Indonesia’s Inflation Analysis Using Hybrid Fourier - Wavelet Multiscale Autoregressive Method

Abstract

Regression analysis is a statistical method to determine the relationship between predictor variables and response variables. Regression approach can be done with parametric and nonparametric approaches. The parametric approach is rigorous with assumptions and must fulfillthe assumptions to get a good model.Meanwhile, the nonparametric approach is not rigorous with assumptions because the method is based on an unknown curve shape approach. Nonparametric regression can be done with several approaches including Fourier and Wavelet methods. The Fourier method is a method based on cosine and sine series. It is very suitable for data that has repetitive or periodic patterns. The Fourier series modeling is less efficient because it requires many coefficients to obtain a good model and it is less able to handle data with sharp jumps. Recently, there has been a combination of two methods called hybrid methods that give better results. In this paper, Indonesia’s inflation data modelling is performed by using hybrid-wavelet. First, the data is modeled using Fourier with small K; then the error Fourier model is modeled by using multiscale waveletautoregressive. In this study, the value of Inflation in Indonesia was modeled from January 2007 to August 2017. The response variable was the inflation value, while the predictor variable was time. The Fourier method with K = 100 generated MSE of 0.846216 and R2 of 80.12%. The Fourier-Wavelet hybrid model with K = 1 generated MSE of 0.31 and R2 of 95%. So that in inflation modeling in Indonesia, the Fourier-Wavelet hybrid regression model generated a better model than the wavelet model with fewer parameters than the Fourier method.