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A note on Johansen's rank conditions and the Jordan form of a matrix 关于Johansen秩条件和矩阵的Jordan形式的注记
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-10-28 DOI: 10.1111/jtsa.12789
Massimo Franchi
{"title":"A note on Johansen's rank conditions and the Jordan form of a matrix","authors":"Massimo Franchi","doi":"10.1111/jtsa.12789","DOIUrl":"https://doi.org/10.1111/jtsa.12789","url":null,"abstract":"<p>This note presents insights on the Jordan structure of a matrix which are derived from an extension of the <span></span><math>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow></math> and <span></span><math>\u0000 <mrow>\u0000 <mi>I</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow></math> conditions in Johansen (1996). It is first observed that these conditions not only characterize, as it is well known, the size (1 or 2) of the largest Jordan block in the Jordan form of the companion matrix but more generally the geometric multiplicities, the algebraic multiplicities and the whole Jordan structure for eigenvalues of index 1 or 2. In the context of the Granger representation theorem, this means that the Johansen rank conditions do more than determine the order of integration of the process. It is then shown that an extension of these conditions leads to the characterization of the Jordan structure of any matrix.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"796-805"},"PeriodicalIF":1.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12789","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273166","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}
引用次数: 0
Estimation for conditional moment models based on martingale difference divergence 基于鞅差分散度的条件矩模型估计
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-10-27 DOI: 10.1111/jtsa.12788
Kunyang Song, Feiyu Jiang, Ke Zhu
{"title":"Estimation for conditional moment models based on martingale difference divergence","authors":"Kunyang Song,&nbsp;Feiyu Jiang,&nbsp;Ke Zhu","doi":"10.1111/jtsa.12788","DOIUrl":"https://doi.org/10.1111/jtsa.12788","url":null,"abstract":"<p>We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD). Our MDD-based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the existing estimation methods in this framework, the MDD-based estimation method adopts a non-integrable weighting function, which could capture more information from unconditional moment restrictions than the integrable weighting function to enhance the estimation efficiency. Due to the nature of shift-invariance in MDD, our MDD-based estimation method can not identify the intercept parameters. To overcome this identification issue, we further provide a two-step estimation procedure for the model with intercept parameters. Under regularity conditions, we establish the asymptotics of the proposed estimators, which are not only easy-to-implement with expectation-based asymptotic variances, but also applicable to time series data with an unspecified form of conditional heteroskedasticity. Finally, we illustrate the usefulness of the proposed estimators by simulations and two real examples.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"727-747"},"PeriodicalIF":1.2,"publicationDate":"2024-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273209","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}
引用次数: 0
A new heteroskedasticity-robust test for explosive bubbles 爆炸性气泡的异方差鲁棒性新试验
IF 1 4区 数学
Journal of Time Series Analysis Pub Date : 2024-10-17 DOI: 10.1111/jtsa.12784
David I. Harvey, Stephen J. Leybourne, A. M. Robert Taylor, Yang Zu
{"title":"A new heteroskedasticity-robust test for explosive bubbles","authors":"David I. Harvey,&nbsp;Stephen J. Leybourne,&nbsp;A. M. Robert Taylor,&nbsp;Yang Zu","doi":"10.1111/jtsa.12784","DOIUrl":"https://doi.org/10.1111/jtsa.12784","url":null,"abstract":"<p>We propose a new class of modified regression-based tests for detecting asset price bubbles designed to be robust to the presence of general forms of both conditional and unconditional heteroskedasticity in the price series. This modification, based on the approach developed in Beare (2018) in the context of conventional unit root testing, is achieved by purging the impact of unconditional heteroskedasticity from the data using a kernel estimate of volatility before the application of the bubble detection methods proposed in Phillips, Shi and Yu (2015) (PSY). The modified statistic is shown to achieve the same limiting null distribution as the corresponding (heteroskedasticity-uncorrected) statistic from PSY would obtain under homoskedasticity, such that the usual critical values provided in PSY may still be used. Versions of the test based on regressions including either no intercept or a (redundant) intercept are considered. Representations for asymptotic local power against a single bubble model are also derived. Monte Carlo simulation results highlight that neither one of these tests dominates the other across different bubble locations and magnitudes, and across different models of time-varying volatility. Accordingly, we also propose a test based on a union of rejections between the with- and without-intercept variants of the modified PSY test. The union procedure is shown to perform almost as well as the better of the constituent tests for a given DGP, and also performs very well compared to existing heteroskedasticity-robust tests across a large range of simulation DGPs.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 5","pages":"846-866"},"PeriodicalIF":1.0,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12784","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767984","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}
引用次数: 0
Local quadratic spectral and covariance matrix estimation 局部二次谱和协方差矩阵估计
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-10-01 DOI: 10.1111/jtsa.12783
