_\tau^{(i)}, i=0,...k are regressors of higher (or similar) frequency than y_t. Given certain assumptions the coefficients can be estimated using usual OLS and they have the familiar properties associated with simple linear regression.

Value

lm object.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

References

Kvedaras V., Zemlys, V. Testing the functional constraints on parameters in regressions with variables of different frequency Economics Letters 116 (2012) 250-254

Examples

##The parameter function
theta_h0 <- function(p, dk, ...) {
   i <- (1:dk-1)/100
   pol <- p[3]*i + p[4]*i^2
   (p[1] + p[2]*i)*exp(pol)
}

##Generate coefficients
theta0 <- theta_h0(c(-0.1,10,-10,-10),4*12)

##Plot the coefficients
##Do not run
#plot(theta0)

##' ##Generate the predictor variable
xx <- ts(arima.sim(model = list(ar = 0.6), 600 * 12), frequency = 12)

##Simulate the response variable
y <- midas_sim(500, xx, theta0)

x <- window(xx, start=start(y))

##Create low frequency data.frame
ldt <- data.frame(y=y,trend=1:length(y))

##Create high frequency data.frame

hdt <- data.frame(x=window(x, start=start(y)))

##Fit unrestricted model
mu <- midas_u(y~fmls(x,2,12)-1, list(ldt, hdt))

##Include intercept and trend in regression

mu_it <- midas_u(y~fmls(x,2,12)+trend, list(ldt, hdt))

##Pass data as partialy named list

mu_it <- midas_u(y~fmls(x,2,12)+trend, list(ldt, x=hdt$x))

MIDAS lag structure

Description

Create a matrix of selected MIDAS lags

Usage

mls(x, k, m, ...)

Arguments

Details

The function checks whether high frequency data is complete, i.e. m must divide length(x).

Value

a matrix containing the lags

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

## Quarterly frequency data
x <- 1:16
## Create MIDAS lag for use with yearly data
mls(x,0:3,4)

## Do not use contemporaneous lag
mls(x,1:3,4)

## Compares with embed when m=1
embed(x,2)
mls(x,0:1,1)

MIDAS lag structure with dates

Description

MIDAS lag structure with dates

Usage

mlsd(x, k, y, ...)

Arguments

Details

High frequency time series is aligned with low frequency time series using date information. Then the high frequency lags are calculated.

To align the time series the low frequency series index needs to be extended by one low frequency period into the past and into the future. If supplied time series object does not support extending time index, a simple heuristic is used.

It is expected that time index for zoo objects can be converted to POSIXct format.

Value

a matrix containing the lags

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys-Balevičius

Examples

# Example with ts objects
x <- ts(c(1:144), start = c(1980, 1), frequency = 12)
y <- ts(c(1:12), start = 1980, frequency = 1)


# msld and mls should give the same results

m1 <- mlsd(x, 0:5, y)

m2 <- mls(x, 0:5, 12)

sum(abs(m1 - m2))

# Example with zooreg

# Convert x to zooreg object using yearmon time index
## Not run: 
xz <- zoo::as.zooreg(x)

yz <- zoo::zoo(as.numeric(y), order.by = as.Date(paste0(1980 + 0:11, "-01-01")))

# Heuristic works here
m3 <- mlsd(xz, 0:5, yz)

sum(abs(m3 - m1))

## End(Not run)

Compute MMM term for high frequency variable

Description

Compute MMM term for high frequency variable

Usage

mmm(X, theta, beta, ...)

Arguments

Value

a vector

Select the model based on given information criteria

Description

Selects the model with minimum of given information criteria and model type

Usage

modsel(
  x,
  IC = x$IC[1],
  test = x$test[1],
  type = c("restricted", "unrestricted"),
  print = TRUE
)

Arguments

Details

This function selects the model from the model selection table for which the chosen information criteria achieves the smallest value. The function works with model tables produced by functions lf_lags_table, hf_lags_table, amidas_table and midas_r_ic_table.

