The Predictive Power of Volatility Pattern Recognition in Stock Market

Abstract

In this paper, we first show that there exists a day pattern in equities volatility and its volatility pattern is different from daily volume profile. To further emphasize on the most important volatility change during the day, we fold the continuous stock minute-by-minute data into n-by-p matrix, where n is number of days and p is number of minutes during trading hour, and decompose the matrix using principal component analysis (PCA). By examining the eigenvectors from the first several principal components, we can confirm the volatility day pattern and use eigenvectors as weight in distance metric in clustering step to generate and forecast volatility pattern. Clustering method K-Means and expectation maximization (EM) for Gaussian mixture model with three different distance metrics are implemented which enable us to optimizing clustering result. With clustered volatility patterns, when new observation comes in as stream, we compare the similarity under specific distance measure. New observation's feature vectors with their loading factors are compared with centroids of clustered patterns as base. Forecasted volatility in the next period is calculated based on likelihood to most similar pattern and conditional probability of change of direction. This mechanism generates a predictive signal. To examine the practicality of this pattern recognition in volatility of equity market, we build a trading algorithm and did back test to check the accuracy and profitability of this idea. Realized volatility calculated by SPY and a representative for implied volatility VXX are treated separately and compared throughout the paper. As a result, test error, profit and loss and risk adjusted return are compared with performance by using fixed volatility profile, as well as comparing with GARCH (1, 1) model for SPY realized volatility and ARMA (1, 1) for VXX as implied volatility. Sharp ratio from weight adjusted investment strategy outperforms both.