Tucker McElroy, Dimitris N. Politis
{"title":"Local quadratic spectral and covariance matrix estimation","authors":"Tucker McElroy,&nbsp;Dimitris N. Politis","doi":"10.1111/jtsa.12783","DOIUrl":"https://doi.org/10.1111/jtsa.12783","url":null,"abstract":"<p>The problem of estimating the spectral density matrix <span></span><math>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>w</mi>\u0000 <mo>)</mo>\u0000 </mrow></math> of a multi-variate time series is revisited with special focus on the frequencies <span></span><math>\u0000 <mrow>\u0000 <mi>w</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow></math> and <span></span><math>\u0000 <mrow>\u0000 <mi>w</mi>\u0000 <mo>=</mo>\u0000 <mi>π</mi>\u0000 </mrow></math>. Recognizing that the entries of the spectral density matrix at these two boundary points are real-valued, we propose a new estimator constructed from a local polynomial regression of the real portion of the multi-variate periodogram. The case <span></span><math>\u0000 <mrow>\u0000 <mi>w</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow></math> is of particular importance, since <span></span><math>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow></math> is associated with the large-sample covariance matrix of the sample mean; hence, estimating <span></span><math>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow></math> is crucial to conduct any sort of statistical inference on the mean. We explore the properties of the local polynomial estimator through theory and simulations, and discuss an application to inflation and unemployment.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"674-691"},"PeriodicalIF":1.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273222","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}
引用次数: 0
Local Whittle estimation in time-varying long memory series 时变长记忆序列的局部Whittle估计
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-10-01 DOI: 10.1111/jtsa.12782
Josu Arteche, Luis F. Martins
{"title":"Local Whittle estimation in time-varying long memory series","authors":"Josu Arteche,&nbsp;Luis F. Martins","doi":"10.1111/jtsa.12782","DOIUrl":"https://doi.org/10.1111/jtsa.12782","url":null,"abstract":"<p>The memory parameter is usually assumed to be constant in traditional long memory time series. We relax this restriction by considering the memory a time-varying function that depends on a finite number of parameters. A time-varying Local Whittle estimator of these parameters, and hence of the memory function, is proposed. Its consistency and asymptotic normality are shown for locally stationary and locally non-stationary long memory processes, where the spectral behaviour is restricted only at frequencies close to the origin. Its good finite sample performance is shown in a Monte Carlo exercise and in two empirical applications, highlighting its benefits over the fully parametric Whittle estimator proposed by Palma and Olea (2010). Standard inference techniques for the constancy of the memory are also proposed based on this estimator.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"647-673"},"PeriodicalIF":1.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12782","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273223","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}
引用次数: 0
Testing for a bubble with a stochastically varying explosive coefficient 具有随机变化爆炸系数的气泡试验
IF 1 4区 数学
Journal of Time Series Analysis Pub Date : 2024-09-27 DOI: 10.1111/jtsa.12768
Eiji Kurozumi, Mikihito Nishi
{"title":"Testing for a bubble with a stochastically varying explosive coefficient","authors":"Eiji Kurozumi,&nbsp;Mikihito Nishi","doi":"10.1111/jtsa.12768","DOIUrl":"https://doi.org/10.1111/jtsa.12768","url":null,"abstract":"<p>In this article, we test for a bubble in a model with a random explosive autoregressive coefficient. We consider two local alternatives and find that versions of recursive stochastic unit root tests are more powerful when facing a randomly explosive process than the recursive right-tailed ADF tests, whereas the latter performs better in a model with a non-stochastic coefficient. We then propose the union of rejections strategy using the recursive right-tailed ADF and stochastic unit root tests. We examine the finite sample properties of the proposed tests using Monte Carlo simulations and observe that the test based on the union of rejections strategy is the second-best, and its power is close to the best one in most cases.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 5","pages":"945-965"},"PeriodicalIF":1.0,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12768","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144768011","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}
引用次数: 0
Simultaneous inference of a partially linear model in time series 时间序列中部分线性模型的同时推理
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-09-26 DOI: 10.1111/jtsa.12781
Jiaqi Li, Likai Chen, Kun Ho Kim, Tianwei Zhou
{"title":"Simultaneous inference of a partially linear model in time series","authors":"Jiaqi Li,&nbsp;Likai Chen,&nbsp;Kun Ho Kim,&nbsp;Tianwei Zhou","doi":"10.1111/jtsa.12781","DOIUrl":"https://doi.org/10.1111/jtsa.12781","url":null,"abstract":"<p>We introduce a new methodology to conduct simultaneous inference of the non-parametric component in partially linear time series regression models where the non-parametric part is a multi-variate unknown function. In particular, we construct a simultaneous confidence region (SCR) for the multi-variate function by extending the high-dimensional Gaussian approximation to dependent processes with continuous index sets. Our results allow for a more general dependence structure compared to previous works and are widely applicable to a variety of linear and non-linear autoregressive processes. We demonstrate the validity of our proposed methodology by examining the finite-sample performance in the simulation study. Finally, an application in time series, the forward premium regression, is presented, where we construct the SCR for the foreign exchange risk premium from the exchange rate and macroeconomic data.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"623-646"},"PeriodicalIF":1.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273559","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}