Value

(invisibly) the best model based on information criteria, midas_r object

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)

mhfr <- hf_lags_table(y~trend+fmls(x,12,12,nealmon),
                      start=list(x=rep(0,3)),
                      from=list(x=0),to=list(x=c(4,6)))

mlfr <- lf_lags_table(y~trend+fmls(x,12,12,nealmon),
                      start=list(x=rep(0,3)),
                      from=list(x=0),to=list(x=c(2,3)))

modsel(mhfr,"BIC","unrestricted")

modsel(mlfr,"BIC","unrestricted")

Normalized Nakagami probability density function MIDAS weights specification

Description

Calculate MIDAS weights according to normalized Nakagami probability density function specification

Usage

nakagamip(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Gradient function for normalized Nakagami probability density function MIDAS weights specification

Description

Calculate gradient function for normalized Nakagami probability density function specification of MIDAS weights.

Usage

nakagamip_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Julius Vainora

Normalized beta probability density function MIDAS weights specification

Description

Calculate MIDAS weights according to normalized beta probability density function specification

Usage

nbeta(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Normalized beta probability density function MIDAS weights specification (MATLAB toolbox compatible)

Description

Calculate MIDAS weights according to normalized beta probability density function specification. Compatible with the specification in MATLAB toolbox.

Usage

nbetaMT(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Gradient function for normalized beta probability density function MIDAS weights specification (MATLAB toolbox compatible)

Description

Calculate gradient function for normalized beta probability density function specification of MIDAS weights.

Usage

nbetaMT_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Gradient function for normalized beta probability density function MIDAS weights specification

Description

Calculate gradient function for normalized beta probability density function specification of MIDAS weights.

Usage

nbeta_gradient(p, d, m)

Arguments

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Normalized Exponential Almon lag MIDAS coefficients

Description

Calculate normalized exponential Almon lag coefficients given the parameters and required number of coefficients.

Usage

nealmon(p, d, m)

Arguments

Details

Given unrestricted MIDAS regression

y_t=\sum_{h=0}^d\theta_{h}x_{tm-h}+\mathbf{z_t}\beta+u_t

normalized exponential Almon lag restricts the coefficients theta_h in the following way:

\theta_{h}=\delta\frac{\exp(\lambda_1(h+1)+\dots+ \lambda_r(h+1)^r)}{\sum_{s=0}^d\exp(\lambda_1(s+1)+\dots+\lambda_r(h+1)^r)}

The parameter \delta should be the first element in vector p. The degree of the polynomial is then decided by the number of the remaining parameters.

Value

vector of coefficients

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

##Load data
data("USunempr")
data("USrealgdp")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
t <- 1:length(y)

midas_r(y~t+fmls(x,11,12,nealmon),start=list(x=c(0,0,0)))

Gradient function for normalized exponential Almon lag weights

Description

Gradient function for normalized exponential Almon lag weights

Usage

nealmon_gradient(p, d, m)

Arguments

Value

the gradient matrix

Author(s)

Vaidotas Zemlys

Out-of-sample prediction precision data on simulation example

Description

The code in the example generates the out-of-sample prediction precision data for correctly and incorrectly constrained MIDAS regression model compared to unconstrained MIDAS regression model.

Format

A data.frame object with four columns. The first column indicates the sample size, the second the type of constraint, the third the value of the precision measure and the fourth the type of precision measure.

Examples

## Do not run:
## set.seed(1001)

## gendata<-function(n) {
##     trend<-c(1:n)
##     z<-rnorm(12*n)
##     fn.z <- nealmon(p=c(2,0.5,-0.1),d=17)
##     y<-2+0.1*trend+mls(z,0:16,12)%*%fn.z+rnorm(n)
##     list(y=as.numeric(y),z=z,trend=trend)
## }

## nn <- c(50,100,200,300,500,750,1000)

## data_sets <- lapply(n,gendata)

## mse <- function(x) {
##     mean(residuals(x)^2)
## }

## bnorm <- function(x) {
##     sqrt(sum((coef(x, midas = TRUE)-c(2,0.1,nealmon(p=c(2,0.5,-0.1),d=17)))^2))
## }

## rep1 <- function(n) {
##     dt <- gendata(round(1.25*n))
##     ni <- n
##     ind <- 1:ni
##     mind <- 1:(ni*12)
##     indt<-list(y=dt$y[ind],z=dt$z[mind],trend=dt$trend[ind])
##     outdt <- list(y=dt$y[-ind],z=dt$z[-mind],trend=dt$trend[-ind])
##     um <- midas_r(y~trend+mls(z,0:16,12),data=indt,start=NULL)
##     nm <- midas_r(y~trend+mls(z,0:16,12,nealmon),data=indt,start=list(z=c(1,-1,0)))
##     am <- midas_r(y~trend+mls(z,0:16,12,almonp),data=indt,start=list(z=c(1,0,0,0)))
##     modl <- list(um,nm,am)
##     names(modl) <- c("um","nm","am")
##     list(norms=sapply(modl,bnorm),
##          mse=sapply(modl,function(mod)mean((forecast(mod,newdata=outdt)-outdt$y)^2)))
## }

