پیش بینی قیمت سهام با استفاده از شبکه های بیزی

Bayesian network is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph. This paper describes the price earnings ratio (P/E ratio) forecast by using Bayesian network. Firstly, the use of clustering algorithm transforms the continuous P/E ratio to the set of digitized values. The Bayesian network for the P/E ratio forecast is determined from the set of the digitized values. NIKKEI stock average (NIKKEI225) and Toyota motor corporation stock price are considered as numerical examples. The results show that the forecast accuracy of the present algorithm is better than that of the traditional time-series forecast algorithms in comparison of their correlation coefficient and the root mean square error. Highlights ► Bayesian network is applied for forecasting Nikkei stock average price and Toyota motor corporation stock price. ► Bayesian network models the stochastic dependency between past stock prices to predict the future stock price. ► The present method is compared with the time-series forecast algorithms such as AR, MA, ARMA and ARCH models. ► The computational accuracy of the present algorithm is 15–20% better than the time-series forecast algorithms.

Stock price forecast is very important for planning of business activity and the national economy. Several time-series forecast algorithms have been applied successively for the stock price forecast (Box et al., 1994 and Brockwell and Davis, 2009). Auto Regressive (AR) model, Moving Average (MA) model, Auto Regressive Moving Average (ARMA) model and AutoRegressive Conditional Heteroskedasticity (ARCH) model (Engle and Ng, 1993) are very popular algorithms. AR model approximates the stock price with previous stock prices and MA model uses, instead of the previous stock prices, the previous error terms. ARMA model is the combinational model of AR and MA models. In ARCH model, the stock price is approximated with the linear combination of the previous stock prices and the error term. The volatility of the error term is approximated with the previous error terms. ARCH model was presented by Engle and Ng (1993) in 1980s. After that, many researchers have presented several improved models from ARCH such as Generalized AutoregRessive Conditional Heteroskedasticity (GARCH) model (Bollerslevb, 1986), Exponential General AutoRegressive Conditional Heteroskedastic (EGARCH) model (Nelson, 1991) and so on. The time-series forecast algorithms usually represent the error distribution according to the normal distribution. Recent studies point out that the distribution of the stock price fluctuation does not follow the normal distribution (Takayasu, 2006). Especially, the analysis of actual stock data reveal that the deviation around ±σ and ±3σ is thicker than the normal distribution. The algorithm based on the normal distribution may not forecast the stock price accurately. Therefore, the stock price forecast by using Bayesian network ( Ben-Gal, 2007 and Pearl and Russell, 2002) is presented in this study. Bayesian network is a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph. The use of the Bayesian network enables the stock price forecast without white noise model. Although the stock price is continuous value, the Bayesian network can deal with the discrete (digitized) values alone. The stock price distribution is digitized firstly by using the clustering algorithms and then, the Bayesian network is used for modeling the stochastic dependencies among the digitized values of the previous stock price. NIKKEI stock average and Toyota motor corporation stock price are considered as examples. While the P/E ratio distribution of NIKKEI stock average is relatively similar to the normal distribution, the P/E ratio distribution of Toyota motor corporation stock price is far from the normal distribution. The present method is compared with AR, MA, ARMA and ARCH on their forecast accuracy. Since the present method depends on the clustering algorithms, two clustering algorithms; uniform clustering and the Ward method, are compared and the effectiveness of the number of clusters (set of digitized numbers) is also discussed. The remaining part of the manuscript is as follows. In Section 2, time-series forecast algorithms are explained briefly. Bayesian network algorithm is described in Section 3 and the present algorithm is explained in Section 4. Numerical results are shown in Section 5. The results are summarized again in Section 6.

The P/E ratio forecast algorithm by using Bayesian network was presented in this study. The P/E ratio values are digitized by clustering the P/E ratio frequency distribution by the uniform clustering or Ward method. Bayesian network for dependency among previous P/E ratio distribution is determined from the digitized P/E ratio values. The forecast accuracy and the correlation coefficient with respect to the actual stock price are compared with the traditional time-series forecast algorithms such as AR, MA, ARMA and ARCH models. Through the numerical example of Nikkei stock average and Toyota motor corporation stock price, the present algorithm using the uniform clustering shows the similar accuracy and the better correlation coefficient against to the time-series forecast algorithms. And in the present algorithm using Ward method, the computational accuracy is improved by 15% (NIKKEI stock average) and 20% (Toyota motor corporation stock price) against the traditional ones. In the next study, we would like to improve the present method still more by developing the P/E ratio digitizing algorithm.