Moving average approach to time series forecasting of stock prices with correction factor

M.W.Kotarinos, C.P.Tsokos

University of South Florida

Tampa, FL, 33620, USA

The object of the present study is to investigate the effectiveness of developed modelling [1-11], including a newly developed forecasting technique for non-stationary financial data. Using actual data from an S&P 500 stock, we develop a classical ARIMA model for the daily closing high and low values of a stock and compare it to the proposed k-th day moving average model. Using residual analysis, the quality and effectiveness both models were evaluated and discussed in regards to their applications to finance and investing.

 

One of the earliest methods of time series analysis was the autoregressive moving average (Wold). This method combined the use of an autoregresor with a moving average to generate a model for stochastic time series phenomenon.

Unfortunately, most time series are non-stationary in nature, meaning they do not hover around a single value, and most analytical methods for time series phenomenon require the use of a stationary series. A refinement to the ARIMA model, the autoregressive integrated moving average, combined Wold's approach with difference filtering to reduce a non-stationary time series to a stationary series through the use of difference filters (Box and Jenkins). Later, this approach was adjusted for seasonal data, resulting in seasonal ARIMA models (Box, Jenkins and Reinsel).

Other notable works in the field of time series analysis include the work of Nobel Laureate Clive Granger, whose work on co-integration of time series data introduced the concept of Granger causality, and Laureate Robert Engle who introduced the ARCH method, which is a forecast of variability of a time series. Recently, Chris Tsokos dedicated an article on the works of Granger which included different kinds of k-th day moving average techniques for time series phenomenon.

As some conclusion we note. Not only did our proposed methodology perform well under residual analysis, but showed market feasibility by producing a significant profit in a competitive market. Most significantly, the stock in question actually followed a downward trend over the period in question, yet our model was able to still identify peak times to buy and sell the given stock. Our model's ability to produce a profit even during a downward trend in stock price shows our approach to be surprisingly robust.

It is interesting to note that neither the classical ARIMA nor a 3-day moving average ARIMA alone produced the best model. By combining these two techniques, we produced a far more accurate forecast than either could achieve separately. Thus, this suggests that while the k-th day moving average approach is a strong alternative to the classical ARIMA, it is not an outright replacement. The 3-day moving average approach showed some issues with the error correction process, while the classical ARIMA model showed a strong improvement.

We have shown that our hybrid approach of combining a hybrid of k-th day moving average and classical ARIMA seems to performed better than either method exclusively. This hybrid approach offers additional flexibility in modeling non-stationary time series phenomenon that serves as a strong alternative to the classical ARIMA approach.

 

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11.       C.P.Tsokos. Modelling of environmental engineering and health problems. Int.J. Problems of nonlinear analysis in engineering systems, No.1(35), v.17, 2011, 1-5 (in English and in Russian).