Forecasting with Adaptive Filtering: A Critical Re-examination

Abstract

Adaptive filtering (AF) is a forecasting method based on weighting historical observations. Its distinct feature is that these weights do not follow any prescribed pattern but are obtained by an optimization procedure. In this paper AF is re-examined, with special emphasis on the theoretical foundations of its distinct weight revision formula, on some implicit and explicit assertions and guidelines for applying AF, and on a comparison of AF with exponential smoothing and regression analysis. It is pointed out that the weight adjustment rule was derived for repeated iterations on one observation and the AF use of this same rule for succesive observations may not necessarily give good fitting and forecasting performance. Several aspects of applying AF are discussed, with some conclusions contradicting those previously reported elsewhere. A test of AF using the standard numerical example failed to substantiate claims of AF's comparative superiority in relation to exponential smoothing.