apt (version 1.0)

ciTarFit: Fitting Threshold Cointegration

Description

Fit a threshold cointegration regression between two time series.

Usage

ciTarFit(y, x, model = c("tar", "mtar"), lag, thresh, 
    small.win, ...)

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: tar or mtar.

lag

number of lags for the threshold cointegration regression.

thresh

a threshold value.

small.win

value of a small window for fitting the threshold cointegration regression.

...

additional arguments to be passed.

Value

• Return a list object of class "ciTarFit" with the following components:
• y
  dependend variable
• x
  independent variable
• model
  model choice
• lag
  number of lags
• thresh
  threshold value
• data.LR
  data used in the long-run regression
• data.CI
  data used in the threshold cointegration regression
• z
  residual from the long-run regression
• lz
  lagged residual from the long-run regression
• ldz
  lagged residual with first difference from the long-run regression
• LR
  long-run regression
• CI
  threshold cointegration regression
• f.phi
  test with the null hypothesis of no threshold cointegration
• f.apt
  test with the null hypothesis of no asymmetric price transmission in the long run
• sse
  value of sum of squared errors
• aic
  value of Akaike Information Criterion
• bic
  value of Bayesian Information Criterion.

Details

This is the main function for threshold autoregression regression (TAR) in assessing the nonlinear threshold relation between two time series variables. It can be used to estimate four types of threshold cointegration regressions. These four types are TAR with a threshold value of zero; consistent TAR with a nonzero threshold; MTAR (momentum TAR) with a threshold value of zero; and consistent MTAR with a nonzero thresold. The option of small window is used in model selection because a comparison of AIC and BIC values should be based on the same number of regression observations.

References

Balke, N.S., and T. Fomby. 1997. Threshold cointegration. International Economic Review 38(3):627-645. 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. Enders, W., and P.L. Siklos. 2001. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19(2):166-176.

See Also

print.ciTarFit; summary.ciTarFit; ciTarLag for lag selection; and ciTarThd for threshold selection;

Examples

data(daVi); data(daCh)
t.tar <- -8.041; t.mtar <- -0.451
mya <- myb <- 3       

(f1 <- ciTarFit(y=daVi, x=daCh, model="tar", lag=mya, thresh=0))
(f2 <- ciTarFit(y=daVi, x=daCh, model="tar", lag=mya, thresh=t.tar))
(f3 <- ciTarFit(y=daVi, x=daCh, model="mtar",lag=myb, thresh=0))
(f4 <- ciTarFit(y=daVi, x=daCh, model="mtar",lag=myb, thresh=t.mtar))
 
r0 <- cbind(summary(f1)$dia, summary(f2)$dia, summary(f3)$dia, 
    summary(f4)$dia)
(r1 <- r0[, c(1,2,4,6,8)])
col.name <- c("item","tar","c.tar","mtar","c.mtar")
diag <- r1[c(1:4, 6:7, 12:14, 8, 9, 11), col.name]
rownames(diag) <- 1:nrow(diag); diag

e1 <- summary(f1)$out; e2 <- summary(f2)$out 
e3 <- summary(f3)$out; e4 <- summary(f4)$out
(r2 <- rbind(e1, e2, e3, e4))

ee <- list(e1, e2, e3, e4); vect <- NULL
for (i in 1:4) {
  ef <- data.frame(ee[i]); ef
  vect2 <- c(paste(ef[3, "estimate"], ef[3, "sign"], sep=""), 
         paste("(", ef[3, "t.value"], ")", sep=""),
         paste(ef[4, "estimate"], ef[4, "sign"], sep=""), 
         paste("(", ef[4, "t.value"], ")", sep=""))    
  vect <- cbind(vect, vect2)
}
item <- c("pos.coeff","pos.t.value", "neg.coeff","neg.t.value")
ve <- data.frame(cbind(item, vect)); colnames(ve) <- col.name
( tab3.b <- rbind(diag, ve)[c(1:2, 13:16, 3:12), ])