We propose bootstrap implementations of the asymptotic Wald, likelihood ratio and Lagrange multiplier tests for the order of integration of a fractionally integrated time series. Our main purpose in doing so is to develop tests which are robust to both conditional and unconditional...

We consider estimation and inference in fractionally integrated time series models driven by shocks which can display conditional and unconditional heteroskedasticity of unknown form. Although the standard conditional sum-of-squares (CSS) estimator remains consistent and asymptotically normal in...

The purpose of this paper is to investigate the tests of Hansen (1991) to detect structural breaks in cointegrated relations using Monte Carlo methods. The evaluation takes place within the linear quadratic model. The evidence for a single regressor suggests that the test have proper size and...

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose augmented Dickey-Fuller (ADF) and Phillips type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift....

This paper proposes two simple tests that are based on certain time domain properties of I(d) processes. First, if a time series follows an I(d) process, then each subsample of the time series also follows an I(d) process with the same value of d. Second, if a time series follows an I(d)...

This paper develops a new test of orthogonality based on a zero restriction on the covariance between the dependent variable and the predictor. The test provides a useful alternative to regression-based tests when conditioning variables have roots close or equal to unity. In this case standard...

This paper provides tables of critical values for some popular tests of cointegration and unit roots. Although these tables are necessarily based on computer simulations, they are much more accurate than those previously available. The results of the simulation experiments are summarized by...

We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of...

Many test statistics in econometrics have asymptotic distributions that cannot be evaluated analytically. In order to conduct asymptotic inference, it is therefore necessary to resort to simulation. Techniques that have commonly been used yield only a small number of critical values, which can...

In an important generalization of zero frequency autoregressive unit root tests, Hylleberg, Engle, Granger, and Yoo (1990) developed regression-based tests for unit roots at the seasonal frequencies in quarterly time series. We develop likelihood ratio tests for seasonal unit roots and show that...