On time series data and optimal parameters

Abstract

Forecasting using time series (TS) models are often based on linear regression or methods using various smoothing techniques. When estimating the parameters used in smoothing techniques, it has become a common practice to optimize the smoothing constants (parameters). This new practice is a result of the ease such methods can be accomplished when using the built in Solver optimization tool in modern spreadsheets. However, the capabilities of Solver can be utilized further to optimize more of the parameters, particularly the initial or starting parameters. This paper presents examples of exponential smoothing techniques, demonstrating improved fits when adopting this idea of optimizing the initial parameters as well as the smoothing constants. It also demonstrates that linear regression is a special case of Holt's exponential smoothing model with trend. Normalization of the seasonal parameters in models incorporating seasonality is also discussed, showing improved fits to TS data. Educators are encouraged to adopt the idea of letting Solver optimize more of the parameters than what is common practice today, in other models and in other fields.