Forecasting Peru’s GDP Growth and Inflation Using TVP-VARMA-SV Models

This paper evaluates the forecasting performance of the time-varying parameter VARMA model with stochastic volatility (TVP-VARMA-SV) of Chan and Eisenstat (2017) for Peru’s GDP growth and inflation over 1994Q1–2019Q4. Seven model specifications are compared using density and point forecast evaluation metrics. The main results show that models with a movingaverage (MA) component generally deliver better forecast performance. Log predictive likelihoods (LPLs) indicate that models with MA, stochastic volatility (SV), or both components provide the best density forecasts at the one-quarter horizon, while simpler VARMA models perform better at the four-quarter horizon. Mean squared forecast errors (MSFEs) and Theil’s U are also lowest for models with an MA component. Probability integral transformation (PIT) histograms show that models with MA and SV components achieve the best calibration at the one-quarter horizon, while raw-moments tests indicate that the TVP-VARMA-SV, VARMA, VAR, and Bayesian model selection (BMS) specifications perform best at the four-quarter horizon. The model confidence set (MCS) frequently includes simpler models, particularly those with an MA term, and Diebold-Mariano tests also tend to favor models with an MA component. Overall, the BMS strategy improves forecast accuracy by dynamically selecting the best-performing models. An extension to exchange rate growth forecasts shows that MA-based models again perform best, with the TVP-VARMA-SV specification delivering the largest gains at the four-quarter horizon. Palabras claves: Modelo VARMA con parámetros cambiantes; Volatilidad estocástica; Estimación Bayesiana; Predicción; Perú. JEL Classification-JE: C11, C22, C32, F47