Time Series Prediction Using Log-Linear Models

Log-linear models are an important tool in time series analysis and are widely used in many areas of scientific research and practical applications. The issue associated with logarithmically transformed dependent variable lies in the need to transform predicted values back to the original scale. This work builds upon a bachelor's thesis that dealt with bias correction in predictions in log-linear models with heterogeneous data using numerical simulations on cross-sectional data. The aim of this thesis is to extend this issue to time series. The existing results are expanded particularly to address the issue of serial correlation in the context of retransforming predicted values from the logarithmic scale to the original level scale. The conducted experiment evaluates the predictive abilities of log-linear models on real time series, specifically on data from the M5 forecasting competition. Besides naive prediction, the quality of predictions obtained using Baser's method, adapted for time series, and a method designed to account for serial correlation combined with heteroskedasticity, is evaluated. Predictions are estimated on several time series using three different models and comparisons are made for 1-step, 3-steps, and 5-steps ahead predictions. The experiment's results show that accounting for autocorrelation is more significant than accounting for heteroskedasticity in the case of 1-step ahead predictions. In multiple steps ahead predictions, this significance decreases sharply.