ARIMA Modeling with Intervention to Forecast and Analyze Chinese Stock Prices

In this study, we demonstrate the usefulness of ARIMA-Intervention time series analysis as both an analytical and forecast tool. The data base for this study is from the PACAP-CCER China Database developed by the Pacific-Basin Capital Markets (PACAP) Research Center at the University of Rhode Island (USA) and the SINOFIN Information Service Inc, affiliated with the China Center for Economic Research (CCER) of Peking University (China). These data are recent and not fully explored in any published study. The forecasting analysis indicates the usefulness of the developed model in explaining the rapid decline in the values of the price index of Shanghai A shares during the world economic debacle stating in China in 2008. Explanation of the fit of the model is described using the latest development in statistical validation methods. We note that the use of a simpler technique although parsimonious will not explain the variation properly in predicting daily Chinese stock prices. Furthermore, we infer that the daily stock price index contains an autoregressive component; hence, one can predict stock returns.


Introduction
In this study, we report an analysis not heretofore reported in the literature and for the data base collected. Our purpose is twofold; (1) to analyze data by implementing ARIMA-Intervention analysis (Box and Tiao, 1975); and to assess the prediction and forecasting of Chinese stock market prices over a lengthy enough period of time where stock prices fluctuated during varying temporal economic movements. We study the Chinese equity markets to understand the predictable properties in this fast growing but volatile market. Previous studies of the Chinese equity markets include Jarrett, Pan and Chen (2009) who studied the relationship between the Macroeconomy of China as it relates to the equity markets of Shanghai and Shenzhen. In addition, Thomas (2001) discussed in detail the workings of the Shanghai equity market over its illustrious history offering insights into the characteristics of the equity markets. His study included the behavior of both domestic and foreign investors in four equity markets. The history discussed is of the twentieth century and not the twenty-first century. Others (Eun and Huang, 2007;Ng and Wu, 2007;Shenoy and Ying, 2007, Weili et al., 2009, Wang et al., 2004and Wang et al., 2007 investigated the rapid growth in the Chinese equity markets and why they became increasing important for investors in global markets. In addition, Bailey, Cai, Cheung and Wang (2006) studied the Shanghai Equity Market and discovered some characteristics concerning order balances of individuals, and institutional investors. Our purpose , here, is to investigate the Chinese equity markets to explain and discover if certain anomalies noted in more developed equity markets are present or not in the Chinese markets.
Following the study of Zhong, Gui and Lui (1999) for the Chinese Bourses (Shanghai and Shenzhen), we selected a newer and finer data base from the PACAP-CCER China Database developed by the Pacific-Basin Capital Markets (PACAP) Research Center at the University of Rhode Island (USA) and the SINOFIN Information Service Inc, affiliated with the China Center for Economic Research (CCER) of Peking University (China). The length of data was for approximately ten years resulting in a time period where analysis can lead to interpretable results. Smaller time periods such as two or three or even four years are usually too small to reduce the effects of disturbances in economic data and more specifically do not produce enough degrees of freedom such that one may identify significant events and factors. A small number of degrees of freedom in sample data may not lead to determining " statistically significant� events even when they exist. The theoretical minimum number of observations for an ARIMA model is p+q+d+1, with the caveat that observations below three result in infinite standard errors. We also require each parameter in a regression equation to have at least one observation (Hyndman and Kostenko, 2007). That would result in a minimum number of observations for our model of five (one for the AR term, one for the difference of price, one for the IV volume, and two for the dummy variable intervention). To further account for randomness in the data we increased the sample size knowing that margins of error decrease proportional to the square of the sample size. [See Hyndman and Kostenko (2007)].
The regression will include for the response variable is the daily price index for the entire data base on daily returns produce by the PACAP-CCER Greater China Database. These data are part of the website created for research on Pacific-Basin nations. [The website and its content is a copyright of PACAP-CCER. All rights reserved. If you have any question or comment, please e.mail to chinadat@etal.uri.edu.]. The data base contains information from 01/1990 to 12/2009. The length of time is long enough for serious investigation which produce results that is not highly influenced by business cycles but long enough for us to create a useful ARIMA-Intervention model for forecasting.

