U.s. Stock Index S & P 500 Trend Forecasting Model

The security market is usually deemed as the epitome of a country's economic situation, because of their complicated relationships. If the relationships between macroeconomic indicators and security market can be used to forecast the trend of stock indices, it will not only help investors make investment decisions to reduce risks, but also benefit the governors who can get suggestions on making polices.In this thesis, based on the theory of portfolio multifactor model, the interactions between macroeconomic factors and S&P 500 index and the changes of daily returns are examined in the US market. Three methods are applied in this research, including the methodology of moving average, neural networks and wavelet neural networks.Moving average is a trend analyzing tool, which is usually used for security technical analysis. In this research, four economic indicators are selected, and transformed by three different methods to get the moving averages of both indicators and S&P 500 index. Comparing the turning point between the index and indicators, manufacturing new orders is found to be a leading indicator of S&P 500.Based on the theory of neural networks, the BP neural network is set up to simulate the close prices of S&P 500 index. Seven macroeconomic factors are selected as the input data. The researchers find that the errors of close prices are larger than expected in both in-sample training process and out-of-sample testing process. To get a more precise sight of short term changes of stock market, the patterns of daily data of S&P 500 index, including lags and moving average of the series, are used to forecast the daily returns of S&P 500. The result indicates that the hit rate of ups and downs of BP model is 56.1%.At last, the theory of wavelet analysis is introduced in the thesis. Combining with BP neural networks, wavelet neural network (WNN) is applied to simulate the close prices of S&P 500 index. Comparing with the results given by BP neural networks, WNN shows some advantages at in-sample fitting errors, and they both perform badly when dealing with the out-of-sample prediction. Considering all the four error assessing standards, WNN is more accurate than BP neural networks. And it is also a very effective method to forecast the daily returns, especially at the prediction of ups and downs of daily returns. The hit rate is approaching 77.8%.