F. Javier Trívez

Unit Roots and Deterministic Trends in Spatial Econometric Models

This article reflects on the relevance of the concept of unit roots in the spatial context. The initial introduction of this topic in the time-series literature caused significant changes in the mainstream econometric methodology. However, the literature specialized in spatial econometric modeling has not extensively dealt with this issue. The current article continues the discussion of the concept of unit roots employed in a spatial context and presents a series of peculiarities that should be noticed. Subsequently, attention focuses on the topic of deterministic trends associated with the scale factor that intervenes in autoregressive spatial processes. The incidence of this type of trend should not be neglected. It induces the risk of finding spurious correlation that should be taken into account.

Forecasting volatility in GARCH models with additive outliers

One of the main concerns of the financial analyst is to obtain an adequate forecast of volatility, given that this is perceived as an explicit measurement of risk. Ever since the seminal work of Engle (1982), the literature has reflected numerous specifications to forecast such volatility (see, in this regard, the recent paper of McAleer (2005)). However, from amongst these specifications, it is undoubtedly the GARCH models proposed by Bollerslev (1986) that have been the most widely employed.y By contrast, only limited attention has been paid to the influence that outliers can have on the forecasting of these GARCH models, even though it is well known that they can markedly distort the analysis of time series. More specifically, their effects are threefold: firstly, they can significantly alter the simple and partial autocorrelation functions used to identify ARCH models (see Burnd and Ord 1984, Tsay 1986, Balke 1993, Chan 1995); secondly, they have a negative effect on the size and power of the Lagrange multipliers (LM) test used to detect the presence of ARCH effects in a time series, leading to important specification errors (Franses et al. 1998, Franses and van Dijk 1997, van Dijk et al. 1999); thirdly, they give rise to an important bias in the estimations of the parameters of the said models (Friedman and Laibson 1989, Lamoureux and Lastrapes 1990, Hotta and Tsay 1998, Sakata and White 1998, Franses and Ghijsels 1999, Franses and van Dijk 1999, Gregory and Reeves 2001, Chan and McAleer 2003). Whilst a number of studies, such as those of Franses and van Dijk (1999), Franses and Ghijsels (1999) or Park (2002), have considered the effects of outliers on the forecasting of these models,z none of them have dealt rigorously with the effects that the different types of outliers (level outliers and volatility outliers) have on the forecasting of volatility, understood in terms of GARCH models as heteroscedastic variance. Against this background, it is the aim of this note to analyse such effects, concentrating on the GARCH model. More specifically, we seek to quantify the effect of two types of additive outliers, namely additive level outliers (hereafter ALO) and additive volatility outliers (hereafter AVO) on the forecasting of the conditional variance of the GARCH(1,1) model. To that end, in section 2 we begin by defining these two types of outliers in the context of the model in question. In section 3, and starting from the ideal, although somewhat unreal, assumption that the parameters of the model, the period in which the outliers take place and their type are all

The impact of spatial elements on the forecasting of Spanish labour series

In this paper, we analyse the ability of a dynamic spatial panel data model without explanatory variables to explain a variable of interest, in this case employment in the fifty Spanish provinces. The best model is a dynamic fixed effect with a spatial lag structure in an equation estimated through the unconditional ML procedure. Predictions derived from this selected model are compared with those derived from fifty seasonal ARIMA models that also treat outlier observations. The results indicate that forecasts derived from a single estimated spatial panel data model are as accurate as those derived from the estimation of fifty seasonal ARIMA models. This shows that spatial panel data models play an important role in forecasting.

Detecting level shifts in ARMA-GARCH (1,1) Models

The purpose of this article is to present a new method to detect level shifts in the context of conditional heteroscedastic models. First, we define precisely what type of outlier we are referring to, a concept that has been scarcely touched in the field of GARCH (1,1) models, and then we go on to present our methodology based on the nature of the Lagrange multiplier tests. The validity and efficiency of the proposed procedure are demonstrated through different simulation experiments. To conclude, we present a practical application of the method to the time series of returns of US short-term interest rates.

Analyzing the effects of level shifts and temporary changes on the identification of ARIMA models

The presence of outliers in time series gives rise to important effects on the sample autocorrelation coefficients. In the case where these outliers are not adequately treated, their presence causes errors in the identification of the stochastic process generator of the time series under study. In this respect, Chan has demonstrated that, independent of the underlying process of the outlier-free series, a level shift (LS) at the limit (i.e. asymptotically and considering an LS of a sufficiently large size) will lead to the identification of non-stationary processes; with respect to a temporary change (TC), this will lead, again at the limit, to the identification of an AR(1) autoregressive process with a coefficient equal to the dampening factor that defines this TC. The objective of this paper is to analyze, by way of a simulation exercise, how large the LS and TC present in the time series must be for the limiting result to be relevant, in the sense of seriously affecting the instruments used at the identification stage of the ARIMA models, i.e. the sample autocorrelation function and the sample partial autocorrelation function.

Specification error caused by level shifts and temporary changes in ARMA–GARCH models

The aim of this article is to analyse the effect of the level shifts and temporary changes on the specification of a model with conditional heteroscedasticity, a concept very little dealt with up to now, the literature focusing more on additive outliers. To do this, we have conducted various Monte Carlo experiments in which the effect of these outliers on the principal model identification tools (descriptive statistics, graphs and heteroscedasticity tests) is analysed.

DYNAMIC MODELING OF INTERREGIONAL ECONOMIC ACTIVITY: AN APPLICATION TO THE SPANISH LABOUR MARKET

This paper focuses on the dynamic relations between Spains principal regional labor markets. An economic base mechanism, some of whose assumptions are redefined, is postulated as the essential behavior hypothesis. The bifurcation hypothesis is resolved having regard to the necessary condition of cointegration between the basic sector and the regional aggregate, using series with quarterly periodicity in this case. The identified bases, which need not coincide in each region, allow a dynamic inter-regional model to be built using vector autoregression with an error correction mechanism. The results are a step towards the spatial disaggregation of Spains labor market and reveal singular dynamic relationships.

Effects of level shifts and temporary changes on the estimation of GARCH models

The aim of this article is to analyse the effect of the level shift and temporary change outliers on the estimation of a model with conditional heteroscedasticity, a concept rarely dealt with up to now, the literature focusing more on additive outliers. To do this, we have conducted various Monte Carlo experiments in which the bias produced by these outliers is analysed.