Mixed causal–noncausal autoregressions with exogenous regressors
提出一种包含外生回归变量的混合因果-非因果自回归模型（MARX），推导了非高斯密度下参数的渐近分布，并通过模拟评估模型选择过程，用于分析汇率和工业生产指数对商品价格的影响。
Summary Mixed causal–noncausal autoregressive (MAR) models have been proposed to model time series exhibiting nonlinear dynamics. Possible exogenous regressors are typically substituted into the error term to maintain the MAR structure of the dependent variable. We introduce a representation including these covariates called MARX to study their direct impact. The asymptotic distribution of the MARX parameters is derived for a class of non‐Gaussian densities. For a Student likelihood, closed‐form standard errors are provided. By simulations, we evaluate the MARX model selection procedure using information criteria. We examine the influence of the exchange rate and industrial production index on commodity prices.