Forecasting Non-Stationary Time Series with the Multiscale Autoregressive (MAR) Model Approach Using the Haar Wavelet Filter at the Rupiah Exchange Rate Against the Dollar

Abstract

Time series data is a collection of a phenomenon that occurs based on a fixed or at the same time index. Time series phenomena often exhibit non-stationary behavior. One of the time series analyses for non-stationary data is the Multiscale Autoregressive Model (MAR). The MAR model chosen is a model that meets the assumptions of normality and white noise. The predictors used in MAR modeling are wavelet coefficients and scales which are the result of decomposition using Maximal Overlap Discrete Wavelet Transform (MODWT), MODWT functions to decompose data based on the level of each wavelet filter (family). The wavelet filters used in this study are Haar. In this study, the model generated from the data that was stationary first was more accurate than the data that was not stationary first.