Model identification via total Frobenius norm of multivariate spectra

IF 3.1 1区数学 Q1 STATISTICS & PROBABILITY

Journal of the Royal Statistical Society Series B-Statistical Methodology Pub Date : 2023-03-31 DOI:10.1093/jrsssb/qkad012

Tucker S McElroy, Anindya Roy

引用次数: 0

Abstract

Abstract We study the integral of the Frobenius norm as a measure of the discrepancy between two multivariate spectra. Such a measure can be used to fit time series models, and ensures proximity between model and process at all frequencies of the spectral density. We develop new asymptotic results for linear and quadratic functionals of the periodogram, and apply the integrated Frobenius norm to fit time series models and test whether model residuals are white noise. The case of structural time series models is addressed, wherein co-integration rank testing is formally developed. Both applications are studied through simulation studies and time series data. The numerical results show that the proposed estimator can fit moderate- to large-dimensional structural timeseries in real time.

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多元光谱的总Frobenius范数模型辨识

摘要研究了Frobenius范数的积分作为两个多元谱之间差异的度量。这种方法可以用于拟合时间序列模型，并确保在谱密度的所有频率上模型和过程之间的接近性。我们对周期图的线性函数和二次函数给出了新的渐近结果，并应用积分Frobenius范数拟合时间序列模型，检验模型残差是否为白噪声。讨论了结构时间序列模型的情况，其中协整秩检验是正式开发的。通过模拟研究和时间序列数据对这两种应用进行了研究。数值结果表明，该估计器可以实时拟合中维到大维结构时间序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Royal Statistical Society Series B-Statistical Methodology 数学-统计学与概率论

CiteScore

8.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Series B (Statistical Methodology) aims to publish high quality papers on the methodological aspects of statistics and data science more broadly. The objective of papers should be to contribute to the understanding of statistical methodology and/or to develop and improve statistical methods; any mathematical theory should be directed towards these aims. The kinds of contribution considered include descriptions of new methods of collecting or analysing data, with the underlying theory, an indication of the scope of application and preferably a real example. Also considered are comparisons, critical evaluations and new applications of existing methods, contributions to probability theory which have a clear practical bearing (including the formulation and analysis of stochastic models), statistical computation or simulation where original methodology is involved and original contributions to the foundations of statistical science. Reviews of methodological techniques are also considered. A paper, even if correct and well presented, is likely to be rejected if it only presents straightforward special cases of previously published work, if it is of mathematical interest only, if it is too long in relation to the importance of the new material that it contains or if it is dominated by computations or simulations of a routine nature.