Synergy Between Classical Econometrics and Machine Learning in Forecasting Pakistan's Consumer Price Index

Forecasting an administratively compiled consumer price index exposes the standing division in the forecasting profession with unusual clarity. Classical econometric specifications deliver interpretable parameters and honest confidence intervals but revert to the mean of the differenced series faster than an inflation episode actually unwinds; machine learning specifications track the non-linear acceleration but return point forecasts with no standard error worth the name. This paper proposes and tests a synergy that assigns each tradition the task it is built for. The monthly Pakistan Consumer Price Index, August 1991 to February 2025 (T = 402), is decomposed by Ensemble Empirical Mode Decomposition into three intrinsic mode functions; a power spectral density rule routes each mode to a stochastic or a deterministic sub block on the share of its energy lying below a low frequency threshold; an ARIMA front end absorbs the linear dependence within each sub-block; and the pooled residual is handed to an LSTM or an XGBoost residual learner whose hyperparameters are selected by Bayesian optimisation against a held out validation loss. Eleven candidate specifications are estimated on a seventy per cent fixed-origin estimation window and compared on the remaining thirty per cent under mean absolute error, root mean squared error, symmetric mean absolute percentage error and the Diebold Mariano test. The results depict that synergy has minimum loss functions instead of stand alone conventional and machine learning models.