A Time-Varying Conditional Parameter Distributed Lag Model with an Application to Crude Oil Market

This paper proposes a new time-varying parameter distributed lag (DL) model. In contrast to the existing methods, which assume parameters to be random walks or regime shifts, our method allows time-varying coefficients of lagged explanatory variables to be conditional on past information. Furthermore, a test for constant-parameter DL model is introduced. The model is then applied to examine time-varying causal effect of inventory on crude oil price and forecast weekly crude oil price. Time-varying causal effect of US commercial crude oil inventory on crude oil price return is presented. In particular, the causal effect of inventory is occasionally positive, which is contrary to some previous research. It's also shown that the proposed model yields the best in and out-of-sample performances compared to seven alternative models including RW, ARMA, VAR, DL, autoregressive-distributed lag (ADL), time-varying parameter ADL (TVP-ADL) and DCB (dynamic conditional beta) models.