Journal of Time Series Analysis最新文献

{"title":"Testing covariance separability for continuous functional data","authors":"Holger Dette,&nbsp;Gauthier Dierickx,&nbsp;Tim Kutta","doi":"10.1111/jtsa.12764","DOIUrl":"10.1111/jtsa.12764","url":null,"abstract":"<p>Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multi-variate functions. Here, the covariance can be so complex that just saving a non-parametric estimate is impractical and structural assumptions are necessary to tame the model. One popular assumption for space-time data is separability of the covariance into purely spatial and temporal factors. In this article, we present a new test for separability in the context of dependent functional time series. While most of the related work studies functional data in a Hilbert space of square integrable functions, we model the observations as objects in the space of continuous functions equipped with the supremum norm. We argue that this (mathematically challenging) setup enhances interpretability for users and is more in line with practical preprocessing. Our test statistic measures the maximal deviation between the estimated covariance kernel and a separable approximation. Critical values are obtained by a non-standard multiplier bootstrap for dependent data. We prove the statistical validity of our approach and demonstrate its practicability in a simulation study and a data example.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"402-420"},"PeriodicalIF":1.2,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12764","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941411","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":"General estimation results for tdVARMA array models","authors":"Abdelkamel Alj,&nbsp;Rajae Azrak,&nbsp;Guy Mélard","doi":"10.1111/jtsa.12761","DOIUrl":"10.1111/jtsa.12761","url":null,"abstract":"<p>The article will focus on vector autoregressive-moving average (VARMA) models with time-dependent coefficients (td) to represent general nonstationary time series, not necessarily Gaussian. The coefficients depend on time, possibly on the length of the series <span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>, hence the name tdVARMA<span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo> </mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> for the models, but not necessarily on the rescaled time <span></span><math>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>/</mo>\u0000 <mi>n</mi>\u0000 </mrow></math>. As a consequence of the dependency on <span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math> of the model, we need to consider array processes instead of stochastic processes. Under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is consistent in probability and asymptotically normal. The theoretical results are illustrated using three examples of bivariate processes, the first two with marginal heteroscedasticity. The first example is a tdVAR<span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo> </mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math>(1) process while the second example is a tdVMA<span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo> </mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math>(1) process. In these two cases, the finite-sample behavior is checked via a Monte Carlo simulation study. The results are compatible with the asymptotic properties even for small <span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>. A third example shows the application of the tdVARMA<span></span><math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mo> </mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> models for a real time series.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"137-151"},"PeriodicalIF":1.2,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864063","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":"Estimating a common break point in means for long-range dependent panel data","authors":"Daiqing Xi,&nbsp;Cheng-Der Fuh,&nbsp;Tianxiao Pang","doi":"10.1111/jtsa.12763","DOIUrl":"10.1111/jtsa.12763","url":null,"abstract":"<p>In this article, we study a common break point in means for panel data with cross-sectional dependence through unobservable common factors, in which the observations are long-range dependent over time and are heteroscedastic and may have different degrees of dependence across panels. First, we adopt the least squares method without taking the data features into account to estimate the common break point and to see how the data features affect the asymptotic behaviors of the estimator. Then, an iterative least squares estimator of the common break point which accounts for the common factors in the estimation procedure is examined. Our theoretical results reveal that: (1) There is a trade-off between the overall break magnitude of the panel data and the long-range dependence for both estimators. (2) The second estimation procedure can eliminate the effects of common factors from the asymptotic behaviors of the estimator successfully, but it cannot improve the rate of convergence of the estimator in most cases. Moreover, Monte Carlo simulations are given to illustrate the theoretical results on finite-sample performance.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"181-209"},"PeriodicalIF":1.2,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738816","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":"A trinomial difference autoregressive process for the bounded \u0000 \u0000 ℤ\u0000 -valued time series","authors":"Huaping Chen,&nbsp;Zifei Han,&nbsp;Fukang Zhu","doi":"10.1111/jtsa.12762","DOIUrl":"10.1111/jtsa.12762","url":null,"abstract":"<p>This article tackles the modeling challenge of bounded <span></span><math>\u0000 <mrow>\u0000 <mi>ℤ</mi>\u0000 </mrow></math>-valued time series by proposing a novel trinomial difference autoregressive process. This process not only maintains the autocorrelation structure presenting in the classical binomial GARCH model, but also facilitates the analysis of bounded <span></span><math>\u0000 <mrow>\u0000 <mi>ℤ</mi>\u0000 </mrow></math>-valued time series with negative or positive correlation. We verify the stationarity and ergodicity of the couple process (comprising both the observed process and its conditional mean process) while also presenting several stochastic properties. We further discuss the conditional maximum likelihood estimation and establish their asymptotic properties. The effectiveness of these estimators is assessed through simulation studies, followed by the application of the proposed models to two real datasets.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"152-180"},"PeriodicalIF":1.2,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141610983","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":"Bootstrapping non-stationary and irregular time series using singular spectral analysis","authors":"Don S. Poskitt","doi":"10.1111/jtsa.12759","DOIUrl":"10.1111/jtsa.12759","url":null,"abstract":"<p>This article investigates the consequences of using Singular Spectral Analysis (SSA) to construct a time series bootstrap. The bootstrap replications are obtained via a SSA decomposition obtained using rescaled trajectories (RT-SSA), a procedure that is particularly useful in the analysis of time series that exhibit nonlinear, non-stationary and intermittent or transient behaviour. The theoretical validity of the RT-SSA bootstrap when used to approximate the sampling properties of a general class of statistics is established under regularity conditions that encompass a very broad range of data generating processes. A smeared and a boosted version of the RT-SSA bootstrap are also presented. Practical implementation of the bootstrap is considered and the results are illustrated using stationary, non-stationary and irregular time series examples.