An Alternative Perspective on Stochastic Coefficient Regression Models
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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 such as social sciences, environmental sciences, etc. To account for variable dependence, the stochastic coefficient regression model was proposed, and there exists several articles that consider statistical inference for this type of model. Most of these methods use the underlying assumption of Gaussianity. In this chapter, we revisit the stochastic coefficient regression model and compare it with some statistical models that have recently been developed. We show that there is an interesting connection between stochastic coefficient regression models and locally stationary time series, which suggests that stochastic coefficient regression models can be fitted to time series whose covariance structure changes slowly over time. We consider methods of testing for randomness of the coefficients and develop parameter estimation methods that require no assumptions on the distribution of the stochastic coefficients, in particular do not require the Gaussianity assumption. Using these methods, we fit the stochastic coefficient regression model to two real data sets and their predictive performances are also examined. 2012 Elsevier B.V.