TARMA.test {tseriesTARMA} | R Documentation |
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",
...
)
Arguments
x |
A univariate time series, either a |
pa |
Real number in |
pb |
Real number in |
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 |
d |
Delay parameter. Defaults to |
thd.range |
Vector of optional user defined threshold range. If missing then |
method |
Fitting method to be passed to |
... |
Additional arguments to be passed to |
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 (Goracci et al. 2021) and (Andrews 2003). 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.
Value
An object of class TARMAtest
with components:
statistic
The value of the
supLM
statistic and its robust versionsupLMh
.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.
Author(s)
Simone Giannerini, simone.giannerini@uniud.it
Greta Goracci, greta.goracci@unibz.it
References
-
Goracci G, Giannerini S, Chan K, Tong H (2023). “Testing for threshold effects in the TARMA framework.” Statistica Sinica, 33(3), 1879-1901. doi: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
for the AR vs TAR asymptotic version of the test with different defaults. TAR.test.B
for the bootstrap version of the AR vs TAR test. TARMAGARCH.test
for the robust version of the test that assumes GARCH innovations. TARMA.sim
to simulate from a TARMA process.
Examples
## 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)