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"81-112"},"PeriodicalIF":1.2,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12759","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549046","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":"Selecting the number of factors in multi-variate time series","authors":"Angela Caro,&nbsp;Daniel Peña","doi":"10.1111/jtsa.12760","DOIUrl":"10.1111/jtsa.12760","url":null,"abstract":"<p>How many factors are there? It is a critical question that researchers and practitioners deal with when estimating factor models. We proposed a new eigenvalue ratio criterion for the number of factors in static approximate factor models. It considers a pooled squared correlation matrix which is defined as a weighted combination of the main observed squared correlation matrices. Theoretical results are given to justify the expected good properties of the criterion, and a Monte Carlo study shows its good finite sample performance in different scenarios, depending on the idiosyncratic error structure and factor strength. We conclude comparing different criteria in a forecasting exercise with macroeconomic data.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"113-136"},"PeriodicalIF":1.2,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12760","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511250","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":"Estimation of non-smooth non-parametric estimating equations models with dependent data","authors":"Francesco Bravo","doi":"10.1111/jtsa.12758","DOIUrl":"10.1111/jtsa.12758","url":null,"abstract":"<p>This article considers estimation of non-smooth possibly overidentified non-parametric estimating equations models with weakly dependent data. The estimators are based on a kernel smoothed version of the generalized empirical likelihood and the generalized method of moments approaches. The article derives the asymptotic normality of both estimators and shows that the proposed local generalized empirical likelihood estimator is more efficient than the local generalized moment estimator unless a two-step procedure is used. The article also proposes novel tests for the correct specification of the considered model that are shown to have power against local alternatives and are consistent against fixed alternatives. Monte Carlo simulations and an empirical application illustrate the finite sample properties and applicability of the proposed estimators and test statistics.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"59-80"},"PeriodicalIF":1.2,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141383025","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 the extent of instability in nearly unstable processes","authors":"Marie Badreau,&nbsp;Frédéric Proïa","doi":"10.1111/jtsa.12751","DOIUrl":"10.1111/jtsa.12751","url":null,"abstract":"&lt;p&gt;This article deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to autoregressive processes where the bridge between stability and instability is expressed by means of time-varying coefficients. The process we consider has a companion matrix &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;&lt;/math&gt; with spectral radius &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;mo&gt;&lt;&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; satisfying &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ρ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;mo&gt;→&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, a situation described as ‘nearly-unstable’. The question we investigate is: given an observed path supposed to come from a nearly unstable process, is it possible to test for the ‘extent of instability’, i.e. to test how close we are to the unit root? In this regard, we develop a strategy to evaluate &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; and to test for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℋ&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;/mrow&gt;&lt;/math&gt; : ‘&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&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;/mrow&gt;&lt;/math&gt;’ against &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℋ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 ","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 1","pages":"33-58"},"PeriodicalIF":1.2,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12751","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141189682","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":"Estimation for Markov Chains with Periodically Missing Observations","authors":"Ursula U. Müller,&nbsp;Anton Schick,&nbsp;Wolfgang Wefelmeyer","doi":"10.1111/jtsa.12747","DOIUrl":"10.1111/jtsa.12747","url":null,"abstract":"<p>When we observe a stationary time series with observations missing at periodic time points, we can still estimate its marginal distribution well, but the dependence structure of the time series may not be recoverable at all, or the usual estimators may have much larger variance than in the fully observed case. We show how non-parametric estimators can often be improved by adding unbiased estimators. We focus on a simple setting, first-order Markov chains on a finite state space, and an observation pattern in which a fixed number of consecutive observations is followed by an observation gap of fixed length, say workdays and weekends. The new estimators perform astonishingly well in some cases, as illustrated with simulations. The approach extends to continuous state space and to higher-order Markov chains.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"45 6","pages":"1006-1019"},"PeriodicalIF":1.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12747","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059171","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":"Fractional stochastic volatility model","authors":"Shuping Shi,&nbsp;Xiaobin Liu,&nbsp;Jun Yu","doi":"10.1111/jtsa.12749","DOIUrl":"10.1111/jtsa.12749","url":null,"abstract":"<p>This article introduces a discrete-time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous-time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time-domain log-likelihood function calculated by the importance sampling technique, and a frequency-domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&amp;P 500 composite index over a sample period spanning 45 years.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 2","pages":"378-397"},"PeriodicalIF":1.2,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12749","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141059316","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}