Band Pass Filters and their Applications in Time Series Analyses

Abstract

Time series play a significant role in deriving and describing almost all real-world processes. Analyzing a time series helps identify the nature of the process and forecast the associated variable. A time series comprises two components; one is regular, and the other is irregular in nature. The regular component has a specific trend (moves up and down), a seasonal trend (often repeats over a time domain—a day, week, month or season) or a cyclic trend (tends to follow its own cycle). The irregular component has random variations which do not have a specific pattern. In this chapter, we study the methods to deal with these random variations, often regarded as “noisy data”. We apply various filters to our data in order to get rid of these “unusual data points”, which create a hindrance in judging the nature of the time series and hence reduce the forecast capacity of the model that uses the data set. This chapter reviews the basic types of filters and their applications in various fields. We have included four classes of active filters—low pass, high pass, band pass and band stop filters—as well as the mathematics behind each of the filters, along with their significance. Band pass filters are typically used to smooth data and study temporal variations for a parameter, ranging from intraseasonal to multidecadal. Further, these filters can be applied to study the lead-lag relationship and autocorrelation. We have tried to incorporate simple applications for each of the filters, which should create interest for young researchers.