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.

中文翻译：

---

具有协变量的时间序列中心子空间及其在预测美国南部松木锯材立木价格中的应用

为了对美国11个南部州收集的松木锯材（PST）每月立木价格\（y_t \）进行建模和预测，我们采用一种新的半参数方法，其中第一阶段采用一种称为“时间序列中央子空间”的非参数方法与协变量”（TSCS-C）来通过单变量时间序列\（\ {d_t \} \）提取关于\（y_t \）的足够信息，该时间序列是一组过去的\（y_t \）值的线性组合以及销售特征的高维协变量向量\（{{\ mathbf {x}}} _ t \）。然后，单独使用\（\ {d_t \} \）作为预测变量序列，以建立\（y_t \）的参数非线性时间序列模型。这为\（y_t \）产生了一个新的半参数非线性时间序列模型。根据每月PST跌幅价格的样本外预测进行评估，结果表明，与另一个半参数非线性时间序列相比，带有协变量\（{{\ mathbf {x}}} _ t \）的半参数模型的平均预测误差最小不具有\（{{\ mathbf {x}}} _ t \）和两个其他参数对等模型的模型，它们基于具有和不具有\（{{\ mathbf {x}}} _ t \）的乘积季节自回归积分移动平均模型。此数据强调了我们的半参数方法首先降低\（{{\ mathbf {x}}} _ t \）的维数和一组过去值\（y_t \）的能力。 大量使用TSCS-C非参数方法，然后生成一个卓越的非线性时间序列模型。