Information recovery in a dynamic statistical Markov model - Douglas J. Miller; George Judge (Econometrics, 2015)
Although economic processes and systems are in general simple in nature, the underlying dynamics are complicated and seldom understood. Recognizing this, in this paper we use a nonstationary-conditional Markov process model of observed aggregate data to learn about and recover causal influence information associated with the underlying dynamic micro-behavior. Estimating equations are used as a link to the data and to model the dynamic conditional Markov process. To recover the unknown transition probabilities, we use an information theoretic approach to model the data and derive a new class of conditional Markov models. A quadratic loss function is used as a basis for selecting the optimal member from the family of possible likelihood-entropy functional(s). The asymptotic properties of the resulting estimators are demonstrated, and a range of potential applications is discussed.
Keywords: C40; C51; 330; conditional moment equations; controlled stochastic process; first-order Markov process; Cressie-Read power divergence criterion; quadratic loss; adaptive behavior