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We examine the relationship between two inflation indices, consumer price index (CPI) and producer price index (PPI) for Mexico, a case study country which has successfully implemented inflation targeting after the economic crisis and high inflationary situation in 1995. Since the causality running from PPI to CPI exemplifies the cost push nature of inflation and the opposite is the indicator of demand pull inflation, this analysis could provide significant policy implications. We contribute to the literature by decomposing the time–frequency relationship between CPI and PPI through continuous wavelet approach. Our results indicate a bidirectional relationship between CPI and PPI. In short periods (1 to 7 months scale) CPI is leading PPI, while for longer periods (8 to 32 months scale) PPI is the leading variable.