Nonparametric Autoregression with Multiplicative Volatility and Additive mean

Nonparametric Autoregression with Multiplicative Volatility and Additive Mean

For over a decade nonparametric modelling has been successfully applied to study nonlinear structures in nancial time series It is well known that the usual nonpara metric models often have less than satisfactory performance when dealing with more than one lag When the mean has an additive structure however better estimation methods are available which fully exploit such a structure Although in...

Diusion approximation for nonparametric autoregression

A nonparametric statistical model of small di€usion type is compared with its discretization by a stochastic Euler di€erence scheme. It is shown that the discrete and continuous models are asymptotically equivalent in the sense of Le Cam's de®ciency distance for statistical experiments, when the discretization step decreases with the noise intensity . Mathematics Subject Classi®cation (1991): P...

Additive-multiplicative stochastic models of financial mean-reverting processes.

We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of vol...

Aggregation, Heterogeneous Autoregression and Volatility of

Asymptotic Equivalence of Nonparametric Autoregression and Nonparametric Regression

where (εi)i=1,...,n are i.i.d. random variables. The unknown autoregression function f is then the target of statistical inference and the development of efficient estimators is a natural task for theoretically oriented statisticians. On the one hand, it has been recognized for a long time that commonly used estimators in model (1) have the same asymptotic behavior as corresponding estimators i...