In this paper, we introduce several test statistics testing the null hypothesis of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure and the trend. We derive analytical limiting distributions for all the tests. The...

Building on work of Hansen (1992, <italic>Econometric Theory</italic> 8, 489–501), we show weak convergence for power transformations of integrated processes, with possibly serially correlated and heterogeneously distributed increments, to stochastic power integrals. The theory is applicable when testing the...

This work develops likelihood-based unit root tests in the noncausal autoregressive (NCAR) model formulated by Lanne and Saikkonen (2011, Journal of Time Series Econometrics 3, Iss. 3, Article 2). The possible unit root is assumed to appear in the causal autoregressive polynomial and for reasons...

In this paper, we derive asymptotic distributions for linearity tests in time-varying smooth transition autoregressive models in the presence of a unit root. The limiting distributions are non-standard because of the unit root assumption, and it is shown that the linearity hypothesis is rejected...

The asymmetric power ARCH model is a recent addition to time series models that may be used for predicting volatility. Its performance is compared with that of standard models of conditional heteroskedasticity such as GARCH. This has previously been done empirically. In this paper the same issue...

In this paper we consider the third-moment structure of a class of nonlinear time series models. Empirically it is often found that the marginal distribution of financial time series is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate...

This paper studies a special class of vector smooth-transition autoregressive (VS- TAR) models containing common nonlinear features (CNFs). To test the existence of CNFs in a VSTAR model, a triangular representation for such a system containing CNFs is proposed. A procedure of testing CNFs in a...