## repr <- function(n,R) {
##     cc <- lapply(1:R,function(i)rep1(n))
##     list(norms=t(sapply(cc,"[[","norms")),mse=t(sapply(cc,"[[","mse")))
## }

## res <- lapply(nn,repr,R=1000)

## norms <- data.frame(nn,t(sapply(lapply(res,"[[","norms"),function(l)apply(l,2,mean))))
## mses <- data.frame(nn,t(sapply(lapply(res,"[[","mse"),function(l)apply(l,2,mean))))


## msd <- melt(mses[-1,],id=1)
## colnames(msd)[2] <- "Constraint"
## nmd <- melt(norms[-1,],id=1)
## colnames(nmd)[2] <- "Constraint"

## msd$Type <- "Mean squared error"
## nmd$Type <- "Distance from true values"
## oos_prec <- rbind(msd,nmd)
## oos_prec$Type <- factor(oos_prec$Type,levels=c("Mean squared error","Distance from true values"))

Plot MIDAS coefficients

Description

Plots logistic function for LSTR MIDAS regression

Usage

plot_lstr(x, term_name, title = NULL, compare = NULL, ...)

Arguments

Details

Plots logistic function for LSTR MIDSAS regression of unrestricted MIDAS regression

Value

a data frame with restricted MIDAS coefficients, unrestricted MIDAS coefficients and lower and upper confidence interval limits. The data frame is returned invisibly.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Plot MIDAS coefficients

Description

Plots MIDAS coefficients of a MIDAS regression for a selected term.

Usage

plot_midas_coef(x, term_name, title, ...)

## S3 method for class 'midas_r'
plot_midas_coef(
  x,
  term_name = NULL,
  title = NULL,
  vcov. = sandwich,
  unrestricted = x$unrestricted,
  ...
)

Arguments

Details

Plots MIDAS coefficients of a selected MIDAS regression term together with corresponding MIDAS coefficients and their confidence intervals of unrestricted MIDAS regression

Value

a data frame with restricted MIDAS coefficients, unrestricted MIDAS coefficients and lower and upper confidence interval limits. The data frame is returned invisibly.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USrealgdp")
data("USunempr")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr), start = 1949)
trend <- 1:length(y)

##24 high frequency lags of x included
mr <- midas_r(y ~ trend + fmls(x, 23, 12, nealmon), start = list(x = rep(0, 3)))

plot_midas_coef(mr)

Plot MIDAS coefficients

Description

Plots MIDAS coefficients of a MIDAS regression for a selected term.

Usage

## S3 method for class 'midas_nlpr'
plot_midas_coef(
  x,
  term_name = NULL,
  title = NULL,
  compare = NULL,
  normalize = FALSE,
  ...
)

Arguments

Details

Plots MIDAS coefficients of a selected MIDAS regression term together with corresponding MIDAS coefficients and their confidence intervals of unrestricted MIDAS regression

Value

a data frame with restricted MIDAS coefficients, unrestricted MIDAS coefficients and lower and upper confidence interval limits. The data frame is returned invisibly.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Plot non-parametric part of the single index MIDAS regression

Description

Plot non-parametric part of the single index MIDAS regression of unrestricted MIDAS regression

Usage

plot_sp(x, term_name, title = NULL, compare = NULL, ...)

Arguments

Value

a data frame with restricted MIDAS coefficients, unrestricted MIDAS coefficients and lower and upper confidence interval limits. The data frame is returned invisibly.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Step function specification for MIDAS weights

Description

Step function specification for MIDAS weights

Usage

polystep(p, d, m, a)

Arguments

Value

vector of coefficients

Author(s)

Vaidotas Zemlys

Gradient of step function specification for MIDAS weights

Description

Gradient of step function specification for MIDAS weights

Usage

polystep_gradient(p, d, m, a)

Arguments

Value

vector of coefficients

Author(s)

Vaidotas Zemlys

Predict method for non-linear parametric MIDAS regression fit

Description

Predicted values based on midas_nlpr object.

