TARMA.test: ARMA versus TARMA (and AR versus TAR) supLM tests for nonlinearity

Description

Heteroskedasticity robust supremum Lagrange Multiplier tests for a ARMA specification versus a TARMA specification. Includes the AR versus TAR test.

Usage

TARMA.test(
  x,
  pa = 0.25,
  pb = 0.75,
  ar.ord,
  ma.ord,
  ma.fixed = TRUE,
  d,
  thd.range,
  method = "CSS-ML",
  ...
)

Value

An object of class TARMAtest with components:

statistic: The value of the supLM statistic and its robust version supLMh.
parameter: A named vector: threshold is the value that maximizes the Lagrange Multiplier values.
test.v: Vector of values of the two LM statistics for each threshold given in thd.range.
thd.range: Range of values of the threshold.
fit.ARMA: The null model: ARMA fit over x.
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.

Arguments

x: A univariate time series, either a ts or zoo object.
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.
ma.ord: Order of the MA part.
ma.fixed: Logical. Only applies to testing ARMA vs TARMA. If TRUE computes the test where only the AR parameters are tested, see Gor21tseriesTARMA for details.
d: Delay parameter. Defaults to 1.
thd.range: Vector of optional user defined threshold range. If missing then pa and pb are used.
method: Fitting method to be passed to arima.
...: Additional arguments to be passed to arima.

Author

Simone Giannerini, simone.giannerini@uniud.it

Greta Goracci, greta.goracci@unibz.it

Details

Implements an asymptotic supremum Lagrange Multiplier test to test an ARMA specification versus a TARMA specification. Both the non-robust supLM and the robust supLMh statistics are returned. If ma.fixed=TRUE (the default), the AR parameters are tested whereas the MA parameters are fixed. If ma.fixed=FALSE both the AR 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 tabulated in Gor21tseriesTARMA and And03tseriesTARMA. These are automatically computed and printed by print.TARMAtest. If ma.ord=0 then the AR versus TAR test is used. Note that when method='CSS', this is equivalent to TAR.test, which uses least squares.

References

Gor23tseriesTARMA
And03tseriesTARMA

Examples

Run this code

## a TARMA(1,1,1,1) where the threshold effect is on the AR parameters
set.seed(123)
x1    <- 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)
TARMA.test(x1, ar.ord=1, ma.ord=1, d=1)
TARMA.test(x1, ar.ord=1, ma.ord=1, d=1, ma.fixed=FALSE) # full TARMA test

## a TARMA(1,1,1,1) where the threshold effect is on the MA parameters
set.seed(212)
x2    <- TARMA.sim(n=100, phi1=c(0.5,0.2), phi2=c(0.5,0.2), theta1=0.6, theta2=-0.6, d=1, thd=0.2)
TARMA.test(x2, ar.ord=1, ma.ord=1, d=1)
TARMA.test(x2, ar.ord=1, ma.ord=1, d=1, ma.fixed=FALSE) # full TARMA test

## a ARMA(1,1)
x3   <- arima.sim(n=100, model=list(order = c(1,0,1),ar=0.5, ma=0.5))
TARMA.test(x3, ar.ord=1, ma.ord=1, d=1)

## a TAR(1,1)
x4   <- TARMA.sim(n=100, phi1=c(0.5,-0.5), phi2=c(0.0,0.8), theta1=0, theta2=0, d=1, thd=0.2)
TARMA.test(x4, ar.ord=1, ma.ord=0, d=1)

## a AR(1)
x5   <- arima.sim(n=100, model=list(order = c(1,0,0),ar=0.5))
TARMA.test(x5, ar.ord=1, ma.ord=0, d=1)

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