Timo Teräsvirta

In this paper, we propose two parametric alternatives to the standard GARCH model. They allow the conditional variance to have a smooth time-varying structure of either additive or multiplicative type. The suggested parameterizations describe both nonlinearity and structural change in the conditional and unconditional variances where the transition between regimes over time is smooth. A modelling strategy for these new time-varying parameter GARCH models is developed. It relies on a sequence of Lagrange multiplier tests, and the adequacy of the estimated models is investigated by Lagrange multiplier type misspecification tests. Finite-sample properties of these procedures and tests are examined by simulation. An empirical application to daily stock returns and another one to daily exchange rate returns illustrate the functioning and properties of our modelling strategy in practice. The results show that the long memory type behaviour of the sample autocorrelation functions of the absolute returns can also be explained by deterministic changes in the unconditional variance.

In this paper we introduce a flexible target zone model that is capable of characterizing the dynamic behaviour of an exchange rate implied by the original target zone model of Krugman (1991) and its modifications. Our framework also enables the modeller to estimate an implicit target zone if it exists. A modelling cycle consisting of specification, estimation, and evaluation stages is constructed. The model is fitted to series of daily observations of the Swedish and the Norwegian currency indices and the estimated models are evaluated.

This paper is concerned with modelling time series by single hidden layer feedforward neural network models. A coherent modelling strategy based on statistical inference is presented. Variable selection is carried out using existing techniques. The problem of selecting the number of hidden units is solved by sequentially applying Lagrange multiplier type tests, with the aim of avoiding the estimation of unidentified models. Misspecification tests are derived for evaluating an estimated neural network model. A small-sample simulation experiment is carried out to show how the proposed modelling strategy works and how the misspecification tests behave in small samples. Two applications to real time series, one univariate and the other multivariate, are considered as well. Sets of one-step-ahead forecasts are constructed and forecast accuracy is compared with that of other nonlinear models applied to the same series.

The paper is concerned with testing super exogeneity in a single equation that can either be linear or partially nonlinear. A joint test for testing both weak exogeneity and a form of invariance, which together amount to super exogeneity, is presented and its properties discussed. The considerations also include testing parameter constancy and modelling parameter nonconstancy prior to testing super exogeneity. The practical application of the tests is demonstrated by an example in which testing super exogeneity in a previously published consumption function for Norway is considered. The results are compared with the previous conclusions and found not to disagree with them.

Starting from a linear error correction model the stability and linearity of a German M1 money demand function are investigated, applying smooth transition regression techniques. Using seasonally unadjusted data from 1961 (1) to 1990 (2) it is found that the money demand equation is both linear and stable. After extending the sampling period until 1994 (2) a clear structural instability due to the monetary unification 1 July 1990 is found and subsequently modelled.

Smooth transition autoregressive models are a flexible family of nonlinear time series models that have also been used for modelling economic data. This paper contributes to the evaluation stage of a proposed specification, estimation, and evaluation cycle of this models by introducing a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM type tests for the hypothesis of remaining nonlinearity and that of parameter constancy. Small sample properties of the F versions of the tests and some alternative tests are investigated by simulation. The results indicate that the proposed tests can be applied in small samples already.

This paper considers testing parameter constancy in linear models when the alternative is that a subset of the parameters follow a stationary vector autoregressive process of known finite order. This kind of a linear model is only identified under the alternative, which usually precludes finding a test statistic with an analytic null distribution. In the present situation, however, it is still possible to derive a test statistic with an asymptotic chi-squared distribution under the null hypothesis and this is done in the paper. The small-sample properties of the test statistic are investigated by simulation and found satisfactory. The test retains its power when the alternative to parameter constancy is a random walk parameter process.