Forecasting Economic Variables Using Markov Quantile Regression Approach

The classical least squares estimation approach has several potential problems when applied to economic variables. Quantile regression, on the other hand, provides us with an alternative way to work in non-Gaussian settings and obtain a more complete picture on the distribution of the forecasted variables. However, how to utilize this extra distributional information to obtain an optimized forecast is of great concern. This thesis intends to overcome this problem and explore the application of quantile regression in the examination of relationship among economic variables and in the prediction of equity returns.

We develop a new methodology that incorporates market evolvement dynamics to combine quantile regression results. We assume that the market state movement is controlled by a three state Markov chain, and the expected return at each state is proportional to different quantiles. The prediction is given as a weighted sum of estimated quantiles where the weights are the transition probabilities. By including market movement process in the prediction, we can obtain a way to combine different quantiles into an optimized point forecast. The empirical results show that our model improves both in sample fitness and prediction accuracy.

Our first application of the new specification is to forecast equity risk premium. With the application of the combination method, we show that our model outperforms both OLS and fixed weighted quantile regression model. We also employ the model to check the relationship between excess return of portfolios and the three Fama French factors. The proposed model fits the data better than OLS, and has greater predictive power. The future work includes generalization of the model and issues regarding portfolio construction.