ARIMA Modeling and Intervention Analysis
We follow the methods of stochastic time-series ARIMA modeling to analyze and find a model for prediction of changes, variation sand interruptions (interventions) in the movement of stock prices for China over time.
ARIMA modeling with intervention may help analysts understand whether economic events such as a "global financial crisis" have impact on the change in Chinese stock prices if it exists (Shanghai A-share simple arithmetic mean index). This will provides information for financial analysts, economic forecasters and decisionmakers to plan for and cope with sudden movements in the prices of Chinese stock. Previously, the application of ARIMA modeling with and without intervention was implemented in such applications as system scheduling and simulation (Ip, 1997;Ip et al., 1999)  As discussed before by Box and Tiao (1975) an intervention model is of the general form: where I t is an intervention or dummy variable that is defined as I t = 1, for t = T and I t = 0 for t ≠ T.
In the transfer function models, the input is a general exogenous times series that influences the output series.
We consider a special situation in which the input is a series of indicator variables that rrepresent the occurrence of identifiable unique events that affect the output variable. The identifiable events are the interventions. We now assume an intervention occurred, hence we ask the question whether evidence exists change in the time series of the type anticipated occurred. Furthermore, what is the estimated size fo this change? Intervention analysis model, introduced by Box and Tiao (1975), is the major work in this area. However, a great deal of the terminology is due to Glass (1972 Alternatives to ARIMA do exist for forecasting stock prices. For example, neural networks popularized in recent years due to increased availability of computer software are comparable to ordinary least squares regression (OLS) regression. However, neural networks are a black box method for providing accurate predictions, but contain little or no explanatory power. Hence, they are inappropriate for this study (see Lievano and Kyper, 2006). To analyze interrupted (intervention) series, sophisticated techniques like Fourier analysis and cross-spectrum analysis are available (see Hill and Lewicki, 2007). However, these techniques are more appropriate for complex time series with cyclical components or the simultaneous analysis of two series respectively, and were not deemed appropriate to test here.

The Analysis of the ARIMA Intervention Model
We include the financial crisis as the intervention of the time series which results in an ARIMA-Intervention model. As the global financial crisis extended to China in September 2008 and beyond, the intervention was initiated at that time. In the Appendix What we learn from the estimated model equation is that the intervention is significant and that prices were inversely related to financial crisis. This is what we would expect the results to be and is likely to be corroborated by studies using other methods for analyzing time series data having been related to the economics of the environment. Furthermore, the volume effect, although statistically significant, leads us to conclude that there is only a tiny effect on the volume of transaction on prices.
The differencing which was necessary to build a time series that was stationary for modeling purposes was also significant and positive. Last, the significant autoregressive coefficient of the first order, i.e., AR (1), led to the estimated coefficient of 0.492162 for lagged value of Yt, i.e., Yt-1.

Additional Analytical Results
In addition the analytical . This variable has an extremely small standard error. The interpretation is obvious at this point that including the intervention term has benefits.

Summary and Conclusions
The stock market price index in China was modeled by the methods of ARIMA-Intervention analysis and produced a fit for one to analyze and draw conclusion concerning how the index behave over time. The results indicate that the World Financial Crisis included China and affected its stock as well as its manufacturing industry. The intervention effect as measured in this study was alarming and clearly felt by the financial industry in China as well as its other component. The negative effect of the stock market decline is likely to correlate with the decline in Chinese manufacturing during the period and to have negative impacts on the Chinese Macroeconomy. In addition, the results corroborate that daily prices of Chinese equity securities have an autoregressive component. Whether this in a permanent or temporary component of the time series requires a more exhaustive study involving long term modeling of financial time series as exemplified by Ray, Jarrett and Chen (1997) in a study of the Japanese stock market index. One very basic conclusion is that we indicated that the use of intervention analysis is very useful in explaining the dynamics of the impact of serious interruptions in an economy and the changes in the time series of a price index in a precise and detailed manner.