|
on Econometric Time Series |
| By: | Marc K. Francke (Vrije Universiteit Amsterdam); Siem Jan Koopman (Vrije Universiteit Amsterdam); Aart de Vos (Vrije Universiteit Amsterdam) |
| Abstract: | State space models with nonstationary processes and fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for the estimation of parameters in time series models with diffuse initial conditions. In this paper we consider profile, diffuse and marginal likelihood functions. The marginal likelihood is defined as the likelihood function of a transformation of the data vector. The transformation is not unique. The diffuse likelihood is a marginal likelihood for a specific data transformation that may depend on parameters. Therefore, the diffuse likelihood can not be used generally for parameter estimation. Our newly proposed marginal likelihood function is based on an orthonormal transformation that does not depend on parameters. Likelihood functions for state space models are evaluated using the Kalman filter. The diffuse Kalman filter is specifically designed for computing the diffuse likelihood function. We show that a modification of the diffuse Kalman filter is needed for the evaluation of our proposed marginal likelihood function. Diffuse and marginal likelihood functions have better small sample properties compared to the profile likelihood function for the estimation of parameters in linear time series models. The results in our paper confirm the earlier findings and show that the diffuse likelihood function is not appropriate for a range of state space model specifications. |
| Keywords: | Diffuse likelihood; Kalman filter; Marginal likelihood; Multivariate time series models; Profile likelihood |
| JEL: | C13 C22 C32 |
| Date: | 2008–04–14 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20080040&r=ets |
| By: | Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In this paper we deal with the problem of non-stationarity encountered in a lot of data sets, mainly in financial and economics domains, coming from the presence of multiple seasonnalities, jumps, volatility, distorsion, aggregation, etc. Existence of non-stationarity involves spurious behaviors in estimated statistics as soon as we work with finite samples. We illustrate this fact using Markov switching processes, Stopbreak models and SETAR processes. Thus, working with a theoretical framework based on the existence of an invariant measure for a whole sample is not satisfactory. Empirically alternative strategies have been developed introducing dynamics inside modelling mainly through the parameter with the use of rolling windows. A specific framework has not yet been proposed to study such non-invariant data sets. The question is difficult. Here, we address a discussion on this topic proposing the concept of meta-distribution which can be used to improve risk management strategies or forecasts. |
| Keywords: | Non-stationarity, switching processes, SETAR processes, jumps, forecast, risk management, copula, probability distribution function. |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00270708_v1&r=ets |
| By: | Abdou Kâ Diongue (UFR SAT - Université Gaston Berger - Université Gaston Berger de Saint-Louis); Dominique Guegan (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, Ecole d'économie de Paris - Paris School of Economics - Université Panthéon-Sorbonne - Paris I); Rodney C. Wolff (School of Mathematical Sciences - Queensland University of Technology) |
| Abstract: | In this paper, we discuss the class of Bilinear GATRCH (BL-GARCH) models which are capable of capturing simultaneously two key properties of non-linear time series : volatility clustering and leverage effects. It has been observed often that the marginal distributions of such time series have heavy tails ; thus we examine the BL-GARCH model in a general setting under some non-Normal distributions. We investigate some probabilistic properties of this model and we propose and implement a maximum likelihood estimation (MLE) methodology. To evaluate the small-sample performance of this method for the various models, a Monte Carlo study is conducted. Finally, within-sample estimation properties are studied using S&P 500 daily returns, when the features of interest manifest as volatility clustering and leverage effects. |
| Keywords: | BL-GARCH process, elliptical distribution, leverage effects, Maximum Likelihood, Monte Carlo method, volatility clustering. |
| Date: | 2008–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00270719_v1&r=ets |