tsDyn (version 0.7-60)

setarTest: Test of linearity

Description

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

numer 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

Value

• A object of class "Hansen99Test" containing:

  -The residual Sum of squares of model AR, 1 threshold TAR and 2 thresholds TAR (SSRs)

  -The Ftest statistic for the test (Ftests)

  -The bootstrap Pvalues (PvalBoot) and critical values (CriticalValBoot) for the test selected, and all Ftest computed (Ftestboot)

  -The thresholds for the original series, obtained from search for 1 thresh (firstBests) and conditional search for 2 thresh (secBests)

  -The number of bootstrap replications (nboot), the lags used (m) and the type of test (type)

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.

References

Hansen (1999) Testing for linearity, Journal of Economic Surveys, Volume 13, Number 5, December 1999 , pp. 551-576(26) avalaible at: http://www.ssc.wisc.edu/~bhansen/papers/cv.htm

See Also

TVAR.LRtest for the multivariate version. SETAR for estimation of the model.

Examples

#Data used by Hansen
sun<-(sqrt(sunspot.year+1)-1)*2

#Test 1vs2 and 1vs3
#setarTest(sun, m=11, thDelay=0:1, nboot=5,trim=0.1, test="1vs")