Unobserved component time series models with Arch disturbances

Abstract

This paper considers how ARCH effects may be handled in time series models formulated in terms of unobserved components. A general model is formulated, but this includes as special cases a random walk plus noise model with both disturbances subject to ARCH effects, an ARCH-M model with a time-varying parameter, and a latent factor model with ARCH effects in the factors. Although the model is not conditionally Gaussian, an approximate filter can be obtained and used as the basis for estimation. The performance of this method is examined on real data sets and Monte Carlo experiments are carried out. The method is extended to handle GARCH and a latent factor model based on the I-distribution.

Likelihood-Based Estimation of Latent Generalized ARCH Structures

“…Both Chou, Engle, and Kane (1992) and Harvey, Ruiz, and Sentana (1992) proposed approximate maximum likelihood estimators to this problem, but the quality of their approximations remains unknown.…”

Gram–Charlier densities: a multivariate approach

“…On the other hand, di¤erent multivariate distributions have been introduced in …nancial econometrics, from which parametric approaches include: Student's t (Harvey et al, 1992), mixtures of Normals (Vlaar and Palm, 1993), skewed Normal (Azzalini and Dalla Valle, 1996), skewed Student's t (Sahu et al (2003) and ), Edgeworth-Sargan (Perote, 2004), Weibull (Malevergne and Sornette, 2004), Kotz-type (Olcay, 2005) and Normal Inverse Gaussian (Aas et al, 2006). Alternatively, any true target distribution can be approximated (…tted) through an in…nite (…nite) Gram-Charlier (GC hereafter) or Edgeworth series in terms of its moments or cumulants (see Sargan (1975Sargan ( , 1976 for the …rst applications of these techniques to econometrics).…”

Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

“…Harvey et al [164] presented the unobserved components structural ARCH, or STARCH, model and proposed an estimation method based on the Kalman filter. These are state space models or factor models in which the innovation is composed of several sources of error where each of the error sources has a heteroscedastic specification of the ARCH form.…”

“…Engle et al [122] and Ng et al [250] applied factor GARCH models on treasury bills and stock returns. Diebold and Nerlove [95], Harvey et al [164], King et al [182] and Alexander [4] proposed latent factor GARCH models, based on the assumption that only a few factors influence the conditional variances and covariances of asset returns, which are not functions of the information set.…”