Candlestick Joint-Distribution Models for Time Series with Clustered Volatility

Abstract

Open-high-low-close price (also OHLC) series have been widely used for the pricemovement analysis of financial time series, including to draw candlestick charts. Modeling these data is complicated by the fact that such data are often unlikely to be samples of stationary stochastic processes, as can be seen in the well-known phenomenon of volatility clustering. In this research, first we try to remedy this matter by using the sequences of differences between high and low prices, which are pointed out to often have higher autocorrelations than the absolute returns of close-price series, and normalize the scales of OHLC by their exponential moving averages. Under our experimental conditions, the Earth Mover's Distance (EMD) between normalized S&P500 training and test data is about one-seventh of the EMD between the unnormalized data. Second, we try to model the normalized data by introducing 6 generative models for them. The EMDs between data generated by our learned models and the normalized test data are about one-sixth of the EMD between the normalized test data and the delta distribution located at the barycenter of the normalized training data. However, they are about 5 times larger than the EMD between the normalized test and training data.