Filtering and Spectral Analysis of Time Series Data: A Signal Processing Perspective and Illustrative Application to Stock Market Index Movement Forecasting

Abstract

Finance and the economy are older fields than the topic of signal processing, and they kept on evolving for centuries without reference to signal processing concepts. However, some advanced mathematical concepts apply to financial system analysis and modeling from the past several decades, along with the development of algorithms in the digital signal processing (DSP) field. The representation of financial systems using mathematical and stochastic models facilitates policy makers to produce realistic, measurable, and controllable quantitative analysis, and thus increases investors’ trust and decisions. The systematic and structured statistical analysis and modeling of financial data is dealt with in the field of “econometrics.” There is a high degree of similarity between some DSP concepts and time-series data analysis in econometrics. For example, moving average (MA) filter is used in DSP for high-frequency noise removal and low-pass filtering, and the same is also used in detecting the trend of the stock price in econometric using time-series analysis. Monitoring the price of the finanancial products and extrapolating their future evolution according to past available information is an objective of time-series modeling; the same can be viewed as a classical signal processing problem. This chapter begins with linear filtering concepts of DSP, which are then correlated to time-series analysis concepts in both time and spectral domain. The basic knowledge of DSP and random signal processing is assumed, and rigorous mathematical proofs for such concepts are avoided. The chapter then describes limitation of conventional linear filters and the remedy using adaptive filtering algorithms is also described. In addition, an application to stock market index movement forecasting is also illustrated using a simulation exercise where the national stock exchange (NSE) index: NIFTY 50 closing values are used to train and test the time-series model. Digital signal processing techniques along with machine learning and data analytic algorithms can play an important role in today’s finanancial system analysis, modeling, prediction, and forecasting. An effort is made here to illustrate how a data scientist working in econometric field can work hand in hand with a digital signal processing researcher and contribute a lot to some fruitful multidisciplinary research outcome.