Help for package mfGARCH

Title:

Mixed-Frequency GARCH Models

Version:

0.2.1

Description:

Estimating GARCH-MIDAS (MIxed-DAta-Sampling) models (Engle, Ghysels, Sohn, 2013, <doi:10.1162/REST_a_00300>) and related statistical inference, accompanying the paper "Two are better than one: Volatility forecasting using multiplicative component GARCH models" by Conrad and Kleen (2020, <doi:10.1002/jae.2742>). The GARCH-MIDAS model decomposes the conditional variance of (daily) stock returns into a short- and long-term component, where the latter may depend on an exogenous covariate sampled at a lower frequency.

Depends:

R (≥ 3.3.0)

License:

MIT + file LICENSE

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.1.1

Imports:

Rcpp, graphics, stats, numDeriv, zoo, maxLik

LinkingTo:

Rcpp

URL:

https://github.com/onnokleen/mfGARCH/

BugReports:

https://github.com/onnokleen/mfGARCH/issues

Suggests:

testthat, dplyr, ggplot2, covr, rmarkdown

NeedsCompilation:

yes

Packaged:

2021-06-17 14:00:19 UTC; onnokleen

Author:

Onno Kleen

[aut, cre]

Maintainer:

Onno Kleen <r@onnokleen.de>

Repository:

CRAN

Date/Publication:

2021-06-17 14:20:02 UTC

Stock returns and financial conditions.

Description

A dataset containing the S&P 500 stock returns and the NFCI

Usage

df_financial

Format

A data frame with 11,306 rows and 5 variables:

date: date
return: daily S&P 500 log returns times 100
rv: 5-minute realized variances
week: a dummy for each year/week combination
nfci: National Financial Conditions Index

Source

https://github.com/onnokleen/mfGARCH/

https://finance.yahoo.com/

https://fred.stlouisfed.org/series/NFCI

https://realized.oxford-man.ox.ac.uk

Mixed-frequency data set.

Description

A dataset containing the S&P 500 stock returns, realized variances and macroeconomic variables

Usage

df_mfgarch

Format

A data frame with 11,938 rows and 11 variables:

date: date
return: daily S&P 500 log returns times 100
open_close: open-close returns
rv: 5-minute realized variances
vix: Cboe VIX
year_week: a dummy for each year/week combination
dhousing: changes in housing starts
dindpro: changes in industrial production
nai: NAI
nfci: National Financial Conditions Index
year_month: a dummy for each year/month combination

Source

https://github.com/onnokleen/mfGARCH/

https://finance.yahoo.com/

https://fred.stlouisfed.org

https://realized.oxford-man.ox.ac.uk

This function estimates a multiplicative mixed-frequency GARCH model. For the sake of numerical stability, it is best to multiply log returns by 100.

Description

This function estimates a multiplicative mixed-frequency GARCH model. For the sake of numerical stability, it is best to multiply log returns by 100.

Usage

fit_mfgarch(
  data,
  y,
  x = NULL,
  K = NULL,
  low.freq = "date",
  var.ratio.freq = NULL,
  gamma = TRUE,
  weighting = "beta.restricted",
  x.two = NULL,
  K.two = NULL,
  low.freq.two = NULL,
  weighting.two = NULL,
  multi.start = FALSE,
  control = list(par.start = NULL)
)

Arguments

data

data frame containing a column named date of type 'Date'.

y

name of high frequency dependent variable in df.

x

covariate employed in mfGARCH.

K

an integer specifying lag length K in the long-term component.

low.freq

a string of the low frequency variable in the df.

var.ratio.freq

specify a frequency column on which the variance ratio should be calculated.

gamma

if TRUE, an asymmetric GJR-GARCH is used as the short-term component. If FALSE, a simple GARCH(1,1) is employed.

weighting

specifies the weighting scheme employed in the long-term component. Options are "beta.restricted" (default) or "beta.unrestricted"

x.two

optional second covariate

K.two

lag lgenth of optional second covariate

low.freq.two

low frequency of optional second covariate

weighting.two

specifies the weighting scheme employed in the optional second long-term component. Currently, the only option is "beta.restricted"

multi.start

if TRUE, optimization is carried out with multiple starting values

control

a list

Value

A list of class mfGARCH with letters and numbers.