引用次数: 0
Generalized covariance-based inference for models set-identified from independence restrictions 基于广义协方差的模型集独立识别推理
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-09-24 DOI: 10.1111/jtsa.12779
Christian Gourieroux, Joann Jasiak
{"title":"Generalized covariance-based inference for models set-identified from independence restrictions","authors":"Christian Gourieroux,&nbsp;Joann Jasiak","doi":"10.1111/jtsa.12779","DOIUrl":"https://doi.org/10.1111/jtsa.12779","url":null,"abstract":"<p>This article develops statistical inference methods for a class of set-identified models, where the errors are known functions of observations and the parameters satisfy either serial or/and cross-sectional independence conditions. This class of models includes the independent component analysis (ICA), Structural Vector Autoregressive (SVAR), and multi-variate mixed causal–non-causal models. We use the Generalized Covariance (GCov) estimator to compute the residual-based portmanteau statistic for testing the error independence hypothesis. Next, we build the confidence sets for the identified sets of parameters by inverting the test statistic. We also discuss the choice (design) of these statistics. The approach is illustrated by simulations examining the under-identification condition in an ICA model and an application to financial return series.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 2","pages":"300-324"},"PeriodicalIF":1.2,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12779","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143253402","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}
引用次数: 0
On buffered moving average models 在缓冲移动平均模型上
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-09-20 DOI: 10.1111/jtsa.12778
Yipeng Zhuang, Dong Li, Philip L. H. Yu, Wai Keung Li
{"title":"On buffered moving average models","authors":"Yipeng Zhuang,&nbsp;Dong Li,&nbsp;Philip L. H. Yu,&nbsp;Wai Keung Li","doi":"10.1111/jtsa.12778","DOIUrl":"https://doi.org/10.1111/jtsa.12778","url":null,"abstract":"<p>There has been growing interest in extending the popular threshold time series models to include a buffer zone for regime transition. However, almost all attention has been on buffered autoregressive models. Note that the classical moving average (MA) model plays an equally important role as the autoregressive model in classical time series analysis. It is therefore natural to extend our investigation to the buffered MA (BMA) model. We focus on the first-order BMA model while extending to more general MA model should be direct in principle. The proposed model shares the piecewise linear structure of the threshold model, but has a more flexible regime switching mechanism. Its probabilistic structure is studied to some extent. A nonlinear least squares estimation procedure is proposed. Under some standard regularity conditions, the estimator is strongly consistent and the estimator of the coefficients is asymptotically normal when the parameter of the boundary of the buffer zone is known. A portmanteau goodness-of-fit test is derived. Simulation results and empirical examples are carried out and lend further support to the usefulness of the BMA model and the asymptotic results.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 4","pages":"599-622"},"PeriodicalIF":1.2,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144273158","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}
引用次数: 0
Non-causal and non-invertible ARMA models: Identification, estimation and application in equity portfolios 非因果和非可逆 ARMA 模型：股票投资组合中的识别、估计和应用
IF 1.2 4区 数学
Journal of Time Series Analysis Pub Date : 2024-09-18 DOI: 10.1111/jtsa.12776
Alain Hecq, Daniel Velasquez-Gaviria
{"title":"Non-causal and non-invertible ARMA models: Identification, estimation and application in equity portfolios","authors":"Alain Hecq,&nbsp;Daniel Velasquez-Gaviria","doi":"10.1111/jtsa.12776","DOIUrl":"10.1111/jtsa.12776","url":null,"abstract":"<p>The mixed causal-non-causal invertible-non-invertible autoregressive moving-average (MARMA) models have the advantage of incorporating roots inside the unit circle, thus adjusting the dynamics of financial returns that depend on future expectations. This article introduces new techniques for estimating, identifying and simulating MARMA models. Although the estimation of the parameters is done using second-order moments, the identification relies on the existence of high-order dynamics, captured in the high-order spectral densities and the correlation of the squared residuals. A comprehensive Monte Carlo study demonstrated the robust performance of our estimation and identification methods. We propose an empirical application to 24 portfolios from emerging markets based on the factors: size, book-to-market, profitability, investment and momentum. All portfolios exhibited forward-looking behavior, showing significant non-causal and non-invertible dynamics. Moreover, we found the residuals to be uncorrelated and independent, with no trace of conditional volatility.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 2","pages":"325-352"},"PeriodicalIF":1.2,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12776","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249549","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}
引用次数: 0
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