Time series central subspace with covariates and its application to forecasting pine sawtimber stumpage prices in the Southern United States

To model and forecast a monthly pine sawtimber (PST) stumpage price, y_t , data collected across 11 southern states in the U.S., we adopt a new semiparametric approach where the first phase adopts a nonparametric method called “Time Series Central Subspace with Covariates” (TSCS-C) to extract sufficient information about y_t through a univariate time series {d_t} , which is a linear combination of a set of past values of y_t and a high dimensional covariate vector 𝐱_t of sale characteristics. Then, {d_t} alone is used as the predictor series to build a parametric nonlinear time series model for y_t . This yields a new semiparametric nonlinear time series model for y_t . Assessment in terms of out-of-sample forecasts of monthly PST stumpage prices show that our semiparametric model with the covariate 𝐱_t has the smallest average forecasting error compared to another semiparametric nonlinear time series model without 𝐱_t and two other parametric counterparts based on multiplicative seasonal autoregressive integrated moving average models with and without 𝐱_t . This data underscores the ability of our semiparametric approach to first reduce the dimensionality of 𝐱_t and a set of past values of y_t significantly using the TSCS-C nonparametric methodology and then to produce a superior nonlinear time series model.