Journal of Time Series Analysis最新文献

{"title":"Local powers of least-squares-based test for panel fractional Ornstein–Uhlenbeck process","authors":"Katsuto Tanaka,&nbsp;Weilin Xiao,&nbsp;Jun Yu","doi":"10.1111/jtsa.12777","DOIUrl":"https://doi.org/10.1111/jtsa.12777","url":null,"abstract":"<p>In recent years, significant advancements have been made in the field of identifying financial asset price bubbles, particularly through the development of time-series unit-root tests featuring fractionally integrated errors and panel unit-root tests. This study introduces an innovative approach for assessing the sign of the persistence parameter (<span></span><math>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow></math>) within a panel fractional Ornstein-Uhlenbeck process, based on the least squares estimator of <span></span><math>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow></math>. This method incorporates three distinct test statistics based on the Hurst parameter (<span></span><math>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow></math>), which can take values in the range of <span></span><math>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow></math>, be equal to <span></span><math>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow></math>, or fall within the interval of <span></span><math>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow></math>. The null hypothesis corresponds to <span></span><math>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow></math>. Based on a panel of continuous records of observations, the null asymptotic distributions are obtained when the time span (<span></span><math>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 </mrow></math>) is fixed and the number of cross sections (<span></span><math>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow></math>) goes to infinity. The power function of the tests is obtained under the local alternative where <span></span><math>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 </mrow></math> is close to zero in the order of <span></span><math>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <msqrt>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 </msqrt>\u0000 <mo>)</mo>\u0000 </mrow></math>. This alternative covers the departure from the unit root hypothesis from the explosive side, enabling the calculation of lower power in bubble tests. The hypothesis testing problem and the local power function","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 5","pages":"997-1023"},"PeriodicalIF":1.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144767993","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":"Mixing properties of non-stationary multi-variate count processes","authors":"Zinsou Max Debaly,&nbsp;Michael H. Neumann,&nbsp;Lionel Truquet","doi":"10.1111/jtsa.12775","DOIUrl":"10.1111/jtsa.12775","url":null,"abstract":"<p>We consider multi-variate versions of two popular classes of integer-valued processes. While the transition mechanism is time-homogeneous, a possible non-stationarity is introduced by an exogeneous covariate process. We prove absolute regularity (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 </mrow>\u0000 <annotation>$$ beta $$</annotation>\u0000 </semantics></math>-mixing) for the count process with exponentially decaying mixing coefficients. The proof of this result makes use of some sort of contraction in the transition mechanism which allows a coupling of two versions of the count process such that they eventually coalesce. We show how this result can be used to prove asymptotic normality of a least squares estimator of an involved model parameter.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"552-581"},"PeriodicalIF":1.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249582","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":"Mean-preserving rounding integer-valued ARMA models","authors":"Christian H. Weiß,&nbsp;Fukang Zhu","doi":"10.1111/jtsa.12774","DOIUrl":"10.1111/jtsa.12774","url":null,"abstract":"<p>In the past four decades, research on count time series has made significant progress, but research on <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℤ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{Z} $$</annotation>\u0000 </semantics></math>-valued time series is relatively rare. Existing <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℤ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{Z} $$</annotation>\u0000 </semantics></math>-valued models are mainly of autoregressive structure, where the use of the rounding operator is very natural. Because of the discontinuity of the rounding operator, the formulation of the corresponding model identifiability conditions and the computation of parameter estimators need special attention. It is also difficult to derive closed-form formulae for crucial stochastic properties. We rediscover a stochastic rounding operator, referred to as mean-preserving rounding, which overcomes the above drawbacks. Then, a novel class of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ℤ</mi>\u0000 </mrow>\u0000 <annotation>$$ mathbb{Z} $$</annotation>\u0000 </semantics></math>-valued ARMA models based on the new operator is proposed, and the existence of stationary solutions of the models is established. Stochastic properties including closed-form formulae for (conditional) moments, autocorrelation function, and conditional distributions are obtained. The advantages of our novel model class compared to existing ones are demonstrated. In particular, our model construction avoids identifiability issues such that maximum likelihood estimation is possible. A simulation study is provided, and the appealing performance of the new models is shown by several real-world data sets.