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

Among the many denoising methods and techniques successfully employed for univariate time series – e.g. based on regression,1 Kalman filter,2,3 decomposition,4 wavelet5,6 and non-linear method7– those based on algorithms of the type Infinite Impulse Response (IIR) exponential filters have been massively used, given their satisfactory performances (see, for example,8 and, more recently9). Such methods are useful for their ability to maximize the amount of relevant information that can be extracted from “real life” time series. In fact, regardless the scientific field time dependent data are collected for (e.g. engineering, economics, physics, environmental), they can never be error–free. In spite of all of the efforts and precautions one might take in order to provide clean data – e.g. robust data acquisition methods, reliable routine checks, sophisticated procedures for error correction, fail safe data storage and data communication lines – reality is way too complex for such procedures to be completely reliable.