TARMAur.test.B {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 hypothesis of a integrated MA process versus a stationary TARMA process.

Usage

TARMAur.test.B(
  x,
  B = 1000,
  pa = 0.25,
  pb = 0.75,
  thd.range,
  method = "ML",
  btype = c("wb.r", "wb.n", "iid"),
  ...
)

Arguments

x

A univariate vector or 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

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.

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 TARMAur.test the supremum Lagrange Multiplier test to test an integrate MA(1) specification versus a stationary TARMA(1,1) specification. The option btype specifies the type of bootstrap as follows:

wb.r

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

wb.n

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

iid

Residual iid bootstrap. See (Goracci et al. 2021).

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 bootstrap p-value of the test.

method

A character string indicating the type of test performed.

d

The delay parameter.

pa

Lower threshold quantile.

Tb

The bootstrap null distribution.

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 for the asymptotic 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.B(x1, B=100) # B=100 for speedup


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