Journal of Time Series Analysis最新文献

{"title":"The Continuous-Time Limit of Quasi Score-Driven Volatility Models","authors":"Yinhao Wu,&nbsp;Ping He","doi":"10.1111/jtsa.12848","DOIUrl":"https://doi.org/10.1111/jtsa.12848","url":null,"abstract":"<div>\u0000 \u0000 <p>This article explores the continuous-time limit of a class of quasi score-driven (QSD) models that characterize volatility. As the sampling frequency increases and the time interval tends to zero, the model weakly converges to a continuous-time stochastic volatility model where the two Brownian motions are correlated, thereby capturing the leverage effect in the market. Subsequently, we identify that a necessary condition for nondegenerate correlation is that the distribution of driving innovations differs from that of computing score, and at least one being asymmetric. We then illustrate this with two typical examples. As an application, the QSD model is used as an approximation for correlated stochastic volatility diffusions and quasi maximum likelihood estimation is performed. Simulation results confirm the method's effectiveness, particularly in estimating the correlation coefficient.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"924-938"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719284","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":"Noising the GARCH Volatility: A Random Coefficient GARCH Model","authors":"Abdelhakim Aknouche,&nbsp;Bader Almohaimeed,&nbsp;Stefanos Dimitrakopoulos","doi":"10.1111/jtsa.70009","DOIUrl":"https://doi.org/10.1111/jtsa.70009","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper proposes a noisy GARCH model with two volatility sequences (an unobserved and an observed/predictive one) and a stochastic time-varying conditional kurtosis. The unobserved volatility equation, equipped with random coefficients, is a linear function of the past squared observations and of the past predictive volatility. The predictive volatility is the conditional mean of the unobserved volatility, thus following the standard GARCH specification, where its coefficients are equal to the means of the random coefficients. The means and the variances of the random coefficients, as well as the unobserved volatilities, are estimated using a three-stage procedure. First, we estimate the means of the random coefficients using the Gaussian quasi-maximum likelihood estimator (QMLE), then the variances of the random coefficients, using a weighted least squares estimator (WLSE), and finally the latent volatilities through a volatility filtering process under the assumption that the random parameters follow an Inverse Gaussian distribution, with the innovation being normally distributed. Hence, the conditional distribution of the model is the Normal Inverse Gaussian (NIG), which entails a closed form expression for the posterior mean of the unobserved volatility and of the random coefficients. Consistency and asymptotic normality of the QMLE and WLSE are established under quite tractable assumptions. The proposed methodology is illustrated with various simulated and real examples. It is shown that the filtered volatility can improve both in-sample and out-of-sample forecasts of the predictive volatility, even when the future observations are unknown and are replaced by their predictions.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"1028-1043"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719211","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":"Testing for Unspecified Periodicities in Binary Time Series","authors":"Finn Schmidtke,&nbsp;Mathias Vetter","doi":"10.1111/jtsa.70004","DOIUrl":"https://doi.org/10.1111/jtsa.70004","url":null,"abstract":"&lt;p&gt;Given random variables &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&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;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;…&lt;/mi&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;/mrow&gt;\u0000 &lt;annotation&gt;$$ {Y}_1,dots, {Y}_n $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&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;i&lt;/mi&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;mn&gt;0&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;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {Y}_iin left{0,1right} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; we test the hypothesis whether the underlying success probabilities &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {p}_i $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are constant or whether they are periodic with an unspecified period length of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mo&gt;≥&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ rge 2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The test relies on an auxiliary integer &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ d $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; which can be chosen arbitrarily, using which a new time series of length &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ d $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is constructed. For this new time series, the test statistic is derived acc","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"984-997"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719226","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":"Permutation Testing for Monotone “Trend”","authors":"Joseph P. Romano,&nbsp;Marius A. Tirlea","doi":"10.1111/jtsa.12850","DOIUrl":"https://doi.org/10.1111/jtsa.12850","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we consider the fundamental problem of testing for monotone trend in a time series. While the term “trend” is commonly used and has an intuitive meaning, it is first crucial to specify its exact meaning in a hypothesis testing context. A commonly used well-known test is the Mann-Kendall test, which we show does not offer Type 1 error control even in large samples. On the other hand, by an appropriate studentization of the Mann-Kendall statistic, we construct permutation tests that offer asymptotic error control quite generally, but retain the exactness property of permutation tests for i.i.d. observations. We also introduce “local” Mann-Kendall statistics as a means of testing for local rather than global trend in a time series. Similar properties of permutation tests are obtained for these tests as well.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"952-966"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719293","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":"Editorial Announcement","authors":"Robert Taylor","doi":"10.1111/jtsa.70077","DOIUrl":"https://doi.org/10.1111/jtsa.70077","url":null,"abstract":"<p>I am delighted to welcome Professor Tommaso Proietti to the editorial board of the <i>Journal of Time Series Analysis</i>, with effect from 1 July 2026.</p><p>Tommaso is Professor of Economic Statistics at the University of Rome Tor Vergata, Italy. He holds a Ph.D. in Statistics from the University of London and previously held positions at the Universities of Perugia, Udine, and Sydney. He is a Senior Fellow at The Rimini Centre for Economic Analysis and a Fellow of Econometric Reviews. His research interests are centred in the analysis of economic and climatological time series. He has served on the editorial boards of several journals, including the <i>International Journal of Forecasting, Econometrics and Statistics, and the International Statistical Review</i>.