In this paper, we investigate the short run and long run causal relationship between wholesale price index (WPI) and consumer price index (CPI) in India over the period from 1994 April to 2015 August. Using a linear cointegration and a nonlinear time series model of threshold cointegration with asymmetric error correction model and spectral Granger causality approach, the study attempts to find the linear and nonlinear cointegration relationship between WPI and CPI in India. Empirical results reveal the non-existence of linear cointegration between the WPI and CPI indices in India. Moreover, using consistent threshold autoregressive (C-TAR) and consistent momentum threshold autoregressive (CM-TAR) model, we find the evidence of non-linear cointegration between WPI and CPI in India over the period from 1994 to 2015. The consistent M-TAR model indicates the presence of threshold cointegration between WPI and CPI, which further suggests the consistent inflationary trends after 1995 in India due to rising per capita income and other macroeconomic indicators. Furthermore, results indicate that WPI and CPI are cointegrated with threshold error correction adjustment, and the adjustment towards long-run equilibrium is asymmetric. This further suggests that WPI and CPI respond differently to positive and negative deviations from the long-run equilibrium after the threshold level. Empirical results further indicate that adjustment towards long-run equilibrium tends to persist more for negative deviations and respond more quickly towards positive deviations. The spectral granger causality results do not reveal the causality from WPI to CPI. However, the Granger causality from the asymmetric error correction model reveals the unidirectional causality, which indicates that CPI Granger causes WPI, support the demand-push inflation in India. CPI Granger causes WPI at very low and high frequencies, which takes an average wavelength of more than 3.6 quarters time in a year. Furthermore, empirical results reveal that WPI and CPI reach equilibrium asymmetrically after the threshold level of the two percentages. In sum, results suggest that the Indian policymakers can emphasis on the demand side rather than supply-side inflation to control the level of inflation after the desired threshold level. Moreover, the central bank of India would give importance to control the unwarranted inflationary trend, which has been caused due to the CPI-based demand-side inflation.