Modeling Concepts and Methods

In this chapter the ideas that we identify as the basis of our approach to time series analysis are outlined. Several topics in parameter estimation and model selection are treated. Akaike’s AIC for parametric model selection is treated first. That treatment includes a discussion of the Kullback-Leibler information, and a theoretical development of the AIC. Also included are treatments of the Householder transformation based least squares estimation, the maximum likelihood method of parameter estimation, (including a method of minimizing a function of several variables), a fairly general discussion of state space modeling including Kalman filter for standard linear Gaussian state space modeling, and general state space modeling.