Smooth transitions, asymmetric adjustment and unit roots

The aim of this paper is to develop a unit root test that takes into account two sources of nonlinearites in data, i.e. asymmetric speed of mean reversion and structural changes. The asymmetric speed of mean reversion is modeled by means of a exponential smooth transition autoregression (ESTAR) function for the autoregressive parameter, whereas structural changes are approximated by a smooth transition in the deterministic components. We find that the proposed test performs well in terms of size and power, in particular when the autoregressive parameter is close to one

Are Fruit and Vegetable Prices Non-linear Stationary? Evidence from Smooth Transition Autoregressive Models

Over the last decade, there has been a growing interest in investigating agricultural commodity prices. We apply two more powerful smooth transition autoregressive models of the non-linear unit-root test - namely, the ESTAR model of Kapetanios et al. [Journal of Econometrics (2003)] and the LSTAR model of Leybourne, et a . [Journal of Time Series Analysis (1998)] - with a view to investigating non-linear stationarity for the retail prices of 8 major kinds of fruit and 18 major kinds of vegetable in Taiwan. The empirical evidence clearly finds that the Kapetanios et al. model provides solid, substantive evidence in favor of a non-linear mean-reverting adjustment for the individual price of 4 kinds of fruit and 5 kinds of vegetable. However, when we employ the Leybourne et al. model, we find that any such similar evidence of non-linear stationarity is considerably weaker. Finally, compared with the traditional linear unit root tests, it is important to note here that, all in all, the non-linear unit root tests do indeed provide much more evidence of the stationarity, albeit to varying degrees. This paper offers some policy implications.Smooth transition autoregressive model; Non-linear stationary; Fruit price; Vegetable price; Taiwan

Dickey-Fuller Type of Tests against Nonlinear Dynamic Models

In this paper we introduce several test statistics of testing the null hypotheses 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 tests. Finite sample properties are examined. The performance of the tests is compared to that of the classical unit root tests by Dickey-Fuller and Phillips and Perron, and is found to be superior in terms of power.Dickey-Fuller test; LSTAR(p); LSTART(p); Nonlinear trends; Parameter constancy; Unit root; Brownian motion;

Is real GDP per capita a stationary process? Smooth transitions, nonlinear trends and unit root testing

The aim of this paper is to provide additional evidence about the order of integration of constant price GDP per capita in a selection of countries. It does so by taking into account the possibility of non-linear deterministic trends and of asymmetric adjustment towards equilibrium. We find evidence of a global stationary ESTAR process around a nonlinear deterministic trend in almost half of the selected countries. These results show that nonlinearities affect real GDP series. By neglecting them, one can draw misleading conclusions from unit root tests. Specifically, the paper questions the so-called stylised fact of a near unit root which has so influenced macroeconomic thought over the past two decades.Real GDP per capita, Unit root tests, Persistence, Nonlinearities, Smooth transitions

Modelling autoregressive processes with a shifting mean

This paper contains a nonlinear, nonstationary autoregressive model whose intercept changes deterministically over time. The intercept is a flexible function of time, and its construction bears some resemblance to neural network models. A modelling technique, modified from one for single hidden-layer neural network models, is developed for specification and estimation of the model. Its performance is investigated by simulation and further illustrated by two applications to macroeconomic time series.deterministic shift, nonlinear autoregression, nonstationarity, nonlinear trend, structural change Classification JEL: C22; C52.

Nonlinear trend stationarity of real exchange rates: the case of the Mediterranean countries

The aim of this article is to provide additional evidence on the fulfilment of the Purchasing Power Parity hypothesis in the so-called Mediterranean countries. In order to test for the empirical validity of such hypothesis, we have applied two types of unit root tests. The first group is due to Bierens (1997) who generalizes the alternative hypothesis to nonlinear trend stationariry and, the second is the Leybourne, Newbold and Vougas (1998) approach that uses a nonlinear specification for the intercept and slope in order to detrend the series. The results suggest that the evidence in favour of the Purchasing Power Parity hypothesis increases when we allow for nonlinear alternatives

Unit root testing

The occurrence of unit roots in economic time series has far reaching consequences for univariate as well as multivariate econometric modelling. Therefore, unit root tests are nowadays the starting point of most empirical time series studies. The oldest and most widely used test is due to Dickey and Fuller (1979). Reviewing this test and variants thereof we focus on the importance of modelling the deterministic component. In particular, we survey the growing literature on tests accounting for structural shifts. Finally, further applied aspects are addressed how to get the size correct and obtain good power at the same time. --Dickey-Fuller,size and power,deterministic components,structural breaks

Inflation persistence and asymmetries: evidence for African countries

In this paper we aim at testing the inflation persistence hypothesis as well as modelling (using logistic smooth transition autoregressive, LSTAR, models) the long run behaviour of inflation rates in a pool of African countries. In order to do so, we rely on unit root tests applied to nonlinear models, i.e. Kapetanios et al. (2003). The results point to the non-persistence of inflation hypothesis for most of the countries. In addition, the estimated models are stable in the sense that the variable tends to remain in the regime (low inflation or high inflation) once reached and changes between regimes are only achieved after a shock.Inflation, Persistence, Unit Roots, Nonlinearities.

Unemployment and common smooth transition trends in Central and Eastern European Countries

In the present paper we analyse the existence of common nonlinear trends in several of Central and Eastern European Countries in order to gain some insight about the degree of labour market integration within the area. In order to do so, we test for the order of integration of the unemployment rates, by applying the Leybourne et al. (1998) and Kapetanios et al. (2003) nonlinear unit root tests. Our results pinpoint the fact that five up to eight unemployment rates are stationary around a nonlinear trend and, by means of Anderson and Vahid (1998) approach, we also find that there is a common trend that drives the long run behaviour of that variable in these countries.Unemployment, Central and Eastern Europe, unit roots, smooth transition, nonlinearities.