This study uses the (partial) cross wavelet analysis and the phase difference to decompose the time frequency effects of oil prices on major aggregate macroeconomic fundamentals (real effective exchange rate index, interest rate yield spread and stock market index) of emerging market economies, aiming to discern the direction of the lead-lag relationship between these variables at different time scales over the period December 1987 to April 2017. Our results suggest that there is a strong coherence between oil prices and the individual components of the macroeconomic fundamentals at higher frequencies (0-1 years) in those economies. The phase difference analysis shows that the variables move within the phase for the widths of higher frequency bands (1-2 and 2-4 years), but it is difficult to ascertain the leading/lagging variables. As a robustness check, the results of the conditional analysis extend the significance of the coherency to 1-2 years. However, the phase difference of the robustness check indicates that oil prices and the macroeconomic fundamentals only move within the phase at lower frequency band widths (4-8 and 8-16 years). The existence of the time-varying comovement between the oil price and the aggregate macroeconomic fundamentals across heterogeneous time frequencies indicates that investors making decisions about their portfolio compositions and policy makers adjusting various economic stabilization schemes for greater stability should take account of varying frequency bands.