Estimation of a two-regime TAR model.
tar(y, p1, p2, d, is.constant1 = TRUE, is.constant2 = TRUE, transform = "no",
center = FALSE, standard = FALSE, estimate.thd = TRUE, threshold,
method = c("MAIC", "CLS")[1], a = 0.05, b = 0.95, order.select = TRUE, print = FALSE)time series
AR order of the lower regime
AR order of the upper regime
delay parameter
if True, intercept included in the lower regime, otherwise the intercept is fixed at zero
similar to is.constant1 but for the upper regime
available transformations: "no" (i.e. use raw data), "log", "log10" and "sqrt"
if set to be True, data are centered before analysis
if set to be True, data are standardized before analysis
if True, threshold parameter is estimated, otherwise it is fixed at the value supplied by threshold
known threshold value, only needed to be supplied if estimate.thd is set to be False.
"MAIC": estimate the TAR model by minimizing the AIC; "CLS": estimate the TAR model by the method of Conditional Least Squares.
lower percent; the threshold is searched over the interval defined by the a*100 percentile to the b*100 percentile of the time-series variable
upper percent
If method is "MAIC", setting order.select to True will enable the function to further select the AR order in each regime by minimizing AIC
if True, the estimated model will be printed
A list of class "TAR" which can be further processed by the by the predict and tsdiag functions.
The two-regime Threshold Autoregressive (TAR) model is given by the following formula: $$ Y_t = \phi_{1,0}+\phi_{1,1} Y_{t-1} +\ldots+ \phi_{1,p} Y_{t-p_1} +\sigma_1 e_t, \mbox{ if } Y_{t-d}\le r $$ $$ Y_t = \phi_{2,0}+\phi_{2,1} Y_{t-1} +\ldots+\phi_{2,p_2} Y_{t-p}+\sigma_2 e_t, \mbox{ if } Y_{t-d} > r.$$ where r is the threshold and d the delay.
Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
# NOT RUN {
data(prey.eq)
prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
# }
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