ciTarFit function

Fitting Threshold Cointegration

Fit a threshold cointegration regression between two time series.

ciTarFit(y, x, model = c('tar','mtar'), lag = 1, thresh = 0,
    small.win = NULL)

Arguments

• y: dependent or left-side variable for the long-run model; must be a time series object.
• x: independent or right-side variable for the long-run model; must be a time series object.
• model: a choice of two models: tar or mtar; the default is tar.
• lag: number of lags for the threshold cointegration regression.
• thresh: a threshold value (default of zero).
• small.win: value of a small window for fitting the threshold cointegration regression; used mainly for lag selection in ciTarLag.

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 threshold. The option of small window will be used in lag selection because a comparison of AIC and BIC values should be based on the same number of regression observations.

Returns

Return a list object of class "ciTarFit" with these 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 1st difference from long-run model

• LR: long-run regression

• CI: threshold cointegration regression

• f.phi: test with a null hypothesis of no threshold cointegration

• f.apt: test with a 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.

Methods

One method is defined as follows:

• print:: Four main outputs from threshold cointegration regression are shown: long-run regression between the two price variables, threshold cointegration regression, hypothesis test of no cointegration, and hypothesis test of no asymmetric adjustment.

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.

Author(s)

Changyou Sun (edwinsun258@gmail.com )

See Also

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

Examples

# see example at daVich