Abstract
In this paper, we introduce a new class of bivariate threshold VAR cointegration models. In the models, outside a compact region, the processes are cointegrated, while in the compact region, we allow different kinds of possibilities. We show that the bivariate processes form a 1/2-null recurrent system. We also find that the convergence rate for the estimators for the coefficients in the outside regime is square-root of the sample size, while the convergence rate for the estimators for the coefficients in the middle regime is much smaller than the sample size. Also, we show that the convergence rate of the cointegrating coefficient is the sample size, which is same as linear cointegration model. The Monte Carlo simulation results suggest that the estimators perform reasonably well in finite samples. Applying the proposed model to study the dynamic relationship between Federal funds rate and 3-month Treasury bill rate, we find that cointegrating coefficients are the same for the two regimes while the short run loading coefficients are different.
Highlights
Linear cointegration models as introduced by Granger (1981) and Engle and Granger (1987) have been extremely influential in econometrics
We show that the convergence rate of the cointegrating coefficient is T, which is same as linear cointegration model
Applying the proposed model to study the dynamic relationship between Federal funds rate and 3-month Treasury bill rate, we find that cointegrating coefficients are the same for the two regimes while the short run loading coefficients are different
Summary
Linear cointegration models as introduced by Granger (1981) and Engle and Granger (1987) have been extremely influential in econometrics. A class of nonlinear models that has enjoyed a similar kind of influence in the time series modeling is the class of threshold models introduced by Tong (1978, 1983) Their analysis has largely been confined to the stationary case. In this region, quite general behavior of {xt} is permitted, i.e. the matrix A is (1.4) can be arbitrary, and including stationary and explosive type behaviours (cf Gao et al 2013 in the univariate case). Markov recurrence theory plays an important role in all of this, not the least in determining the different convergence rates for the estimators in different regions OP (.) means stochastic order same as, oP (.) means stochastic order less than. ⊗ denotes Kronecker product, vec denotes vectorization, Aτ denotes transpose of a matrix A
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