Forecasting the Time Series of Apple Inc.’s Stock Price

Jordan Berninger
MAS, 2018
Co-advisors: Juana Sanchez and Qing Zhou
The 21st Century has been defined by the exponential growth of the information technology (IT) industry, the smart phone and the personal computer. Apple Inc. has played a major role in that growth, with Apple products widely considered emblematic of the IT revolution. The health of Apple Inc. is a predictor of the health of the industry and industries that depend on it. Apple’s stock price is an indicator of Apple’s health. Therefore, it is of particular interest to have good models to predict the stock price of such a hallmark company of this IT revolution. Statistical time series analysis is of paramount importance to do that. This thesis compares the forecasting performance of univariate and multivariate time series models of Apple stock’s opening price for the first day of each month. Among well-known univariate models, we consider Autoregressive Integrated Moving Average (ARIMA) models, ARIMA with Generalized Autoregressive Conditional Heteroscedascity (GARCH) and Exponential Smoothing, all models where the predicted opening price depends on past values of itself and nothing else. Among multivariate methods known in time series analysis, we consider Vector Autoregression (VAR), which endogenizes all the variables considered, and classical linear regression with ARIMA residuals. We fit these models to an “in-sample“ (training set) of historical opening price from January 1990 to September 2016, and use them to forecast 12 months “out of sample“ (test set) October 2016 to September 2017. In the multivariate models, the predictors of Apple’s opening price are: the stock price of the S&P500, Microsoft and Texas Instruments. We hypothesize a positive correlation of Apple’s stock with the S&P500 stock, a negative correlation with its competitor Microsoft and a positive correlation with Apple’s supplier, Texas Instruments. We compare the forecasts from each model with the actual values of the “out of sample“ time series (the test set) to assess forecasting performance according to the Root Mean Square Error (RMSE). We find that an average forecast consisting of the average of all those models’ forecasts, what is known in the forecasting industry as ”the consensus forecast,” has the lowest RMSE for the 12-month test set. This is an important result, not only because it explains the decades’ old practice of considering averages of forecasts from many models as “ the forecast“ of any relevant economic variable, but also because it highlights the benefits of integrating multiple classical models to obtain a good predictive performance.
2018