Test of linearity against threshold of Hansen (1999) with bootstrap distribution
Usage
setarTest(x, m, d = 1, steps = d, series, thDelay = 0, nboot=10, trim=0.1,
test=c("1vs", "2vs3"), hpc=c("none", "foreach"),check=FALSE)
Arguments
x
time series
m, d, steps
embedding dimension, time delay, forecasting steps
series
time series name (optional)
thDelay
'time delay' for the threshold variable (as multiple of embedding time delay d)
nboot
number of bootstrap replications
trim
trimming parameter indicating the minimal percentage of observations in each regime
test
Type of test. See details
hpc
Possibility to run the bootstrap on parallel core. See
details in TVECM.HStest
check
Possibility to check if the bootstrap is correct by not sampling the residuals. The result given should be the same as in the original data
Details
Estimation of the first threshold parameter is made with CLS, a conditional search with one iteration is made for the second threshold. The Ftest comparing the residual sum of squares (SSR) of each model is computed.
F_{ij}=T( (S_{i}-S_{j})/S_{j} )
where S_{i} is the SSR of the model with i regimes (and so i-1 thresholds).
Three test are avalaible. The both first can be seen as linearity test, whereas the third can be seen as a specification test: once the 1vs2 or/and 1vs3 rejected the linearity and henceforth accepted the presence of a threshold, is a model with one or two thresholds preferable?
Test 1vs2: Linear AR versus 1 threshold TAR
Test 1vs3: Linear AR versus 2 threshold2 TAR
Test 2vs3: 1 threshold TAR versus 2 threshold2 TAR
The both first are computed together and avalaible with test="1vs". The third test is avalaible with test="2vs3".
The homoskedastic bootstrap distribution is based on resampling the residuals from H0 model (ar for test 1vs, and setar(1) for test 2vs3), estimating the threshold parameter and then computing the Ftest, so it involves many computations and is pretty slow.
Value
A object of class "Hansen99Test" containing:
SSRs
The residual Sum of squares of model AR, 1 threshold TAR and 2 thresholds TAR
Ftests
The Ftest statistic for the test
PvalBoot
The bootstrap p-values for the test selected
CriticalValBoot
The critical values for the test selected
Ftestboot
All the F-test computed
firstBests, secBests
The thresholds for the original series, obtained from search for 1 thresh (firstBests) and conditional search for 2 thresh (secBests)
nboot,m,type
The number of bootstrap replications (nboot), the lags used (m) and the type of test (type)