Problems of Nonnormality and Multicollinearity for Forecasting Methods Based on Least Squares

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Abstract
Many popular forecasting and time-series analysis methods assume that the variable to be forecast can be expressed as a linear function of a set of predictors. The predictors may include variables related in either a correlative or causal fashion to the response variable, lagged values of this variable, or known mathematical functions of time. The method of least squares is used almost exclusively to estimate the parameters in these models. This paper discusses two hazards in the indiscriminant use of least squares; nonnormality of the observations on the variable of interest and multicollinearity among the predictors. Robust estimation methods are suggested as alternatives to least squares for nonnormal data, and a robust version of exponential smoothing is developed. A small Monte Carlo study indicates that the robust procedure can be superior to ordinary exponential smoothing in many situations. The sources and effects of multicollinearity are discussed, and several diagnostic statistics are presented. Methods for dealing with multicollinearity are reviewed, including collecting additional data, variable selection, and biased estimation. An example of ridge regression is included.