Pilar Olave

Bootstrapping forecast intervals in ARCH models

In this paper we develop a bootstrap method for the construction of prediction intervals for an ARMA model when its innovations are an autoregressive conditional heteroscedastic process. We give a proof of the validity of the proposed bootstrap for this process. For this purpose we prove the convergence to zero in probability of the Mallows metric between the empirical distribution function and the theoretical distribution function of the residuals. The potential of the proposed method is assessed through a simulation study.

Adjusting Forecast Intervals in Arch-M Models

In this paper, we extend predictor expressions from an ARMA model with GARCH(1,1) innovations that allow for the conditional variance to be a regressor variable. We also obtain all the theoretical moments of the multi-step prediction error distribution from this model. The forecast error has a distribution that depends nontrivially on the information set and, therefore, the classical forecast intervals do not work well. To improve those forecast intervals, we suggest adjusting the quantile of the conditional distribution for the s-step-ahead forecast error by means of the Cornish-Fisher asymptotic expansion.

The efficacy of university training programmes: a semi-parametric Bayesian approach

A semi-parametric Bayesian methodology based on Coxs proportional hazards model is proposed in order to evaluate the efficacy of training programmes offered by the University of Zaragoza (Spain) in the labour market insertion process. To this end, a matched comparison group has been designed in which university students completing vocational training courses are compared with eligible non-participants especially chosen for their similarity to the former group in terms of the factors affecting future employment prospects. The study shows that training courses were generally effective for job market insertion of university leavers, increasing their chances of avoiding unemployment by around 6.56% for a standard course. Effectiveness depends, however, on the university leavers professional career choice.

Evaluating value at risk using selection criteria of the model and the information set

This article proposes a new methodology to estimate the Value at Risk (VaR) in a time varying heteroscedastic dynamic regression context. The methodology assumes that the form of the model and its information set may also change over time and takes into account the uncertainty associated with the joint selection of model and information set, providing more reliability to the elaborated forecasts. A Bayesian framework is adopted and a cross validation selection criterion, asymptotically equivalent to the Bayes factor, is proposed. Finally, we estimate the VaR on line of five international equity indexes. Our VaR estimations tend to follow the evolution of the series more closely than classical procedures by keeping the coverage properties.

Studying the relationship between unemployment periods in Spain: a nonparametric approach

The effect of successive periods of unemployment according to household type has not been analysed in any depth with respect to the Spanish labour market. In this article, we propose a nonparametric methodology based on a data-driven likelihood ratio function to describe the dependence between the duration of successive periods of unemployment according to different household typologies. This study, which uses a very large data set, specifically, the Spanish sample of the European Community Household Panel (ECHP), first reveals a weak dependence between the consecutive unemployment durations in the case of the most frequent household typology. In addition, we find that the first months of the previous spells of unemployment have a significant impact on subsequent expected unemployment duration.

Semi-parametric Bayesian Analysis of the Proportional Hazard Rate Model An Application to the Effect of Training Programs on Graduate Unemployment

Abstract In this paper, we introduce a semi-parametric Bayesian methodology based on the proportional hazard model that assumes that the baseline hazard function is constant over segments but, by contrast to what is usually assumed in the literature, with the periods at which the function changes not being specified in advance. The methodology is applied to explore the impact of Vocational Training courses offered by the University of Zaragoza (Spain) on the duration of the initial periods of unemployment experienced by graduate leavers. The framework is very flexible and allows us, in particular, to capture the presence of seasonality in the job insertion of graduates.

Joint Selection of the Model and the Information Set in Heteroskedastic Dynamic Models

Abstract The aim of this paper is to propose a number of semiautomatic criteria for the joint selection of the model and the information set in the heteroskedastic context considered in Lejeune [Lejeune, B. (1997). Second order pseudo-maximum likelihood estimation and conditional variance misspecification. University of Liège, ERUDITE and CORE]. Particular cases of this methodology are the posterior information criterion (PIC) and the posterior information criterion for a forecasts (PICF) of Phillips [Phillips, P. C. B. (1996). Econometric model determination. Econometrica 64:763–812] and Phillips and Ploberger [Phillips, P. C. B., Ploberger, W. (1994). Posterior odds testing for a unit root with data-based model selection. Econometric Theory 10:774–808] and the Bayesian information criterion (BIC) criterion of Schwarz [Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6:461–464]. Sufficient conditions for the weak and strong consistencies of the proposed criteria are provided. Furthermore, the behaviors of these criteria are analyzed in the presence of structural changes.

Estimation of the Inter-occurrence Time Between Events from Incomplete Data. Analysis of Periods of Unemployment in Spain

This work analyzes the stochastic variable representing the waiting times between two consecutive events of a stationary renewal process, such as periods of unemployment of different individuals in a specific population. This data has been obtained through cross-sectional sampling: a specific point in time t is chosen, and a random sample of the individuals who are unemployed at the time t is extracted. For each individual we are interested in the unemployment period including t. However, in practice these values are not observable, and the only fact we can ascertain is the time from the inclusion of the individual in the previous unemployment period to the sampling time t. Our data also includes the corresponding values of a certain set of covariates (for example, the time spent on employment training courses or the age of the individual). Using non parametric techniques, an estimation of the conditional mean has been obtained, given the sex and age groups of the individuals. This is a more natural approach than other methods based on the estimation of the hazard rate, thus avoiding pre-established forms for the inclusion of covariates.

AutoRegressive Conditional Heteroscedastic Models

The linear models presented so far in cross-section data and in time series assume a constant variance and covariance function, that is to say, the homoscedasticity is assumed.

Variations in returns/volatility and persistence in variance. An application to the Spanish stock market

A methodology is proposed to select the information set in ARMA-GARCH models in order to forecast the future evolution of an univariate heteroscedastic time series when it is suspected that the DGP is time changing. Using this methodology the stability of the DGP in the Spanish Stock Market is analysed. In this case it is shown that the DGP is time-varying and, in particular, the persistence in variance is over-valued using classical methods. Furthermore, the predictive intervals obtained have better coverage properties, by more adequately reflecting the uncertainty associated to the evolution of the time series being analysed.