TARMAur.test {tseriesTARMA}

Unit root supLM test for an integrated MA versus a stationary TARMA process

Description

Implements a supremum Lagrange Multiplier unit root test for the null hypiythesis of a integrated MA process versus a stationary TARMA process.

Usage

TARMAur.test(x, pa = 0.25, pb = 0.75, thd.range, method = "ML", ...)

Arguments

x

A univariate vector or 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

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.

Details

Implements an asymptotic supremum Lagrange Multiplier test to test an integrate MA(1) specification versus a stationary TARMA(1,1) specification. This is an asymptotic test and the value of the test statistic has to be compared with the critical values tabulated in (Chan et al. 2024) and available in supLMQur. The relevant critical values are automatically shown upon printing the test, see print.TARMAtest.

Value

An object of class TARMAtest 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.ARMA

The null model: IMA(1) fit over x.

sigma2

Estimated innovation variance from the IMA fit.

data.name

A character string giving the name of the data.

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.

Author(s)

Simone Giannerini, [e-mail]

Greta Goracci, [e-mail]

References

• Chan K, Giannerini S, Goracci G, Tong H (2024). “Testing for threshold regulation in presence of measurement error.” Statistica Sinica, 34(3). https://doi.org/10.5705/ss.202022.0125.

See Also

TARMAur.test.B for the bootstrap version of the test. print.TARMAtest for the print method.

Examples

## a TARMA(1,1,1,1) 
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)
TARMAur.test(x1)


## a IMA(1,1)
x2   <- arima.sim(n=100, model=list(order = c(0,1,1),ma=0.6))
TARMAur.test(x2)