par - vector of estimated parameters
rob.std.err - sandwich/HAC-type standard errors
broom.mgarch - a broom-like data.frame with entries 1) estimate: column of estimated parameters 2) rob.std.err - sandwich/HAC-type standard errors 3) p.value - p-values derived from sandwich/HAC-type standard errors 4) opg.std.err - Bollerslev-Wooldrige/OPG standard errors for GARCH processes 5) opg.p.value - corresponding alternative p-values
tau - fitted long-term component
g - fitted short-term component
df.fitted - data frame with fitted values and residuals
K - chosen lag-length in the long-term component
weighting.scheme - chosen weighting scheme
llh - log-likelihood value at estimated parameter vector
bic - corresponding BIC value
y - dependent variable y
optim - output of the optimization routine
K.two - lag-lenth of x.two if two covariates are employed
weighting.scheme.two - chosen weighting scheme of x.two (if K.two != NULL)
tau.forecast - one-step ahead forecast of the long-term component
variance.ratio - calculated variance ratio
est.weighting - estimated weighting scheme
est.weighting.two - estimated weighting scheme of x.two (if K.two != NULL)

Examples

## Not run: 
fit_mfgarch(data = df_financial, y = "return", x = "nfci", low.freq = "week", K = 52)
fit_mfgarch(data = df_mfgarch, y = "return", x = "nfci", low.freq = "year_week", K = 52,
x.two = "dindpro", K.two = 12, low.freq.two = "year_month", weighting.two = "beta.restricted")

## End(Not run)

This function plots the weighting scheme of an estimated GARCH-MIDAS model

Description

This function plots the weighting scheme of an estimated GARCH-MIDAS model

Usage

plot_weighting_scheme(x)

Arguments

x

mfGARCH object obtained by fit_mfgarch

This function simulates a GARCH-MIDAS model. Innovations can follow a standard normal or student-t distribution.

Description

This function simulates a GARCH-MIDAS model. Innovations can follow a standard normal or student-t distribution.

Usage

simulate_mfgarch(
  n.days,
  mu,
  alpha,
  beta,
  gamma,
  m,
  theta,
  w1 = 1,
  w2,
  K,
  psi,
  sigma.psi,
  low.freq = 1,
  n.intraday = 288,
  student.t = NULL,
  corr = 0
)

Arguments

n.days

number of days

mu

alpha

alpha

beta

beta

gamma

gamma

m

theta

theta

w1

w2

K

psi

psi

sigma.psi

sigma.psi

low.freq

number of days per low-frequency period

n.intraday

number of maximum intraday returns

student.t

either NULL or degrees of freedom

corr

correlation between innovations (should only be used for daily tau)

Examples

simulate_mfgarch(n.days = 200, mu = 0, alpha = 0.06, beta = 0.92, gamma = 0, m = 0,
theta = 0.1, w1 = 1, w2 = 3, K = 12, psi = 0.98, sigma.psi = 0.1, low.freq = 10)

This function simulates a GARCH-MIDAS model where the short-term GARCH component is replaced by its diffusion limit, see Andersen (1998)

Description

This function simulates a GARCH-MIDAS model where the short-term GARCH component is replaced by its diffusion limit, see Andersen (1998)

Usage

simulate_mfgarch_diffusion(
  n.days,
  mu,
  alpha,
  beta,
  m,
  theta,
  w1 = 1,
  w2,
  K,
  psi,
  sigma.psi,
  low.freq = 1,
  n.intraday = 288
)

Arguments

n.days

number of days

mu

alpha

alpha

beta

beta

m

theta

theta

w1

w2

K

psi

psi

sigma.psi

sigma.psi

low.freq

low.freq

n.intraday

n.intraday

Examples

## Not run: simulate_mfgarch_diffusion(n.days = 200, mu = 0, alpha = 0.06, beta = 0.92, m = 0,
theta = 0.1, w1 = 1, w2 = 3, K = 12, psi = 0.98, sigma.psi = 0.1, low.freq = 10)
## End(Not run)

Simulate a GARCH-MIDAS similar to Wang/Ghysels with lagged RVol as covariate

Description

Simulate a GARCH-MIDAS similar to Wang/Ghysels with lagged RVol as covariate

Usage

simulate_mfgarch_rv_dependent(
  n.days,
  mu,
  alpha,
  beta,
  gamma,
  m,
  theta,
  w1 = 1,
  w2,
  K,
  n.intraday = 288,
  low.freq = 1,
  rvol = FALSE
)

Arguments

n.days

number of days

mu

alpha

alpha

beta

beta

gamma

gamma

m

theta

theta

w1

w2

K

n.intraday

number of maximum intraday returns, default 288

low.freq

number of days per low frequency

rvol

if TRUE, the square root of the realized variance is used as a covariate

Examples

simulate_mfgarch_rv_dependent(n.days = 2200, mu = 0, alpha = 0.06, beta = 0.92, gamma = 0, m = 0,
  theta = 0.1, w1 = 1, w2 = 3, K = 3, low.freq = 22)