A Study on S&P 500 Index Stock Return and Volatility Using Arima and Garch Modeling

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A Study on S&P 500 Index Stock Return and Volatility using ARIMA and GARCH Modeling Kaiyuan Song, Di Wu Summary In this project we first checked consistency and seasonality of S&P500 index stock performance by splitting its recent twenty years historical data into ten two year data and built ARIMA and GARCH models for each sub-period. We found that the models are considerably consistent before 2007-2008 sub-period, and there exists some minor seasonality in several subperiods, but no particular pattern can be identified for the whole period. We then tried to predict future return, volatility and VaR using the model we built for the last sub-period based on rolling forecast procedure. Though the fitted values of 10th sub-period model are…show more content…
All of the fitted returns are very close to zero as expected and all fitted volatilities vary according to fluctuations in actual returns: it goes up when there were large fluctuations and vice versa. Two sample plots are shown below: Our prediction model, the tenth period model, fitted the data especially well as illustrated below. Not only the volatility prediction were accurate, the mean part also provides considerably nice fit. With the excellent fit from our prediction model, we expect our predictions to be fairly dependable. Nonetheless, when comparing actual future return with our predicted return and volatility obtained from 5-day ahead rolling forecast procedure, the results were rather unsatisfactory. All of the predicted volatilities were considerably high and did not move along with real fluctuations in return series, which resulted in very significant value at risk. In addition, the return predictions were no much better than just using sample means, which were all very close to zero, to predict future return. The prediction vs actual return plot for 60 days is shown below. To improve our predictions, particularly for volatility part, one-step ahead rolling predictions were computed, and its prediction vs actual return plot is illustrated below: Due to the return predictions made by ARIMA were similar to one-step results and not much better than sample mean prediction, we focused on volatility part and found that one-step

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