Smoothing parameter estimation for first order discrete time infinite impulse response filters

Abstract

Discrete time Infinite Impulse Response low-pass filters are widely used in many fields such as engineering, physics and economics. Once applied to a given time series, they have the ability to pass low frequencies and attenuate high frequencies. As a result, the data are expected to be less noisy. A properly filtered signal, is generally more informative with positive repercussions involving qualitative aspects – e.g. visual inspection and interpretation – as well as quantitative ones, such as its digital processing and mathematical modelling. In order to effectively disentangle signal and noise, the filter smoothing constant, which controls the degree of smoothness in First Order Discrete Time Infinite Impulse Response Filters, has to be carefully selected. The proposed method conditions the estimation of the smoothing parameter to a modified version of the information criterion of the type Hannan - Quinn which in turns is built using the Estimated Log Likelihood Function of a model of the class SARIMA (Seasonal Auto Regressive Moving Average). Theoretical evidences as well as an empirical study conducted on a particularly noisy time series will be presented.