Rickard Sandberg

Dickey–Fuller Type of Tests against Nonlinear Dynamic Models*

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 power performance of the tests is compared with that of the unit-root tests by Phillips and Perron [Biometrika (1988), Vol. 75, pp. 335–346], and Leybourne, Newbold and Vougas [Journal of Time Series Analysis (1998), Vol. 19, pp. 83–97]. In the presence of a gradual change in the deterministics and in the dynamics, our tests are superior in terms of power.

Convergence To Stochastic Power Integrals For Dependent Heterogeneous Processes

Building on work of Hansen (1992, Econometric Theory 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 unit root or cointegration hypothesis in nonlinear systems by regression-based test statistics.

Testing for a Unit Root in Noncausal Autoregressive Models

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 of identification the error term of the model is supposed to be non-Gaussian. In order to derive the tests, asymptotic properties of the maximum likelihood estimators are established under the unit root hypothesis. The limiting distributions of the proposed tests depend on a nuisance parameter determined by the distribution of the error term of the model. A simple procedure to handle this nuisance parameter dependence in applications is proposed. Finite sample properties of the tests are examined by means of Monte Carlo simulations. The results show that the size properties of the tests are satisfactory and the power against stationary NCAR alternatives is significantly higher than the power of conventional Dickey-Fuller tests and the M-tests of Lucas (1995, Econometric Theory 11, 331-346). In an empirical application to a Finnish interest rate series evidence in favour of a stationary NCAR model with leptokurtic errors is found.

Testing Parameter Constancy in Unit Root Autoregressive Models Against Multiple Continuous Structural Changes

This article considers tests for logistic smooth transition autoregressive (LSTAR) models accommodating multiple time dependent transitions between regimes when the data generating process is a random walk. The asymptotic null distributions of the tests, in contrast to the standard results in Lin and Teräsvirta (1994), are nonstandard. Monte Carlo experiments reveal that the tests have modest size distortions and satisfactory power against LSTAR models with multiple smooth breaks. The tests are applied to Swedish unemployment rates and the hysteresis hypothesis is over-turned in favour of an LSTAR model with two transitions between extreme regimes.

Least Absolute Deviation Based Unit Root Tests in Smooth Transition Type of Models

Building on work by Phillips (Econ. Theory 7:450–463, 1991), we derive LAD based unit root tests in a first-order ESTAR model with strong mixing innovations. Further theoretical results are derived and LAD based unit root tests in general nonlinear first-order dynamic models admitting a Taylor-series approximation are thereby easily obtained.

Unit Root Testing in Multiple Smooth Break Models with Nonlinear Dynamics: UNIT ROOT TESTING IN MULTIPLE SMOOTH BREAK MODELS

This work builds a flexible model accommodating nonlinear dynamics around a trend function with multiple (up to m) gradual shifts. Such a model is suitable for capturing the behavior of many post World War II economic time‐series subject to the onset of external causes such as oil crises, financial crises, technology changes and regulatory changes. Deriving unit root tests in this nonlinear model is of particular interest. In fact, the options of a general trend specification and nonlinear dynamics are critical to remedy unit root tests not being biased toward a non‐rejection of a unit root hypothesis and prevents the first‐differences of a series from being used too often. An asymptotic theory for the unit root tests is also established. The unit root tests are applied to G7 industrial production series, and evidence in favor of nonlinear trend ‘stationary’ models is found in a majority of the cases. The merits of the new model are further demonstrated in an estimation exercise for the US industrial production series, and evidence of four gradual shifts in the trend, different growth patterns for different periods, and business cycle asymmetries is found.

Sample Moments and Weak Convergence to Multivariate Stochastic Power Integrals

This work considers sample moments arising from least squares, least absolute deviation, and extremum estimators of linear and nonlinear multivariate systems with I(1) regressors. The sample moments are shown to converge weakly to multivariate stochastic power integrals, and these results can be considered as a multivariate generalization of the univariate results reported earlier.