Journal of Time Series Analysis最新文献

In many organizations, accurate forecasts are essential for making informed decisions in a variety of applications, from inventory management to staffing optimization. Whatever forecasting model is used, changes in the underlying process can lead to inaccurate forecasts, which will be damaging to decision-making. At the same time, models are becoming increasingly complex, and identifying change through direct modeling is problematic. We present a novel framework for online monitoring of forecasts to ensure they remain accurate. By utilizing sequential changepoint techniques on the forecast errors, our framework allows for the real-time identification of potential changes in the process caused by various external factors. We show theoretically that some common changes in the underlying process will manifest in the forecast errors and can be identified faster by identifying shifts in the forecast errors than within the original modeling framework. Moreover, we demonstrate the effectiveness of this framework on numerous forecasting approaches through simulations and show its effectiveness over alternative approaches. Finally, we present two concrete examples, one from Royal Mail parcel delivery volumes and one from NHS A&E admissions relating to gallstones.

In this paper, we propose a new test for the detection of a change in a non-linear (auto-)regressive time series as well as a corresponding estimator for the unknown time point of the change. To this end, we consider an at-most-one-change model and approximate the unknown (auto-)regression function by a neural network with one hidden layer. It is shown that the test has asymptotic power of one for a wide range of alternatives, not restricted to changes in the mean of the time series. Furthermore, we prove that the corresponding estimator converges to the true change point with the optimal rate $��{�O�}_{�P�}�(�1�/�n�)�$ and derive the asymptotic distribution. Some simulations illustrate the behavior of the estimator with a special focus on the misspecified case, where the true regression function is not given by a neural network. Finally, we apply the estimator to some financial data.

The analysis of time-indexed functional data plays an important role in the field of business and economic statistics. In the literature, statistical inference for functional time series often involves reducing the dimension of functional data to a finite dimension $��K�$, followed by the use of tools from multivariate analysis. The effectiveness of such an approach hinges on certain assumptions that are difficult to check in practice, and also, the results can be sensitive to the choice of $��K�$. In this article, we propose a fully functional approach based on sample splitting and illustrate it for several testing problems, including one and two-sample mean testing and change point testing. Asymptotic properties of the new test statistics are derived under both the null and local alternatives in the general setting of Hilbert space-valued time series. Simulation studies and a real data example are also presented to demonstrate the encouraging finite sample performance of the proposed tests.

We propose a nonparametric portmanteau test for detecting changes in the unconditional mean of a univariate time series which may display either long or short memory. Our approach is designed to have power against, among other things, cases where the mean component of the series displays abrupt level shifts, deterministic trending behaviour, or is subject to some form of time-varying, continuous change. The test we propose is simple to compute, being based on ratios of periodogram ordinates, has a pivotal limiting null distribution of known form which reduces to the multiple of a $��{�\chi �}_{�2�}^{�2�}�$ random variable in the case where the series is short memory, and has power against a wide class of time-varying mean models. A Monte Carlo simulation study into the finite sample behaviour of the test shows it to have both good size properties under the null for a range of long and short memory series and to exhibit good power against a variety of plausible time-varying mean alternatives. Because of its simplicity, we recommend our periodogram ratio test as a routine portmanteau test for whether the mean component of a time series can reasonably be treated as constant.

We develop a new method to detect change points in the distribution of functional data based on integrated CUSUM processes of empirical characteristic functionals. Asymptotic results are presented under conditions allowing for low-order moments and serial dependence in the data establishing the limiting null-distribution of the proposed test statistics, as well as their consistency to detect and localize change points in the distribution of functional data. A key consideration in defining these test statistics is the measure used to integrate the CUSUM process over function space. We show that using a measure generated by Brownian motion leads to generally consistent tests. Further, using this measure allows for computationally simple approximations of the necessary integrals, as well as simulation and permutation-based methods to calibrate detection thresholds for change point analysis. The proposed methods are thoroughly investigated and compared to other existing functional data change point methods in simulation experiments, and are further applied to detect change points in models for continuous electricity demand and high-frequency asset price returns.

Panels of random functions are common in applications of functional data analysis. They often occur when sequences of functions are observed at a number of different locations. We propose a methodology to monitor for structural breaks in such panels and to identify the changing components with statistical certainty. Our approach relies on a Full-CUSUM statistic that has proved to be powerful in finite dimensions but has not been applied to functional data. To account for the practically relevant problem of sparsity, we formulate our results for triangular arrays of nonstationary, sparse estimators. The derivation of our asymptotic theory relies on new Gaussian approximations on the Banach space of continuous functions, which imply new convergence results for the change point detectors. We illustrate our approach with a simulation study and application to intraday returns on exchange traded funds.

This paper proposes a moving sum methodology for detecting multiple change points in high-dimensional time series under a factor model, where changes are attributed to those in loadings as well as emergence or disappearance of factors. We establish the asymptotic null distribution of the proposed test for family-wise error control and show the consistency of the procedure for multiple change point estimation. Simulation studies and an application to a large dataset of volatilities demonstrate the competitive performance of the proposed method.

We consider the problem of sequential (online) estimation of a single change point in a piecewise linear regression model under a Gaussian setup. We demonstrate that certain CUSUM-type statistics attain the minimax optimal rates for localizing the change point. Our minimax analysis unveils an interesting phase transition from a jump (discontinuity in function values) to a kink (a change in slope). Specifically, for a jump, the minimax rate is of order $��\log �\left(�n�\right)�/�n�$, whereas for a kink it scales as $��{�\left(�\log �\left(�n�\right)�/�n�\right)�}^{�1�/�3�}�$, given that the sampling rate is of order $��1�/�n�$. We further introduce an online algorithm based on these detectors, which optimally identifies both a jump and a kink, and is able to distinguish between them. Notably, the algorithm operates with constant computational complexity and requires only constant memory per incoming sample. Finally, we evaluate the empirical performance of our method on both simulated and real-world data sets. An implementation is available in the R package FLOC on GitHub.