Unit root tests are considered for time series with innovational outliers. The function representing the outliers can have a very general nonlinear form and additional deterministic mean and trend terms are allowed for. Prior to the tests the deterministic parts and other nuisance parameters of...

In this paper we study new nonlinear GARCH models mainly designed for time series with highly persistent volatility. For such series, conventional GARCH models have often proved unsatisfactory because they tend to exaggerate volatility persistence and exhibit poor forecasting ability. Our main...

The use of asymptotic critical values in stationarity tests against the alternative of a unit rot process is known to lead to overrejections in finite samples when the considered process is stationary but highly persistent. We claim that in recent parametric tests this is caused by estimation...

A new kind of mixture autoregressive model with GARCH errors is introduced and applied to the U.S. short-term interest rate. According to the diagnostic tests developed in the paper and further informal checks the model is capable of capturing both of the typical characteristics of the...

Two types of unit root tests which accommodate a structural level shift at a known point in time are extended to the situation where the break date is unknown. It is shown that for any estimator for the break date the tests have the same asymptotic distribution as the corresponding tests under...

A number of unit root tests which accommodate a deterministic level shift at a known point in time are compared in a Monte Carlo study. The tests differ in the way they treat the deterministic term of the DGP. It turns out that Phillips-Perron type tests have very poor small sample properties...

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius and others we also consider an alternative class of tests which is based on estimating the trend parameters of the...

Tests for the cointegrating rank of a vector autoregressive process are considered which allow for possible exogenous shifts in the mean of the data generation process. The break points are assumed to be known a priori. It is proposed to estimate and remove the deterministic terms such as mean,...

Likelihood ratio (LR) tests for the cointegrating rank of a vector autoregressive (VAR) process have been developed under different assumptions regarding deterministic terms. For instance, nonzero mean terms and linear trends have been accounted for in some of the tests. In this paper we provide...