Stocks & Commodities V. 28:5 (32-39): Signal Processing Basics by Glenn A. Barlis

Signal Processing Basics by Glenn A. Barlis

This is the second of a series of articles that examine stock price analysis using the mathematical methods of signal processing. Here you will learn about tools for detecting trends and smoothing them.

In the first part of this series, I proposed a model for price time series that could be analyzed using signal processing techniques:

Equation 1-1a: P = Constant + trend + cyclical components + noise

or Equation 1-1b:

P = c + f(t)trend + Sum[f(t)cycles ] + f(t)noise

One way to view this model of price action is to think in terms of the frequency of price changes. From a frequency perspective, this model can be restated in terms of: 1 Low-frequency components c + f(t)trend + f(t)cycles where cycles terms have very long periods compared to the trading horizon 2 f(t)cycles terms where the cycle period is on the same order of magnitude of the trading horizon 3 f(t)cycles + noise where the high-frequency and noise terms result in price variations that are much shorter than our trading horizon. In the first article of the series, I described the cyclical components along with analysis tools such as the fast Fourier transform (Fft). In this second article, I will discuss the trend and low-frequency components and introduce tools for trend detection and low-pass filtering (smoothing).