The paper is about an approach for parametric inference on instantaneously transformed stationary processes. The paper discusses the asymptotics of the Whittle estimator of the parameters involved and also provides the explicit expression of the asymptotic covariance matrix which does not necessarily require the innovation Gaussianity assumption. As a specific instantaneous transformation, the paper introduces a new version of the Box-Cox transformation and investigates in detail the vector ARMA processes implemented by that transformation, proposing a computation-intensive procedure for parametric estimation and testing. As a computationally feasible test not relying upon the knowledge of the explicit analytic form of the asymptotic covariance matrix or on the information equality, the paper proposes a Monte Carlo Wald test, providing illustrative simulation and real-data examples.
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机译：这篇论文是关于瞬时转换平稳过程的参数推断的一种方法。本文讨论了所涉及参数的Whittle估计的渐近性，并提供了渐近协方差矩阵的明确表示，而不一定需要创新高斯假设。作为特定的瞬时转换，本文介绍了Box-Cox转换的新版本，并详细研究了由该转换实现的矢量ARMA流程，提出了用于参数估计和测试的计算密集型过程。作为一种在计算上不依赖于渐近协方差矩阵的显式解析形式的知识或信息均等性的可行测试，本文提出了蒙特卡洛·沃尔德（Monte Carlo Wald）检验，提供了说明性的仿真和实际数据示例。
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