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 ...
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.
