论文检索

函数型数据序列周期图的最大值AI 解读

We study the periodogram operator of a sequence of functional data. Using recent advances in Gaussian approximation theory, we derive the asymptotic distribution of the maximum norm over all fundamental frequencies. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Our theory can be used for detecting periodic signals in functional time series when the length of the period is unknown. We demonstrate…

函数型时间序列的周期性检验AI 解读

We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully…

动态函数主成分AI 解读

Summary We address the problem of dimension reduction for time series of functional data (Xt:t∈Z). Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each X t represents one intraday curve. We argue that functional principal component analysis, though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time…

平稳函数型时间序列的预测AI 解读

This article addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical tractability and the current lack of advanced functional time series methodology. It is shown here how standard multivariate prediction techniques can be used in this context. The connection between functional and multivariate predictions is…

弱依赖函数型数据AI 解读

Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time series, and the central issue in the analysis of such data consists in taking into account the temporal dependence of these functional observations. Examples include daily curves of financial transaction data and daily patterns of geophysical…

多元时间序列模型协方差结构的突变检测AI 解读

In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric…