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

Abstract

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 $${{\mathbf {x}}}_t$$ 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 $${{\mathbf {x}}}_t$$ has the smallest average forecasting error compared to another semiparametric nonlinear time series model without $${{\mathbf {x}}}_t$$ and two other parametric counterparts based on multiplicative seasonal autoregressive integrated moving average models with and without $${{\mathbf {x}}}_t$$ . This data underscores the ability of our semiparametric approach to first reduce the dimensionality of $${{\mathbf {x}}}_t$$ 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.