Usage

## S3 method for class 'midas_nlpr'
predict(object, newdata, na.action = na.omit, ...)

Arguments

Details

predict.midas_nlpr produces predicted values, obtained by evaluating regression function in the frame newdata. This means that the appropriate model matrix is constructed using only the data in newdata. This makes this function not very convenient for forecasting purposes. If you want to supply the new data for forecasting horizon only use the function forecast.midas_r. Also this function produces only static predictions, if you want dynamic forecasts use the forecast.midas_r.

Value

a vector of predicted values

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Predict method for MIDAS regression fit

Description

Predicted values based on midas_r object.

Usage

## S3 method for class 'midas_r'
predict(object, newdata, na.action = na.omit, ...)

Arguments

Details

predict.midas_r produces predicted values, obtained by evaluating regression function in the frame newdata. This means that the appropriate model matrix is constructed using only the data in newdata. This makes this function not very convenient for forecasting purposes. If you want to supply the new data for forecasting horizon only use the function forecast.midas_r. Also this function produces only static predictions, if you want dynamic forecasts use the forecast.midas_r.

Value

a vector of predicted values

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USrealgdp")
data("USunempr")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr), start = 1949)

##24 high frequency lags of x included
mr <- midas_r(y ~ fmls(x, 23, 12, nealmon), start = list(x = rep(0, 3)))

##Declining unemployment
xn <- rnorm(2 * 12, -0.1, 0.1)

##Only one predicted value, historical values discarded
predict(mr, list(x = xn))

##Historical values taken into account
forecast(mr, list(x = xn))

Predict method for semi-parametric MIDAS regression fit

Description

Predicted values based on midas_sp object.

Usage

## S3 method for class 'midas_sp'
predict(object, newdata, na.action = na.omit, ...)

Arguments

Details

predict.midas_sp produces predicted values, obtained by evaluating regression function in the frame newdata. This means that the appropriate model matrix is constructed using only the data in newdata. This makes this function not very convenient for forecasting purposes. If you want to supply the new data for forecasting horizon only use the function forecast.midas_r. Also this function produces only static predictions, if you want dynamic forecasts use the forecast.midas_r.

Value

a vector of predicted values

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys-Balevičius

Calculate data for hAh_test and hAhr_test

Description

Workhorse function for calculating necessary matrices for hAh_test and hAhr_test. Takes the same parameters as hAh_test

Usage

prep_hAh(x)

Arguments

Value

a list with necessary matrices

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

See Also

hAh_test, hAhr_test

Realized volatility of S&P500 index

Description

Realized volatility of S&P500(Live) index of the period 2000 01 03 - 2013 11 22

Format

A data.frame object with two columns. First column contains date id, and the second the realized volatility for S&P500 index.

Source

No longer available. Read the statement here: https://oxford-man.ox.ac.uk/research/realized-library/

References

Heber, Gerd and Lunde, Asger, and Shephard, Neil and Sheppard, Kevin Oxford-Man Institute's realized library, Oxford-Man Institute, University of Oxford (2009)

Examples

## Do not run:
## The original data contained the file OxfordManRealizedVolatilityIndices.csv. 
## The code below reproduces the dataset.

## rvi <- read.csv("OxfordManRealizedVolatilityIndices.csv",check.names=FALSE,skip=2)
## ii <- which(rvi$DateID=="20131112")
## rvsp500 <- na.omit(rvi[1:ii,c("DataID","SPX2.rv")]

Create table for different forecast horizons

Description

Creates tables for different forecast horizons and table for combined forecasts

Usage

select_and_forecast(
  formula,
  data,
  from,
  to,
  insample,
  outsample,
  weights,
  wstart,
  start = NULL,
  IC = "AIC",
  seltype = c("restricted", "unrestricted"),
  test = "hAh_test",
  ftype = c("fixed", "recursive", "rolling"),
  measures = c("MSE", "MAPE", "MASE"),
  fweights = c("EW", "BICW", "MSFE", "DMSFE"),
  ...
)

Arguments

Details

Divide data into in-sample and out-of-sample. Fit different forecasting horizons for in-sample data. Calculate accuracy measures for individual and average forecasts.

