Semiparametric Modeling of Consumer Price Index

Abstract

Many classical data, for example, exchange rate, stock price, and consumer price index (CPI) data cannot be analyzed under independent observation assumption. In addition, some time series data cannot be modeled well into a fully linear model, for instance, CPI, price of raw materials for some certain industries and price of some industrial products data in which monetary crisis of Indonesia in 1998 has caused a dramatic effect on the time series of CPI, price of raw materials and industrial products. A semiparametric model is a mixture model between parametric and nonparametric models. If we apply it to time series data, we will obtain a semiparametric time series model known as partly linear autoregressive model:  y₁= β y_t-1 + g ( y_t-2 ,..., y_t-p ) + ε_t for t > p + 1. Here β is an unknown parameter to be estimated, g(.) is an unknown function in R^p-1 , ε_t are i.i.d. random errors with E ( ε₁ ) = 0 and E ( ε_1² ) < ∞, and ε_t are independent of y_s for all s = 1 , 2 ,..., p and t > p + 1 . Based on the model above, we investigate a model for general consumer price index (GCPI) of Jember data recorded monthly from January 1998 to December 2002 by Statistic Center Bureau of Jember.