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 proposed simulation study evaluates the predictive performance of log-linear models on time series whose error term exhibits varying degrees of heteroskedasticity and autocorrelation and follows different distributions. In addition to the naive approach, the results of the method proposed by Baser (adapted for time series) are compared with a method newly developed to account for both heteroskedasticity and autocorrelation. The methods are tested across prediction horizons of varying lengths. The thesis also includes an application of the evaluated methods to real time series, specifically to data from the M5 Forecasting Competition, using models of varying complexity. The results show that accounting for autocorrelation brings a clear benefit, especially in one-step-ahead predictions. However, as the prediction horizon increases, the advantage of autocorrelation correction gradually diminishes.