Estimation of Time -Varying Linear Regression with Unknown Time -Volatility via Continuous Generalization of the Akaike Information Criterion

The problem of estimating time-varying regression is inevitably concerned with the necessity to choose the appropriate level of model volatility ranging from the full stationarity of instant regression models to their absolute independence of each other. In the stationary case the number of regression coefficients to be estimated equals that of regressors, whereas the absence of any smoothness assumptions augments the dimension of the unknown vector by the factor of the time-series length. The Akaike Information Criterion is a commonly adopted means of adjusting a model to the given data set within a succession of nested parametric model classes, but its crucial restriction is that the classes are rigidly defined by the growing integer-valued dimension of the unknown vector. To make the Kullback information maximization principle underlying the classical AIC applicable to the problem of time-varying regression estimation, we extend it onto a wider class of data models in which the dimension of the parameter is fixed, but the freedom of its values is softly constrained by a family of continuously nested a priori probability distributions. Keywords—Time varying regression, time-volatility of regression coefficients, Akaike Information Criterion (AIC), Kullback information maximization principle.