Package 'mfGARCH'

Title: Mixed-Frequency GARCH Models
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.
Authors: Onno Kleen [aut, cre]
Maintainer: Onno Kleen <[email protected]>
License: MIT + file LICENSE
Version: 0.2.1
Built: 2025-03-03 04:33:34 UTC
Source: https://github.com/onnokleen/mfgarch

Help Index

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

mu
alpha

alpha
beta

beta
gamma

gamma
m

m
theta

theta
w1

w1
w2

w2
K

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

mu
alpha

alpha
beta

beta
m

m
theta

theta
w1

w1
w2

w2
K

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

mu
alpha

alpha
beta

beta
gamma

gamma
m

m
theta

theta
w1

w1
w2

w2
K

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)