LOCAL ASYMPTOTIC NORMALITY OF GENERAL CONDITIONALLY HETEROSKEDASTIC AND SCORE-DRIVEN TIME-SERIES MODELS

The paper establishes the local asymptotic normality property for general conditionally heteroskedastic time series models of multiplicative form, ϵ_t = σ_t(θ₀)η_t, where the volatility σ_t(θ₀) is a parametric function of {ϵ_s,s < t}, and (η_t) is a sequence of i.i.d. random variables with common density fθ₀. In contrast with earlier results, the finite dimensional parameter θ₀ enters in both the volatility and the density specifications. To deal with nondifferentiable functions, we introduce a conditional notion of the familiar quadratic mean differentiability condition which takes into account parameter variation in both the volatility and the errors density. Our results are illustrated on two particular models: the APARCH with asymmetric Student-t distribution, and the Beta-t-GARCH model, and are extended to handle a conditional mean.