Value

a list containing forecasts, tables of accuracy measures and the list with selected models

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

### Sets a seed for RNG ###
set.seed(1001)
## Number of low-frequency observations
n<-250
## Linear trend and higher-frequency explanatory variables (e.g. quarterly and monthly)
trend<-c(1:n)
x<-rnorm(4*n)
z<-rnorm(12*n)
## Exponential Almon polynomial constraint-consistent coefficients
fn.x <- nealmon(p=c(1,-0.5),d=8)
fn.z <- nealmon(p=c(2,0.5,-0.1),d=17)
## Simulated low-frequency series (e.g. yearly)
y<-2+0.1*trend+mls(x,0:7,4)%*%fn.x+mls(z,0:16,12)%*%fn.z+rnorm(n)
##Do not run
## cbfc<-select_and_forecast(y~trend+mls(x,0,4)+mls(z,0,12),
## from=list(x=c(4,8,12),z=c(12,24,36)),
## to=list(x=rbind(c(14,19),c(18,23),c(22,27)),z=rbind(c(22,27),c(34,39),c(46,51))),
## insample=1:200,outsample=201:250,
## weights=list(x=c("nealmon","almonp"),z=c("nealmon","almonp")),
## wstart=list(nealmon=rep(1,3),almonp=rep(1,3)),
## IC="AIC",
## seltype="restricted",
## ftype="fixed",
## measures=c("MSE","MAPE","MASE"),
## fweights=c("EW","BICW","MSFE","DMSFE")
## )

Simulate MIDAS regression response

Description

Simulates one or more responses from the distribution corresponding to a fitted MIDAS regression object.

Usage

## S3 method for class 'midas_r'
simulate(
  object,
  nsim = 999,
  seed = NULL,
  future = TRUE,
  newdata = NULL,
  insample = NULL,
  method = c("static", "dynamic"),
  innov = NULL,
  show_progress = TRUE,
  ...
)

Arguments

Details

Only the regression innovations are simulated, it is assumed that the predictor variables and coefficients are fixed. The innovation distribution is simulated via bootstrap.

Value

a matrix of simulated responses. Each row contains a simulated response.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USrealgdp")
data("USunempr")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr), start = 1949)
trend <- 1:length(y)

##24 high frequency lags of x included
mr <- midas_r(y ~ trend + fmls(x, 23, 12, nealmon), start = list(x = rep(0, 3)))

simulate(mr, nsim=10, future=FALSE)

##Forecast horizon
h <- 3
##Declining unemployment
xn <- rep(-0.1, 12*3)
##New trend values
trendn <- length(y) + 1:h

simulate(mr, nsim = 10, future = TRUE, newdata = list(trend = trendn, x = xn))

Split mixed frequency data into in-sample and out-of-sample

Description

Splits mixed frequency data into in-sample and out-of-sample datasets given the indexes of the low frequency data

Usage

split_data(data, insample, outsample)

Arguments

Details

It is assumed that data is a list containing mixed frequency data. Then given the indexes of the low frequency data the function splits the data into two subsets.

Value

a list with elements indata and outdata containing respectively in-sample and out-of-sample data sets

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

#Monthly data
x <- 1:24
#Quartely data
z <- 1:8
#Yearly data
y <- 1:2
split_data(list(y=y,x=x,z=z),insample=1,outsample=2)

Updates weights in MIDAS regression formula

Description

Updates weights in a expression with MIDAS term

Usage

update_weights(expr, tb)

Arguments

Details

For a MIDAS term fmls(x, 6, 1, nealmon) change weight nealmon to another weight.

Value

an expression with changed weights

Author(s)

Vaidotas Zemlys

Examples

update_weights(y~trend+mls(x,0:7,4,nealmon)+mls(z,0:16,12,nealmon),list(x = "nbeta", z = ""))

Create a weight function selection table for MIDAS regression model

Description

Creates a weight function selection table for MIDAS regression model with given information criteria and weight functions.

Usage

weights_table(
  formula,
  data,
  start = NULL,
  IC = c("AIC", "BIC"),
  test = c("hAh_test"),
  Ofunction = "optim",
  weight_gradients = NULL,
  ...
)

Arguments

Details

This function estimates models sequentially increasing the midas lag from kmin to kmax of the last term of the given formula

Value

a midas_r_ic_table object which is the list with the following elements:

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

Examples

data("USunempr")
data("USrealgdp")
y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
trend <- 1:length(y)
mwr <- weights_table(y~trend+fmls(x,12,12,nealmon),
                     start=list(x=list(nealmon=rep(0,3),
                     nbeta=c(1,1,1,0))))

mwr