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"530-551"},"PeriodicalIF":1.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206452","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":"Forecasting the yield curve: the role of additional and time-varying decay parameters, conditional heteroscedasticity, and macro-economic factors","authors":"João F. Caldeira,&nbsp;Werley C. Cordeiro,&nbsp;Esther Ruiz,&nbsp;André A.P. Santos","doi":"10.1111/jtsa.12769","DOIUrl":"10.1111/jtsa.12769","url":null,"abstract":"<p>In this article, we analyse the forecasting performance of several parametric extensions of the popular Dynamic Nelson–Siegel (DNS) model for the yield curve. Our focus is on the role of additional and time-varying decay parameters, conditional heteroscedasticity, and macroeconomic variables. We also consider the role of several popular restrictions on the dynamics of the factors. Using a novel dataset of end-of-month continuously compounded Treasury yields on US zero-coupon bonds and frequentist estimation based on the extended Kalman filter, we show that a second decay parameter does not contribute to better forecasts. In concordance with the preferred habitat theory, we also show that the best forecasting model depends on the maturity. For short maturities, the best performance is obtained in a heteroscedastic model with a time-varying decay parameter. However, for long maturities, neither the time-varying decay nor the heteroscedasticity plays any role, and the best forecasts are obtained in the basic DNS model with the shape of the yield curve depending on macroeconomic activity. Finally, we find that assuming non-stationary factors is helpful in forecasting at long horizons.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 2","pages":"258-285"},"PeriodicalIF":1.2,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12769","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206451","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":"Weighted discrete ARMA models for categorical time series","authors":"Christian H. Weiß,&nbsp;Osama Swidan","doi":"10.1111/jtsa.12773","DOIUrl":"10.1111/jtsa.12773","url":null,"abstract":"<p>A new and flexible class of ARMA-like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so-called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>φ</mi>\u0000 </mrow>\u0000 <annotation>$$ varphi $$</annotation>\u0000 </semantics></math>-mixing solution as well as closed-form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite-sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real-world data application.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"505-529"},"PeriodicalIF":1.2,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12773","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206453","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":"Improved estimation of dynamic models of conditional means and variances","authors":"Weining Wang,&nbsp;Jeffrey M. Wooldridge,&nbsp;Mengshan Xu","doi":"10.1111/jtsa.12770","DOIUrl":"10.1111/jtsa.12770","url":null,"abstract":"<p>Using ‘working’ assumptions on conditional third and fourth moments of errors, we propose a method of moments estimator that can have improved efficiency over the popular Gaussian quasi-maximum likelihood estimator (GQMLE). Higher-order moment assumptions are not needed for consistency – we only require the first two conditional moments to be correctly specified – but the optimal instruments are derived under these assumptions. The working assumptions allow both asymmetry in the distribution of the standardized errors as well as fourth moments that can be smaller or larger than that of the Gaussian distribution. The approach is related to the generalized estimation equations (GEE) approach – which seeks the improvement of estimators of the conditional mean parameters by making working assumptions on the conditional second moments. We derive the asymptotic distribution of the new estimator and show that it does not depend on the estimators of the third and fourth moments. A simulation study shows that the efficiency gains over the GQMLE can be non-trivial.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"458-490"},"PeriodicalIF":1.2,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12770","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206454","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":"Estimating lagged (cross-)covariance operators of Lp-m-approximable processes in Cartesian product Hilbert spaces","authors":"Sebastian Kühnert","doi":"10.1111/jtsa.12772","DOIUrl":"10.1111/jtsa.12772","url":null,"abstract":"<p>Estimating parameters of functional ARMA, GARCH and invertible processes requires estimating lagged covariance and cross-covariance operators of Cartesian product Hilbert space-valued processes. Asymptotic results have been derived in recent years, either less generally or under a strict condition. This article derives upper bounds of the estimation errors for such operators based on the mild condition <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}^p $$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math>-approximability for each lag, Cartesian power(s) and sample size, where the two processes can take values in different spaces in the context of lagged cross-covariance operators. Implications of our results on eigen elements and parameters in functional AR(MA) models are also discussed.