In a previous post, we presented a time series analysis of the SP500 index and demonstrated its mean-reverting and trending behaviour. Subsequently, we designed trading strategies exploiting these mean-reverting and trending properties of SP500.

Does this mean that the SP500, and stock market indices in general, can be predicted?

In a recent publication [1], the author utilized multiple linear regression in order to study the predictability of the SP500 index. We note that,

*In statistics, linear regression is a linear approach to modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. Read more*

The article concluded that by using relevant market variables, investors can accurately predict financial markets to a certain extent.

*In this study, we used multiple linear regression for the stock prediction of the SPX index. Here we created three different regression models on a daily, weekly, and monthly basis. The models obtained were used for predicting the closing price of the SPX index. Each model proved statistically significant. From the results of each model, we can conclude that our monthly model forecasted better than our weekly and daily models.*

The author also emphasized that the prediction is more accurate in the monthly timeframe than in the daily and weekly timeframes.

*We concluded that our monthly frame held the best adjusted AR 2 value of 0.95, meaning 95% of the variance in the closing price of the SPX is explained by our independent variables. Therefore, we conclude that investors and analysts must use higher-timeframe models to see general trends. Our forecasting error shows that our MAPE value for our best model is 5.2% whereas our worst model MAPE value is 5.6%. As such, our models underestimate by creating more negative errors where MPE = -0.45 and -0.48. When analyzing the results obtained from comparing our predicted line to our actual line, our models identify and follow the trend within the market index. Thus, we can conclude that the pricing model of the markets is predictable to a certain extent.*

This finding is consistent with the well-known observation that the markets are less noisy in the higher timeframe than in the lower one. Design your strategies accordingly.

**References**

[1] LT. Martinez, *The Effective Predictors of the SPX Index*, The Michigan Journal of Business, Volume XII, Issue I, 2021

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