Journal of Time Series Analysis最新文献

{"title":"Some recent trends in embeddings of time series and dynamic networks","authors":"Dag Tjøstheim,&nbsp;Martin Jullum,&nbsp;Anders Løland","doi":"10.1111/jtsa.12677","DOIUrl":"10.1111/jtsa.12677","url":null,"abstract":"<p>We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal components for time series, the literature on time-varying nonlinear embedding is rather sparse. The most promising approaches in the literature is neural network based, and has recently performed well in forecasting competitions. We also touch on different forms of dynamics in topological data analysis (TDA). The last part of the article deals with embedding of dynamic networks, where we believe there is a gap between available theory and the behavior of most real world networks. We illustrate our review with two simulated examples. Throughout the review, we highlight differences between the static and dynamic case, and point to several open problems in the dynamic case.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 5-6","pages":"686-709"},"PeriodicalIF":0.9,"publicationDate":"2023-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46354498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Factor models for high-dimensional functional time series I: Representation results","authors":"Marc Hallin,&nbsp;Gilles Nisol,&nbsp;Shahin Tavakoli","doi":"10.1111/jtsa.12676","DOIUrl":"10.1111/jtsa.12676","url":null,"abstract":"<p>In this article, which consists of two parts (Part I: representation results; Part II: estimation and forecasting methods), we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). In Part I, we establish a representation result stating that, under mild assumptions on the covariance operator of the cross-section, we can represent each FTS as the sum of a common component driven by scalar factors loaded via functional loadings, and a mildly cross-correlated idiosyncratic component. Our model and theory are developed in a general Hilbert space setting that allows for mixed panels of functional and scalar time series. We then turn, in Part II, to the identification of the number of factors, and the estimation of the factors, their loadings, and the common components. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well-established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common components, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number <math>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow></math> of series and the number <math>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow></math> of time observations diverge thus extend to the functional context the ‘blessing of dimensionality’ that explains the success of factor models in the analysis of high-dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide a finer understanding of the interplay between   <math>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow></math> and <math>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow></math> for estimation purposes. We conclude with an application to forecasting mortality curves, where we demonstrate that our approach outperforms existing methods.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 5-6","pages":"578-600"},"PeriodicalIF":0.9,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43248757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Factor models for high-dimensional functional time series II: Estimation and forecasting","authors":"Shahin Tavakoli,&nbsp;Gilles Nisol,&nbsp;Marc Hallin","doi":"10.1111/jtsa.12675","DOIUrl":"10.1111/jtsa.12675","url":null,"abstract":"<p>This article is the second one in a set of two laying the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). Part I establishes a representation result by which, under mild assumptions on the covariance operator of the cross-section, any FTS admits a canonical representation as the sum of a common and an idiosyncratic component; common components are driven by a finite and typically small number of scalar factors loaded via functional loadings, while idiosyncratic components are only mildly cross-correlated. Building on that representation result, Part II is dealing with the identification of the number of factors, their estimation, the estimation of their loadings and the common components, and the resulting forecasts. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well-established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common components, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number <math>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow></math> of series and the number <math>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow></math> of time points diverge thus extend to the functional context the ‘blessing of dimensionality’ that explains the success of factor models in the analysis of high-dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide a finer understanding of the interplay between <math>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow></math> and <math>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow></math> for estimation purposes. We conclude with an application to forecasting mortality curves, where our approach outperforms existing methods.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 5-6","pages":"601-621"},"PeriodicalIF":0.9,"publicationDate":"2022-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42515220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Detecting relevant changes in the spatiotemporal mean function","authors":"Holger Dette,&nbsp;Pascal Quanz","doi":"10.1111/jtsa.12674","DOIUrl":"10.1111/jtsa.12674","url":null,"abstract":"&lt;p&gt;For a spatiotemporal process &lt;math&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;&lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;…&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;&lt;/math&gt;, where &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; denotes the set of spatial locations and &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; the time domain, we consider the problem of testing for a change in the sequence of mean functions &lt;math&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;∣&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;…&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;&lt;/math&gt;. In contrast to most of the literature, we are not interested in arbitrarily small changes but only in changes with a norm exceeding a given threshold. Asymptotically distribution free tests are proposed, which do not require the estimation of the long-run spatiotemporal covariance structure. In particular, we consider a fully functional approach and a test based on the cumulative sum paradigm, investigate the large sample properties of the corresponding test statistics and stu","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 5-6","pages":"505-532"},"PeriodicalIF":0.9,"publicationDate":"2022-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12674","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41321936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Editorial Announcement: Journal of Time Series Analysis Distinguished Authors 2022","authors":"Robert Taylor","doi":"10.1111/jtsa.12673","DOIUrl":"10.1111/jtsa.12673","url":null,"abstract":"<p>In recognition of authors who have made significant contributions to this Journal, the <i>Journal of Time Series Analysis</i> runs a scheme to honour those authors by naming them as a <i>Journal of Time Series Analysis Distinguished Author</i>. The qualifying criterion for this award is 3.5 points where authors are awarded 1 point for each single-authored article, ½ point for each double-authored article, 1/3 point for each triple-authored article, and so on, that they have published in the <i>Journal of Time Series Analysis</i> since its inception. Distinguished Authors are entitled to a one-year free on-line subscription to the Journal to mark the award, and will also receive a certificate commemorating the award.