Statistical inference for stochastic coefficient regression models

The classical multiple regression model plays a very important role in statistical analysis. The typical assumption is that changes in the response variable, due to a small change in a given regressor, is constant over time. In other words, the rate of change is not influenced by any unforeseen external variables and remains the same over the entire time period of observation. This strong assumption may, sometimes, be unrealistic, for example, in areas like social sciences, environmental sciences etc. In view of this, we propose stochastic coefficient regression (SCR) models with stationary, correlated random errors and consider their statistical inference. We assume that the coefficients are stationary processes, where each admits a linear process representation. We propose a frequency domain method of estimation, the advantage of this method is that no assumptions on the distribution of the coefficients are necessary. We illustrate the methodology with simulations and compare their performance. These models are fitted to two real data sets and their predictive performance are also examined.