Input data analysis and model selection in time series

Time series are data sets that contain consecutive observation values of a variable. These observations may change over time due to environmental or systematic effects. Therefore, while estimating with time series models, instead of training the model with the whole set of observations, the data can be divided into sections starting from the very end, and the most relevant periods from these sections will be used in the forecasting model. In this study, the CUSUM algorithm, which is a change point analysis method, is used to determine the length of the training dataset. This algorithm is integrated with ARIMA and Holt's Winter methods, which are popular prediction models, and forecasts are generated and evaluated on the test data.For validation, the same prediction models are trained on the whole data set, and its performance is used as a benchmark to evaluate the proposed approach. Furthermore, to show the importance of determining the change points in the time series, training data sets were created with fixed-time time windows, and estimates were made with these sets, and their performances were measured. It is observed that the models trained with the"correct" part of the time series have smaller MSE values as compared to the prediction results obtained from the other two methods, that is, more realistic results were obtained.