ABSTRACT
In the statistical analysis of time series, measurements of a phenomenon with uncertainty are considered to be the realization of a random variable that follows a certain probability distribution. Time series models and statistical models, in general, are built to specify this probability distribution based on data. This chapter introduces a basic criterion for evaluating the closeness between the true probability distribution and the probability distribution specified by a model. It derives a unified approach for building statistical models including the maximum likelihood method and the information criterion. Though the K-L information was introduced as a criterion for the goodness of fit of a statistical model in the previous section, it is rarely used directly to evaluate an actual statistical model except for the case of a Monte Carlo experiment for which the true distribution is known.
