TARMAGARCH.test: ARMA GARCH versus TARMA GARCH supLM test for nonlinearity
In tseriesTARMA: Analysis of Nonlinear Time Series Through Threshold Autoregressive Moving Average Models (TARMA) Models

TARMAGARCH.test

R Documentation

ARMA GARCH versus TARMA GARCH supLM test for nonlinearity

Description

Implements a supremum Lagrange Multiplier test for a ARMA-GARCH specification versus a TARMA-GARCH specification. Both the AR and MA parameters are tested. Also includes the ARCH case.

Usage

TARMAGARCH.test(
  x,
  pa = 0.25,
  pb = 0.75,
  ar.ord = 1,
  ma.ord = 1,
  arch.ord = 1,
  garch.ord = 1,
  d = 1,
  thd.range,
  ...
)

Arguments

`x`	A univariate time series.
`pa`	Real number in `[0,1]`. Sets the lower limit for the threshold search to the `100*pa`-th sample percentile. The default is `0.25`
`pb`	Real number in `[0,1]`. Sets the upper limit for the threshold search to the `100*pb`-th sample percentile. The default is `0.75`
`ar.ord`	Order of the AR part. It must be a positive integer
`ma.ord`	Order of the MA part. It must be a positive integer
`arch.ord`	Order of the ARCH part. It must be a positive integer
`garch.ord`	Order of the GARCH part. It must be a non negative integer.
`d`	Delay parameter. Defaults to `1`.
`thd.range`	Vector of optional user defined threshold range. If missing then `pa` and `pb` are used.
`...`	Additional arguments to be passed to `ugarchfit`.

Details

Implements an asymptotic supremum Lagrange Multiplier test to test an ARMA-GARCH specification versus a TARMA-GARCH specification. In other words, the test is robust with respect to heteroskedasticity. Both the AR parameters and the MA parameters are tested. This is an asymptotic test and the value of the test statistic has to be compared with the critical values reported in the output and taken from \insertCiteAnd03tseriesTARMA. It includes the ARCH case if garch.ord=0. The null ARMA-GARCH model is estimated in one step with the function ugarchfit from the package rugarch. The estimated AR and MA polynomials are checked for stationarity and invertibility.

Value

A list of class htest with components:

statistic: The value of the supLM statistic.
parameter: A named vector: threshold is the value that maximises the Lagrange Multiplier values.
test.v: Vector of values of the LM statistic for each threshold given in thd.range.
thd.range: Range of values of the threshold.
fit: The null model: ARMA-GARCH fit using rugarch.
sigma2: Estimated innovation variance from the ARMA fit.
data.name: A character string giving the name of the data.
prop: Proportion of values of the series that fall in the lower regime.
p.value: The p-value of the test. It is NULL for the asymptotic test.
method: A character string indicating the type of test performed.
d: The delay parameter.
pa: Lower threshold quantile.
dfree: Effective degrees of freedom. It is the number of tested parameters.

Author(s)

Simone Giannerini, simone.giannerini@uniud.it

Greta Goracci, greta.goracci@unibz.it

References

\insertRef
Ang23tseriesTARMA
\insertRef
Gor21tseriesTARMA
\insertRef
And03tseriesTARMA

Examples

## Function to simulate from a ARMA-GARCH process

arma11.garch11 <- function(n, ph, th, a, b, a0=1, rand.gen = rnorm, innov = rand.gen(n, ...),
n.start = 500, start.innov = rand.gen(n.start, ...),...){

  #  Simulates a ARMA(1,1)-GARCH(1,1) process
  #  with parameters ph, th, a, b, a0.
  #         x[t] <- ph*x[t-1] + th*eps[t-1] + eps[t]
  #       eps[t] <- e[t]*sqrt(v[t])
  #         v[t] <- a0 + a*eps[t-1]^2 + b*v[t-1];
  # ph  : AR
  # th  : MA
  # a   : ARCH
  # b   : GARCH

  # checks
  if(abs(a+b)>=1)   stop("model is not stationary")
  if(b/(1-a)>=1) stop("model has infinite fourth moments")

  if (!missing(start.innov) && length(start.innov) < n.start)
    stop(gettextf("'start.innov' is too short: need %d points", n.start), domain = NA)
  e <- c(start.innov[1L:n.start], innov[1L:n])
  ntot <- length(e)
  x <- v <- eps <- double(ntot)
  v[1]   <- a0/(1.0-a-b);
  eps[1] <- e[1]*sqrt(v[1])
  x[1]   <- eps[1];
  for(i in 2:ntot){
    v[i]   <- a0 + a*eps[i-1]^2 + b*v[i-1];
    eps[i] <- e[i]*sqrt(v[i])
    x[i]   <- ph*x[i-1] + th*eps[i-1] + eps[i]
  }
  if (n.start > 0)  x <- x[-(1L:n.start)]
  return(ts(x));
}

## **************************************************************************
## Comparison between the robust and the non-robust test in presence of GARCH errors
## Simulates from the ARMA(1,1)-GARCH(1,1)

set.seed(12)
x1 <- arma11.garch11(n=100, ph=0.9, th=0.5, a=0.85, b=0.1, a0=1,n.start=500)
TARMAGARCH.test(x1, ar.ord=1, ma.ord=1, arch.ord=1, garch.ord=1, d=1)
TARMA.test(x1, ar.ord=1, ma.ord=1, d=1, ma.fixed=FALSE)

## a TARMA(1,1,1,1) where the threshold effect is on the AR parameters
set.seed(123)
x2  <- TARMA.sim(n=100, phi1=c(0.5,-0.5), phi2=c(0.0,0.8), theta1=0.5, theta2=0.5, d=1, thd=0.2)
TARMAGARCH.test(x2, ar.ord=1, ma.ord=1, d=1)

tseriesTARMA documentation built on Oct. 8, 2024, 5:11 p.m.