Advances in Mathematical Physics

Volume 2016, Article ID 8045656, 7 pages

http://dx.doi.org/10.1155/2016/8045656

## The Interval Slope Method for Long-Term Forecasting of Stock Price Trends

School of Computer and Information Engineering, Beijing Technology and Business University, Beijing 100048, China

Received 3 November 2015; Accepted 3 February 2016

Academic Editor: Doojin Ryu

Copyright © 2016 Chun-xue Nie and Xue-bo Jin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A stock price is a typical but complex type of time series data. We used the effective prediction of long-term time series data to schedule an investment strategy and obtain higher profit. Due to economic, environmental, and other factors, it is very difficult to obtain a precise long-term stock price prediction. The exponentially segmented pattern (ESP) is introduced here and used to predict the fluctuation of different stock data over five future prediction intervals. The new feature of stock pricing during the subinterval, named the interval slope, can characterize fluctuations in stock price over specific periods. The cumulative distribution function (CDF) of MSE was compared to those of MMSE-BC and SVR. We concluded that the interval slope developed here can capture more complex dynamics of stock price trends. The mean stock price can then be predicted over specific time intervals relatively accurately, in which multiple mean values over time intervals are used to express the time series in the long term. In this way, the prediction of long-term stock price can be more precise and prevent the development of cumulative errors.

#### 1. Introduction

Stock price is a typical and complex type of time series data. The prediction of stock prices has been an active area of research in econometrics, signal processing, pattern recognition, and machine learning for some time. Stock traders and investors are extremely interested in stock market prediction because of the considerable profits that can be reaped by trading stocks. Traditionally, the basic methodology for financial time series has been statistical methods such as autoregressive and moving average model (ARMA), autoregressive integrated moving average model (ARIMA), and generalized autoregressive conditional heteroskedasticity (GARCH), which require the linear variation in the stock prices to remain stationary. In general, the statistical models cannot adapt to changes in the process. Accordingly, traditional statistical methods cannot predict stock performance very well when tracking the complexity of the stock markets [1].

Recently, many machine learning systems have been used to predict stock prices. These include artificial neural net (ANN) [2, 3], Bayes networks [4], genetic programming [5], support vector regression (SVR) [6], user analysis [7], sentiment analysis [8], and hybrid networks [9–15]. Accordingly, machine learning methods can be used to track the complexity and nonstationary nature of the stock markets in short-term prediction. These methods predict long-term trends only with great difficulty. Existing methods of long-term stock prediction mainly include the following: use of the recursive iteration prediction to obtain the long term prediction trend [12]; however, this method involves accumulative error, and the cumulative error increases with the number of steps in the prediction process. By using a moving window algorithm to delete older data and take in new data, the prediction model can be updated in sequence [6]. The length of the moving window also has considerable influence on the accuracy of the modeling process. This system can only show the mean stock price during the prediction interval and cannot show the details of changes in the stock trend during this interval. In addition, the present methods use the mean value directly as a feature of the stock trend prediction. Regarding the fluctuations in larger time series, the mean values of the interval weaken the fluctuation characteristics of the time series and reduce the long-term accuracy of the forecast. For these reasons, the prediction of stock price is still a worthwhile issue.

Long-term time series forecasts have other applications, such as the host load prediction. Load prediction is crucial to efficient resource utilization in dynamic cloud computing environments. Di et al. used the exponentially segmented pattern (ESP) [16] to predict the host load in the cloud. They proposed the use of 9 different features to characterize the recent load fluctuation in the evidence subinterval. They were able to predict the mean load over consecutive time intervals.

In this paper, the exponentially segmented pattern (ESP) is used to predict the fluctuation of stock price over consecutive future time intervals. While we give a new feature of stock price in the subinterval, namely, interval slope to characterize the stock price fluctuation over a set period. The interval slope can be used to determine the mean of stock in the subinterval. The support vector regression and the Bayes classifier were used to predict the stock price trend and verify the effectiveness of the interval slope of the stock price in the subinterval.

In this paper, the following contributions are made:(i)The exponentially segmented pattern (ESP) is here used to predict fluctuations in different stock data over a long period and can accurately predict not only mean stock price over a future time interval but also the mean stock price over consecutive future time intervals. In this way, the prediction of long-term stock price can be more precise and the generation of cumulative errors can be prevented.(ii)The use of new features of stock pricing in the subinterval, namely, interval slope, is here proposed to better characterize the stock price fluctuation over some time period.

The rest of the paper is organized as follows. In Section 2, the long-term stock price prediction model is introduced. In Section 3, experiments and comparisons of different models are made. Conclusions are given in Section 4.

#### 2. Model-Based Prediction of Long-Term Trends in Stock Price

The predictive objective is to predict the fluctuation of opening price over a long period. Multiple precise mean values over time interval are used to express the time series long-term trend.

The proposed stock price trend prediction model involves the following three steps: first, using the ESP principle, the estimated data segment is split into a set of consecutive segments, whose lengths increase exponentially. The interval slope is used to describe the features of each interval. Then, machine learning methods, SVR and MMSE-BC, were used to produce the transformation model of the data which is used to predict the mean stock price for the next interval. Multiple precise mean values over time interval are used to express the long-term trends in the time series. In this way, the prediction of stock price in the long term can be performed precisely without generating cumulative errors.

##### 2.1. Exponentially Segmented Pattern (ESP) and Transformation of Segments

The objective of the current work is to predict trends in the patterns of fluctuation of stock price over the consecutive future time intervals. The most important step of the proposed stock price trend pattern prediction is that the estimated data segment is split into a set of consecutive segments by ESP principle, whose lengths increase exponentially. An example of ESP is shown in Figure 1. At a current time point , the estimated data segment is split into a set of consecutive segments whose lengths increased exponentially. The length of each following segment was , where . For each segment over the consecutive future time intervals, the mean values were denoted by , where .