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"582-595"},"PeriodicalIF":1.2,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12772","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206455","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":"Self-normalization inference for linear trends in cointegrating regressions","authors":"Cheol-Keun Cho","doi":"10.1111/jtsa.12771","DOIUrl":"10.1111/jtsa.12771","url":null,"abstract":"&lt;p&gt;In this article, statistical tests concerning the trend coefficient in cointegrating regressions are addressed for the case when the stochastic regressors have deterministic linear trends. The self-normalization (SN) approach is adopted for developing inferential methods in the integrated and modified ordinary least squares (IMOLS) estimation framework. Two different self-normalizers are used to construct the SN test statistics: a functional of the recursive IMOLS estimators and a functional of the IMOLS residuals. These two self-normalizers produce two SN tests, denoted by &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;SN&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ϵ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {T}^{mathrm{SN}}left(epsilon right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &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;τ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;δ&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;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;η&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;^&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⊥&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {tau}_{delta_1}left({hat{eta}}_T^{perp}right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; respectively. Neither test requires studentization with a heteroskedasticity and autocorrelation consistent (HAC) estimator. A trimming parameter &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"491-504"},"PeriodicalIF":1.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12771","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206456","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":"The Granger–Johansen representation theorem for integrated time series on Banach space","authors":"Phil Howlett,&nbsp;Brendan K. Beare,&nbsp;Massimo Franchi,&nbsp;John Boland,&nbsp;Konstantin Avrachenkov","doi":"10.1111/jtsa.12766","DOIUrl":"10.1111/jtsa.12766","url":null,"abstract":"<p>We prove an extended Granger–Johansen representation theorem (GJRT) for finite- or infinite-order integrated autoregressive time series on Banach space. We assume only that the resolvent of the autoregressive polynomial for the series is analytic on and inside the unit circle except for an isolated singularity at unity. If the singularity is a pole of finite order the time series is integrated of the same order. If the singularity is an essential singularity the time series is integrated of order infinity. When there is no deterministic forcing the value of the series at each time is the sum of an almost surely convergent stochastic trend, a deterministic term depending on the initial conditions and a finite sum of embedded white noise terms in the prior observations. This is the extended GJRT. In each case the original series is the sum of two separate autoregressive time series on complementary subspaces – a singular component which is integrated of the same order as the original series and a regular component which is not integrated. The extended GJRT applies to all integrated autoregressive processes irrespective of the spatial dimension, the number of stochastic trends and cointegrating relations in the system and the order of integration.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"432-457"},"PeriodicalIF":1.2,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12766","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206457","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":"Dependence properties of stochastic volatility models","authors":"Piotr Kokoszka,&nbsp;Neda Mohammadi,&nbsp;Haonan Wang","doi":"10.1111/jtsa.12765","DOIUrl":"10.1111/jtsa.12765","url":null,"abstract":"<p>The concepts of physical dependence and approximability have been extensively used over the past two decades to quantify nonlinear dependence in time series. We show that most stochastic volatility models satisfy both dependence conditions, even if their realizations take values in abstract Hilbert spaces, thus covering univariate, multi-variate and functional models. Our results can be used to apply to general stochastic volatility models a multitude of inferential procedures established for Bernoulli shifts.</p>","PeriodicalId":49973,"journal":{"name":"Journal of Time Series Analysis","volume":"46 3","pages":"421-431"},"PeriodicalIF":1.2,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jtsa.12765","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206458","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}