Comparison of Approaches to Implementing Bagging in Time Series Modelling

In the paper comparison of approaches to bagging with use of bootstraps of various size has been made. The bagging strategy in classification is interpreted as strengthening of simple classifiers. In case the time component appears, the main idea is converted to an attempt to determine the properties of the data distribution to which the remainder of the time series belongs, obtained after deleting the trend and the seasonal part. Based on the data of the remainder of the time series, several new time series (bootstraps) are formed. Then, they are averaged (or a function is applied to them). Thus, a new value of the remainder is constructed. The series is reconstructed from the updated remainder, trend, and seasonality. This operation assumes that the variance of the time series remainder is reduced, allowing more accurate prediction. It is of interest to establish the relationship between the accuracy of the prediction of the model built on the updated remainder and parameters of bootstraps. In the paper the relationship between the length of the bootstrap from which the updated remainder is constructed and the accuracy of the forecast for the test period is investigated. Several approaches are presented in the computational experiment: linear bagging, moving blocks bootstrap (MBB), circular begging (CB), and construction of stationary bootstraps (stationary bagging (SB)). Using the M3 dataset as an example, the accuracy of the bagging approaches is compared to each other and to the accuracy of the standard ARIMA/ETS models.