Times Varying Spectral Coherence Examination of Consumer Price Indices in Pakistan: A Wavelet Transform

Aim of this study is to examine the coherence of consumer price indices (CPI) variants in Pakistan using time series data. The techniques of data analysis are descriptive statistics and wavelet analysis. Plots of CPI variants show more frequent changes as compared to the base year / month from January 1990 to January 2008 and comparatively minor fluctuation subsequently. Wavelet power spectra of CPI General Index (CPI-Gen), CPI Food MoM (CPI-FMoM), CPI General YoY (CPI-GenYoY), and CPI Food YoY (CPI-FYoY) show weak correlation between wavelets and mother wavelet at low frequency bands, and vice versa at high frequency bands in sample period. In CPI Food Index and CPI General MoM, there is very strong correlation between the mother and daughter wavelets. Cross wavelet spectra show that CPI-General vs CPI-Food, CPI General vs CPI General (YoY), and CPI Food vs CPI Food (YoY)) at low frequency bands have weak co-movements, whereas, that is strong at high frequency bands. Cross wavelet spectra of CPI-General vs. CPI General (MoM) and CPI-Food vs. CPI-Food (MoM, at high bands have very strong co-movement. Wavelet coherence spectra show that at low frequency bands there is high coherence and correlation among variables, whereas, that is relatively low at high frequency bands. Wavelet coherence spectra as contained of CPI-General vs. CPI General (MoM), and CPI-Food vs. CPI Food (MoM) at high frequency bands show very weak coherence and correlation and the results also show that both the variables are in phase at most of the frequency and time resolutions.