Parameter Estimation Based on Prediction
In this chapter, we discuss the parameter estimation problem for stationary time series. The method of maximum likelihood is usually not tractable since the joint distribution of the time series does not have analytical expression even if the model is identified. Instead, an alternative method is to estimate the parameters of the time series model by minimizing contrast function. We introduce a new class of contrast functions for parameter estimation from the prediction problem, which is quite different from other existing literature. Under both settings for a stationary process with finite and infinite variance innovations, we investigate asymptotic properties of such minimum contrast estimators. It is shown that the contrast function corresponding to the prediction error is asymptotically the most efficient in the class. In our simulation, we compare the relative efficiency and robustness against randomly missing observations for different contrast functions among the class.