TAR.test.B {tseriesTARMA}

AR versus TAR bootstrap supLM test for nonlinearity

Description

Implements various bootstrap supremum Lagrange Multiplier tests for a AR specification versus a TAR specification.

Usage

TAR.test.B(
  x,
  B = 1000,
  pa = 0.25,
  pb = 0.75,
  ar.ord,
  d = 1,
  btype = c("iid", "wb.h", "wb.r", "wb.n"),
  ...
)

Arguments

x

A univariate time series.

B

Integer. Number of bootstrap resamples. Defaults to 1000.

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.

btype

Bootstrap type, can be one of 'iid','wb.h','wb.r','wb.n', see Details.

...

Additional arguments to be passed to arima.

Details

Implements the bootstrap version of TAR.test the supremum Lagrange Multiplier test to test an AR specification versus a TARMA specification. The option btype specifies the type of bootstrap as follows:

iid

Residual iid bootstrap. See (Giannerini et al. 2022), (Giannerini et al. 2023).

wb.h

Stochastic permutation of (Hansen 1996).

wb.r

Residual wild bootstrap with Rademacher auxiliary distribution. See (Giannerini et al. 2022), (Giannerini et al. 2023).

wb.n

Residual wild bootstrap with Normal auxiliary distribution. See (Giannerini et al. 2022), (Giannerini et al. 2023).

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: 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 bootstrap p-value of the test.

method

A character string indicating the type of test performed.

Tb

The bootstrap null distribution.

Author(s)

Simone Giannerini, [e-mail]

Greta Goracci, [e-mail]

References

• Giannerini S, Goracci G, Rahbek A (2022). “The validity of bootstrap testing in the threshold framework.” doi:10.48550/ARXIV.2201.00028, https://arxiv.org/abs/2201.00028.

• Giannerini S, Goracci G, Rahbek A (2023). “The validity of bootstrap testing in the threshold framework.” Journal of Econometrics, in press. https://doi.org/10.1016/j.jeconom.2023.01.004.

• 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.

• Giannerini S, Goracci G (2021). “Estimating and Forecasting with TARMA models.” University of Bologna.

• Hansen BE (1996). “Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis.” Econometrica, 64(2), 413–430. ISSN 00129682, 14680262, https://doi.org/10.2307/2171789.

See Also

TAR.test for the heteroskedastic robust asymptotic test. TARMAGARCH.test for the robust version of the test with respect to GARCH innovations. TARMA.sim to simulate from a TARMA process.

Examples

## a TAR(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, theta2=0, d=1, thd=0.2)
TAR.test.B(x1, ar.ord=1, d=1)
TAR.test.B(x1, ar.ord=1, d=1, btype='wb.r')
TAR.test.B(x1, ar.ord=1, d=1, btype='wb.h')

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