Prediction-Based Estimating Functions  

Oleh:

Sorensen, Michael

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: The Econometrics Journal vol. 3 no. 2 (2000), page 123-147.
Topik: Asymptotic normality; Consistency; Diffusion processes; Discrete time observation of continuous time models; Linear predictors; Martingale estimating functions; Mixing; Optimal estimating functions; Stochastic differential equation; Stochastic volatility model; Stock prices; Sum of Ornstein–Uhlenbeck-type processes; Quasi-likelihood.
Fulltext: 123.pdf (561.73KB)

Isi artikel

A generalization of martingale estimating functions is presented which is useful when there are no natural or easily calculated martingales that can be used to construct a class of martingale estimating functions. An estimating function of the new type, which is based on linear predictors, is called a prediction-based estimating functions. Special attention is given to classes of prediction-based estimating functions given by a finite-dimensional space of predictors. It is demonstrated that such a class of estimating functions has most of the attractive properties of martingale estimating functions. In particular, a simple expression is found for the optimal estimating function. This type of prediction-based estimating functions only involve unconditional moments, in contrast to the martingale estimating functions where conditional moments are required. Thus, for applications to discretely observed continuous time models, a considerably smaller amount of simulation is, in general, needed for these than for martingale estimating functions. This is also true of the optimal prediction-based estimating functions. Conditions are given that ensure the existence, consistency and asymptotic normality of the corresponding estimators. The new method is applied to inference for sums of Ornstein– Uhlenbeck-type processes and stochastic volatility models. Stochastic volatility models are studied in considerable detail. It is demonstrated that for inference about models by Hull and White and Chesney and Scott, an explicit optimal prediction-based estimating function can be found so that no simulations are needed.

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