Multiscale Autoregressive (MAR) Models with MODWT Decomposition on Non-Stationary Data

Time series forecasting often shows behavior that is non-stationary, so it is necessary to do a forecasting method that can predict non-stationary data in order to obtain good forecast results, including Autoregressive Integrated Moving Average (ARIMA) and Multiscale autoregressive (MAR). The characteristics of this model do not include predictor variables in the model. The MAR model is a model that performs the transformation process using wavelet. The MAR Model adopts an autoregressive (AR) time series model with predictors used are wavelet and scale coefficients. The wavelet and scale coefficients are obtained by decomposing using Maximal Overlap Discrete Wavelet Transformation (MODWT). MODWT functions to decipher data based on the level of each wavelet filter. This research aims to determine the best forecasting model using the ARIMA and MAR models. Testing performed on non-stationary data, so the ARIMA and MAR models can be used in this research. This research is expected to be able to obtain the best time series model and the most suitable to be used in predicting on non-stationary data.