This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including exponential smoothing methods and moving averages. The bootstrap procedure is motivated by asymptotic arguments and provides well-calibrated uniform-in-time coverage, enabling scalable uncertainty quantification in streaming or large-scale time-series settings. This makes the method suitable for tasks such as adaptive anomaly detection, online monitoring, or streaming A/B testing. Simulation studies demonstrate good finite-sample performance of our method across a range of nonstationary scenarios. In summary, this offers a practical resampling framework that complements online trend estimation with reliable statistical inference.
This paper presents an algorithm for computing the GIC and the TIC of the nonstationary state-space models. The gradient and Hessian of the log-likelihood neccesary in computing the GIC are obtained by the differential filter that is derived by extending the Kalman filter. Three examples of the nonstationary time series models, i.e., the trend model, statndard seasonal adjustment model and the seasonal adjustment model with stationary AR component are presented to exemplified the specification of structural matrices.
The goodness of the long-term prediction in the state-space model was evaluated using the squared long-term prediction error. In order to estimate the model parameters suitable for long-term prediction, we devised a modified log-likelihood corresponding to the long-term prediction error variance. Trend models and seasonally adjusted models with and without AR component are examined as examples.
Information from frequency bands in biomedical time series provides useful summaries of the observed signal. Many existing methods consider summaries of the time series obtained over a few well-known, pre-defined frequency bands of interest. However, these methods do not provide data-driven methods for identifying frequency bands that optimally summarize frequency-domain information in the time series. A new method to identify partition points in the frequency space of a multivariate locally stationary time series is proposed. These partition points signify changes across frequencies in the ti…
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this paper, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad class of parameters under mild assumptions. The proposed framework covers all parameters which may be expressed as nonli…
The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the gradient and the Hessian matrix of the log-likelihood by extending the Kalman filter without resorting to the numerical difference. Different from the previous paper(Kitagawa 2020), it is assumed that the observation noise variance R=1. It is known that for univariate time series, by maximizing the log-likelihood of this restricted model, we can obtain the same es…
The Fourier Decomposition Method for nonlinear and nonstationary time series analysis
Indian Institute of Technology Delhi（德里印度理工学院）；Jaypee Institute of Information Technology（贾伊皮信息技术学院）；Samsung R & D Institute India - Delhi（三星印度研发中心-德里）
Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying second-order structure (of the differenced series). However, often we require inference on the second-order behaviour of the original series, for example, when performing trend estimation. In this article, we propose a method, using differencing, to jointly estimate the time-varying trend and second-order structure of a nonstationary time series, within the …
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonpara…
In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm (Bara…
A Structure-Preserving Assessment of VBPBB for Time Series Imputation Under Periodic Trends, Noise, and Missingness Mechanisms
Department of Epidemiology and Biostatistics, College of Integrated Health Sciences, University at Albany, State University of New York（纽约州立大学奥尔巴尼分校综合健康科学学院流行病学与生物统计系）；NYS Department of Health（纽约州卫生部）
Global Forecasting Models (GFM) that are trained across a set of multiple time series have shown superior results in many forecasting competitions and real-world applications compared with univariate forecasting approaches. One aspect of the popularity of statistical forecasting models such as ETS and ARIMA is their relative simplicity and interpretability (in terms of relevant lags, trend, seasonality, and others), while GFMs typically lack interpretability, especially towards particular time series. This reduces the trust and confidence of the stakeholders when making decisions based on the …
