Tests for parameter constancy and predictive accuracy in linear model by using student zed residuals

Abstract

Statistical models are fitted for a variety of reasons. One important reason is that of trying to observe relationships between the variables. A second reason for fitting model is to assist in carrying out a prediction; it is used in some selection processes. Thus, after having fitted a regression model from the sample of observations, one may often centers on some specific value of independent variable, and one may required to predict the value of the dependent variable likely to be associated with the specific value of the independent variable. This specific value of independent variable may lie within the range of sample independent values or more frequently, one may concerned with predicting dependent variable for a value of independent variable outside the sample observations. One of the independent criteria for an estimated depression equation is that it should have relevance for data outside the sample data used in the estimation. This criterion is embodied in the notion of parameter constancy that is the parametric vector should apply both outside and within the sample data. Parameter constancy can be examined by using a test of predictive accuracy. This research paper proposes tests for parameter constancy and predictive accuracy with different parameter vectors in the forecast period by using internally studentized residuals.