TAR.test {tseriesTARMA}

AR versus TARMA supLM robust test for nonlinearity

Description

Implements a heteroskedasticity robust supremum Lagrange Multiplier test for a AR specification versus a TAR specification. Includes the classic (non robust) AR versus TAR test.

Usage

TAR.test(x, pa = 0.25, pb = 0.75, ar.ord, d = 1)

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.

d

Delay parameter. Defaults to 1.

Details

Implements a heteroskedasticity robust asymptotic supremum Lagrange Multiplier test to test an AR specification versus a TAR specification. This is an asymptotic test and the value of the test statistic has to be compared with the critical values tabulated in (Goracci et al. 2021) or (Andrews 2003). Both the non-robust supLM and the robust supLMh statistics are returned.

Value

An object of class TARMAtest with components:

statistic

A named vector with the values of the classic supLM and robust supLMh statistics.

parameter

A named vector: threshold is the value that maximises the Lagrange Multiplier values.

test.v

Matrix 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: AR fit over x.

sigma2

Estimated innovation variance from the AR 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, [e-mail]

Greta Goracci, [e-mail]

References

• Goracci G, Giannerini S, Chan K, Tong H (2023). “Testing for threshold effects in the TARMA framework.” Statistica Sinica, 33(3), 1879-1901. https://doi.org/10.5705/ss.202021.0120.

• Andrews DWK (2003). “Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum.” Econometrica, 71(1), 395-397. doi:10.1111/1468-0262.00405.

See Also

TAR.test.B for the bootstrap version of the test. TARMA.test for the ARMA vs TARMA asymptotic version of the test, which includes also the AR vs TAR test, with different defaults. TARMAGARCH.test for the robust version of the ARMA vs TARMA test with respect to GARCH innovations. TARMA.sim to simulate from a TARMA process.

Examples

set.seed(123)
## a TAR(1,1) ---------------
x1   <- 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)
TAR.test(x1, ar.ord=1, d=1)

## a AR(1)    ----------------
x2   <- arima.sim(n=100, model=list(order=c(1,0,0), ar=0.5))
TAR.test(x2, ar.ord=1, d=1)