Adaptive Forecasting with Orthogonal Polynomial Models

Abstract

The analysis of time series data can be significantly eased by the use of orthogonal polynomials. This technique is based on traditional regression analysis, but the necessity for solving the associated normal equations is eliminated. Also, the orthogonal polynomial technique includes a means to statistically test the level of fit of the independent terms in a forecast model (e.g., constant, linear, or quadratic). This paper shows the application of orthogonal polynomial technique to the analysis of time series data, but more importantly develops a mathematical means for updating the forecast model from one period to the next without completely recomputing the model from stored historical data. This result considerably improves the ease of application of the orthogonal polynomial technique and increases the value of the technique in practice.