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70077","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719274","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":"Adaptive Estimation for Weakly Dependent Functional Times Series","authors":"Hassan Maissoro,&nbsp;Valentin Patilea,&nbsp;Myriam Vimond","doi":"10.1111/jtsa.70006","DOIUrl":"https://doi.org/10.1111/jtsa.70006","url":null,"abstract":"<p>We propose adaptive mean and autocovariance function estimators for stationary functional time series under <span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>𝕃</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <mi>m</mi>\u0000 </mrow></math>-approximability assumptions. These estimators are designed to adapt to the regularity of the curves and to accommodate both sparse and dense data designs. The sample paths are observed with error at possibly random design points. Data-driven local bandwidths are selected by minimizing explicit quadratic risk bounds that exploit the local regularity of the process. As a first step, we introduce a local regularity estimator and derive a nonasymptotic concentration bound for it. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"1013-1027"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719309","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 Conditional Tail Expectation Type Risk Measure for Time Series","authors":"Yuri Goegebeur,&nbsp;Armelle Guillou,&nbsp;Jing Qin","doi":"10.1111/jtsa.12853","DOIUrl":"https://doi.org/10.1111/jtsa.12853","url":null,"abstract":"&lt;p&gt;We consider the estimation of the conditional expectation &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝔼&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;h&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&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;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&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;p&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, provided &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;𝔼&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;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;&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, at extreme levels, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&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;t&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;t&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;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {left({X}_tright)}_{tin mathbb{Z}} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a strictly stationary time series, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;U&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {U}_X $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"967-983"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12853","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719188","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":"Nonlinear Wavelet Threshold Estimation of Time-Varying Covariance Matrices in a Log-Euclidean Manifold","authors":"Gabriel Bailly,&nbsp;Rainer von Sachs","doi":"10.1111/jtsa.70011","DOIUrl":"https://doi.org/10.1111/jtsa.70011","url":null,"abstract":"<div>\u0000 \u0000 <p>We tackle the problem of estimating time-varying covariance matrices (TVCM; i.e., covariance matrices with entries being time-dependent curves) whose elements show inhomogeneous smoothness over time (e.g., pronounced local peaks). To address this challenge, wavelet denoising estimators are particularly appropriate. Specifically, we model TVCM using a signal-noise model within the Riemannian manifold of symmetric positive definite matrices (endowed with the log-Euclidean metric) and use the intrinsic wavelet transform, designed for curves in Riemannian manifolds. Within this non-Euclidean framework, the proposed estimators preserve positive definiteness. Although linear wavelet estimators for smooth TVCM achieve good results in various scenarios, they are less suitable if the underlying curve features singularities. Consequently, our estimator is designed around a nonlinear thresholding scheme, tailored to the characteristics of the noise in covariance matrix regression models. The effectiveness of this novel nonlinear scheme, equipped with a variety of new intrinsic thresholding rules, is assessed by deriving mean-squared error consistency and by numerical simulations, and its practical application is demonstrated on TVCM of electroencephalography (EEG) data showing abrupt transients over time.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"1044-1065"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719292","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 Deviations From the White Noise Assumption for Non-Stationary Time Series","authors":"Patrick Bastian","doi":"10.1111/jtsa.70005","DOIUrl":"https://doi.org/10.1111/jtsa.70005","url":null,"abstract":"<p>We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time series. Second, we address the problem that a white noise test is usually not performed because one believes in this hypothesis, but because one thinks that the white noise hypothesis may be approximately true. A classical example is checking the residuals of a model fit, because one suspects that a postulated model describes the unknown relation well. This reflects a meanwhile classical paradigm of Box (1976) that “all models are wrong but some are useful”. We address this point of view by investigating if the maximum deviation of the local autocovariance functions from 0 exceeds a given threshold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Δ</mi>\u0000 </mrow>\u0000 <annotation>$$ Delta $$</annotation>\u0000 </semantics></math> that can either be specified by the user or chosen in a data-dependent way. The formulation of the problem in this form raises several mathematical challenges, which do not appear when one is testing the classical white noise hypothesis. We use high-dimensional Gaussian approximations for dependent data to furnish a bootstrap test, prove its validity, and showcase its performance on both synthetic and real data. In particular, we inspect log returns of stock prices and show that our approach reflects some observations of Fama (1970) regarding the efficient market hypothesis.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"998-1012"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.70005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148719321","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":"Modeling Nonstationary Time Series Using Locally Stationary Basis Processes","authors":"Shreyan Ganguly,&nbsp;Peter F. Craigmile","doi":"10.1111/jtsa.70015","DOIUrl":"10.1111/jtsa.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be an unrealistic assumption. We define a class of locally stationary processes, which can lead to more accurate uncertainty quantification over making an invalid assumption of stationarity. This class of processes assumes the model parameters to be time-varying and parameterizes them in terms of a transformation of basis functions that ensures that the processes are locally stationary. We develop methods and theory for parameter estimation in this class of models, and propose a test that allows us to examine certain departures from stationarity. We assess our methods using simulation studies and apply these techniques to the analysis of an electroencephalogram time series.</p>\u0000 </div>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"47 5","pages":"1066-1082"},"PeriodicalIF":1.2,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148354664","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}