A new approach to forecasting based on exponential smoothing with independent regressors

This thesis is concerned with integrating regressors into the very successful exponential smoothing model. An initial trial is conducted to integrate regressors as a direct extension to the existing class of models with time-invariant regressor parameters introduced by Hyndman, Koehler, Ord & Snyder (2008). Several variations of model structures are investigated for models with time-varying regressor parameters. Similarly a number of alternative model structures are also considered for models with time-invariant regressor parameters. An important property the proposed model should have is the ability to produce stable forecasts. Unfortunately, all the proposed model structures with time-varying regressor parameter that are constructed via this approach are found to have an undesirable characteristic, which puts them at risk of producing unstable long-term forecasts. Attention is then turned to constructing the desired model based on integrating regressors into Holt’s linear exponential smoothing method. It is observed that the growth term in Holt’s linear method is actually a regression parameter for a time trend. This finding opens a way for more general regressor to be included in place of the time trend. Not only that, it paves a way for a set of regressors be included into the exponential smoothing models with an explainable rationale for the resultant model structure. Similarly, two types of model structure are considered for the second method of integration, one with time-varying regressor parameters and another one with time-invariant regressor parameters. The most striking feature of the second integration approach is that, the model with time-varying parameters is found to have one of the desirable characteristics which avoids the risk of unstable long-term forecasts. For this approach, however, the use of differenced regressors leads to a new problem that is the possibility for the regression parameter to explode if the associated differenced regressor values are zero or close to zero. Fortunately, this problem can be solved by the introduction of a switching procedure. The new models are tested empirically using both simulated and real data. The analysis performed with simulated data, suggests that the proposed model with time-varying regressor parameters has an ability to properly react to the change in the magnitude of parameter. When applied on several deseasonalized real data sets, it performs the best at forecasting the short-term residents departing from Australia to other countries, and being second best in forecasting the passenger vehicles sales in Australia, compared to some other selected forecasting techniques. The proposed new approach again proves its worth by being the best in many scenarios involving forecasting tourism demand in Malaysia compared to other exponential smoothing models. Tourist arrivals from three origin countries, which can have a seasonal component are used in this analysis. The new forecasting method is ranked first when used to forecast tourist arrivals from Singapore (for 1, 2 and 4-step ahead forecasts), Australia (for 1 and 2-step ahead forecasts) and the United Kingdom (for 2 and 3-step ahead forecasts).