Statistical inference for time-varying ARCH processes

Abstract

In this paper the class of ARCH$(\infty )$ models is generalized to the nonstationary class of ARCH$(\infty )$ models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation ``locally stationary ARCH$(\infty )$ process.'' The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH$(p)$ processes ($p<\infty$) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.

Published at http://dx.doi.org/10.1214/009053606000000227 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (24)

• Nonparametric regression for locally stationary time series
• Multiscale local change point detection with applications to value-at-risk
• Locally Stationary Functional Time Series
• Normalized least-squares estimation in time-varying ARCH models
• Mixing properties of ARCH and time-varying ARCH processes
• Detecting gradual changes in locally stationary processes
• A recursive online algorithm for the estimation of time-varying ARCH parameters
• A test for stationarity based on empirical processes
• UD-based pairwise and MIMO Kalman-like filtering for estimation of econometric model structures
• Multiscale Jump Testing and Estimation Under Complex Temporal Dynamics
• Analyzing initial stage of COVID-19 transmission through Bayesian time-varying model
• Contrast estimation of general locally stationary processes using coupling
• Quantile Spectral Analysis for Locally Stationary Time Series
• Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model
• Parameter stability and semiparametric inference in time-varying ARCH models
• On the estimation of locally stationary functional time series
• Testing instantaneous causality in presence of non constant unconditional variance
• Statistical inference for continuous-time locally stationary processes using stationary approximations
• Smooth Online Parameter Estimation for time varying VAR models with application to rat's LFP data
• A Class of Time-Varying Vector Moving Average Models: Nonparametric Kernel Estimation and Application
• Dynamic detection of anomalous regions within distributed acoustic sensing data streams using locally stationary wavelet time series
• Locally stationary long memory estimation
• Lag length identification for VAR models with non-constant variance
• Estimation and Model Identification of Locally Stationary Varying-Coefficient Additive Models