Adaptive Estimation in ARCH Models

Adaptive Estimation in Arch Models

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly ident...

Adaptive density estimation for general ARCH models

Pseudo-maximum Likelihood Estimation of Arch(∞) Models

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH(∞) processes are established. The conditions are shown to hold in case of exponential and hyperbolic decay in the ARCH weights, though in the latter case a faster decay rate is required for the central limit theorem than for the law of large numbers. Particula...

Normalised Least - Squares Estimation in Time - Varying Arch Models

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since the parameters are changing over time, a successful estimator needs to perform well for small samples....

Bayesian Estimation of Change-Point in Unobserved-ARCH Models

Change-point problem deals with sudden change in the distribution of a set of given data. Change in financial time series is a common event, because many factors for example some news, etc. may affect the series and cause change. In this work, we intend to detect the time of change-point, using Bayesian methods in Unobserved-ARCH models. We estimate the model and the time of the change-point.