apt (version 1.0)

ciTarThd: Threshold Selection for Threshold Cointegration Regression

Description

Select the best threshold for threshold cointegration regression by sum of squared errors

Usage

ciTarThd(y, x, model = c("tar", "mtar"), lag, th.range = 0.15, 
    digits = 3, ...)

Arguments

y

dependent or left-side variable for the long-run regression.

x

independent or right-side variable for the long-run regression.

model

a choice of two models, either tar or mtar.

lag

number of lags.

th.range

the percentage of observations to be excluded from the search.

digits

number of digits used in rounding outputs.

...

additional arguments to be passed.

Value

• Return a list object of class "ciTarThd" with the following components:
• model
  model choice
• lag
  number of lags
• th.range
  the percentage of observations excluded
• th.final
  the best threshold value
• ssef
  the best (i.e., lowest) value of SSE
• obs.tot
  total number of observations in the raw data
• obs.CI
  number of observations used in the threshold cointegration regression
• basic
  a brief summary of the major outputs
• path
  a data frame of the search record (number of regression, threshold value, SSE, AIC, and BIC values).

Details

The best threshold is determined by fitting the regression for possible threshold values, sorting the results by sum of squared errors (SSE), and selecting the best with the lowest SSE. To have sufficient observations on either side of the threshold value, certain percentage of observations on the top and bottoms are excluded from the search path. This is usually set as 0.15 by the th.range (Chan 1993).

References

Chan, K.S. 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics 21(1):520-533. Enders, W., and C.W.J. Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16(3):304-311.

See Also

plot.ciTarThd for the graphical trend; ciTarFit; and ciTarLag

Examples

data(daVi); data(daCh)

# 1. best threshold value for tar
t3 <- ciTarThd(y=daVi, x=daCh, model="tar", lag=0); 
(th.tar <- t3$basic)
plot(t3)

# 2. best threshold value for mtar 
t4 <- ciTarThd(y=daVi, x=daCh, model="mtar", lag=0) 
(th.mtar <- t4$basic)
plot(t4)

# 3. best threshold by lag; 
# The following two loops are executable.
# But it may take about 5 to 10 minutes to run 
# because there are over 1,000 linear regressions in the loops.

for (i in 1:12) {
     t3a <- ciTarThd(y=daVi, x=daCh, model="tar", lag=i) 
     th.tar[i+2] <- t3a$basic[,2]
 }
th.tar

for (i in 1:12) {
     t4a <- ciTarThd(y=daVi, x=daCh, model="mtar", lag=i) 
     th.mtar[i+2] <- t4a$basic[,2]
 }
th.mtar

# 4. The final result of threshold selection are as follows.
# The best threshold values do not vary much by lag. 
# This is not suprising because more lagged values do not 
# reduce SSE much.

t.tar <- -8.041; t.mtar <- -0.451    # lag = 0 to 4
t.tar <- -8.701; t.mtar <- -0.451    # lag = 5 to 12