</p><p>In addition to the lists of Distinguished Authors announced previously in Volume 41 issue 4 (July 2020), Volume 42 Issue 1 (January 2021) and Volume 43 Issue 1 (January 2022), the <i>Journal of Time Series Analysis</i> is very pleased to welcome (in alphabetical order):</p><p>Francesco Bravo,</p><p>Evangelos E. Ioannidis,</p><p>Piotr Kokoszka,</p><p>Dong Li,</p><p>and</p><p>Pierre Perron</p><p>to the list of <i>Journal of Time Series Analysis Distinguished Authors</i> for 2022 based on their publications in the Journal appearing up to and including Volume 43 Issue 6 (November 2022).</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 1","pages":"3"},"PeriodicalIF":0.9,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12673","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49535149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the asymptotic behavior of bubble date estimators","authors":"Eiji Kurozumi,&nbsp;Anton Skrobotov","doi":"10.1111/jtsa.12672","DOIUrl":"10.1111/jtsa.12672","url":null,"abstract":"<p>In this study, we extend the three-regime bubble model of Pang et al. (2021, <i>Journal of Econometrics</i>, 221(1):227–311) to allow the forth regime followed by the unit root process after recovery. We provide the asymptotic and finite sample justification of the consistency of the collapse date estimator in the two-regime AR(1) model. The consistency allows us to split the sample before and after the date of collapse and to consider the estimation of the date of exuberation and date of recovery separately. We have also found that the limiting behavior of the recovery date varies depending on the extent of explosiveness and recovering.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 4","pages":"359-373"},"PeriodicalIF":0.9,"publicationDate":"2022-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12672","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49449711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On highly skewed fractional log-stable noise sequences and their application","authors":"Harry Pavlopoulos,&nbsp;George Chronis","doi":"10.1111/jtsa.12671","DOIUrl":"10.1111/jtsa.12671","url":null,"abstract":"&lt;p&gt;Considering log-LFSN (log-linear fractional stable noise) sequences &lt;math&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Y&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;ℤ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;&lt;/math&gt;, driven by non-Gaussian one-sided LFSN &lt;math&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;ℤ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;&lt;/math&gt; with constant skewness intensity &lt;math&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;, for any &lt;math&gt;\u0000 &lt;mi&gt;δ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;&lt;/math&gt; and &lt;math&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;&lt;/math&gt;, we show that the auto-covariance function (ACVF) &lt;math&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;γ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 4","pages":"337-358"},"PeriodicalIF":0.9,"publicationDate":"2022-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12671","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48740120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to the article “Regular multidimensional stationary time series”","authors":"Tamás Szabados","doi":"10.1111/jtsa.12670","DOIUrl":"10.1111/jtsa.12670","url":null,"abstract":"&lt;p&gt;In Theorem 2.1 which was the main result of the article it was implicitly assumed that for any regular &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;-dimensional weakly stationary time series &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; of rank &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, there exists an analytic spectral factor &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Φ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;z&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; of the form &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Φ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msqrt&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;π&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msqrt&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;˜&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, where &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Λ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; is the &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 3","pages":"331-332"},"PeriodicalIF":0.9,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12670","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47948551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"System identification using autoregressive Bayesian neural networks with nonparametric noise models","authors":"Christos Merkatas,&nbsp;Simo Särkkä","doi":"10.1111/jtsa.12669","DOIUrl":"10.1111/jtsa.12669","url":null,"abstract":"<p>System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks, which leads to flexible uncertainty quantification. Hamiltonian Monte Carlo sampler within a Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in real time series.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 3","pages":"319-330"},"PeriodicalIF":0.9,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12669","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49302262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A nonparametric predictive regression model using partitioning estimators based on Taylor expansions","authors":"Jose Olmo","doi":"10.1111/jtsa.12668","DOIUrl":"10.1111/jtsa.12668","url":null,"abstract":"<p>This article proposes a nonparametric predictive regression model. The unknown function modeling the predictive relationship is approximated using polynomial Taylor expansions applied over disjoint intervals covering the support of the predictor variable. The model is estimated using the theory on partitioning estimators that is extended to a stationary time series setting. We show pointwise and uniform convergence of the proposed estimator and derive its asymptotic normality. These asymptotic results are applied to test for the presence of predictive ability. We develop an asymptotic pointwise test of predictive ability using the critical values of a Normal distribution, and a uniform test with asymptotic distribution that is approximated using a <i>p</i>-value transformation and Wild bootstrap methods. These theoretical insights are illustrated in an extensive simulation exercise and also in an empirical application to forecasting high-frequency based realized volatility measures. Our results provide empirical support to the presence of nonlinear autoregressive predictability of these measures for the constituents of the Dow Jones index.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"44 3","pages":"294-318"},"PeriodicalIF":0.9,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41718162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}