Tryphon T. Georgiou
We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.
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The classical regular and partial autocorrelation functions are powerful tools for stationary time series modelling and analysis. However, it is increasingly recognized that many time series are not stationary and the use of classical global autocorrelations can give misleading answers. This article introduces two estimators of the local partial autocorrelation function and establishes their asymptotic properties. The article then illustrates the use of these new estimators on both simulated and real time series. The examples clearly demonstrate the strong practical benefits of local estimator…
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new measure enjoys several complimentary advantages compared to existing autocorrelation measures for functional data, since it both 1) describes a notion of sign or direction of serial dependence in the series, and 2) is more robust to outliers. The asymptotic properties of estimators of the spherical autocorrelation are established, and are used to construct …
A new version of the partial autocorrelation plot and a new family of subset autoregressive models are introduced. A comprehensive approach to model identification, estimation and diagnostic checking is developed for these models. These models are better suited to efficient model building of high-order autoregressions with long time series. Several illustrative examples are given.
Autocorrelation Test under Frequent Mean Shifts
针对频繁均值漂移下的时间序列，提出移位免疫Portmanteau（SIP）检验，可靠检验自相关且对均值漂移鲁棒，并应用于纳米孔测序数据。
Autocorrelation functions for point-process time series
本文针对点过程时间序列提出基于分箱的自相关图方法，假设其服从对数高斯强度的双随机泊松模型，建立自相关渐近分布，通过仿真验证其检测ARMA模型模式的能力，并展示两个实际应用实例。
On the partial autocorrelation function for locally stationary time series: characterization, estimation and inference
本文针对短程依赖局部平稳时间序列，刻画了局部PACF的性质，提出基于筛法OLS的估计与检验方法，配套乘子自助法和R包，经模拟与实证验证有效。
White noise testing for functional time series via functional quantile autocorrelation
本文提出了一种新的非线性检验方法，用于检测功能时间序列中的序列依赖性，基于功能分位数自相关框架，具有鲁棒性，能处理潜在的异常值和复杂非线性依赖。
A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. In this paper, we elaborate on the Toeplitz autocorrelation matrix to the autocorrelation and cross-correlation of residuals and squared residuals block matrix. We derive a new portmanteau test statistic using the log of the determinant of the mth autocorrelations and cross-correlations block matrix. The asymptotic distribution of the proposed test statistic is derived as a linear combination of chi-squared distributions and can be approximated by a gamma distribution. This test is applied to identify …
One form of big data are signals - time series of consecutive values. In physical experiments, billions of values can now be measured within a second. Signals of heart and brain in intensive care, as well as seismic waves, are measured with 100 up to 1000 Hz over hours, days or even years. A song of 3 minutes on CD comprises 16 million values. Music and seismic vibrations basically consist of harmonic oscillations for which classical tools like autocorrelation and spectrogram work well. This note presents similar tools for all kinds of rhythmic processes, with non-linear distortion, artefacts,…
Concurrent time series commonly arise in various applications, including when monitoring the environment such as in air quality measurement networks, weather stations, oceanographic buoys, or in paleo form such as lake sediments, tree rings, ice cores, or coral isotopes, with each monitoring or sampling site providing one of the time series. The goal in such applications is to extract a common time trend or signal in the observed data. Other examples where the goal is to extract a common time trend for multiple time series are in stock price time series, neurological time series, and quality c…
We complement the theory developed in Preinerstorfer and Pötscher (2016) with further finite sample results on size and power of heteroskedasticity and autocorrelation robust tests. These allows us, in particular, to show that the sufficient conditions for the existence of size-controlling critical values recently obtained in Pötscher and Preinerstorfer (2018) are often also necessary. We furthermore apply the results obtained to tests for hypotheses on deterministic trends in stationary time series regressions, and find that many tests currently used are strongly size-distorted.
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide …
Deep Time-Series Forecasting in 10 Years: A Survey
本文从自相关建模角度综述了深度时间序列预测的进展，提出新的分类体系并分析了模型架构与学习目标的演进，填补了现有研究的空白。
On Robust Inference in Time Series Regression
针对时间序列回归中OLS-HAC推断的四个主要缺陷，提出简单易行的DURBIN动态回归程序，通过模拟验证其能有效避免这些问题，提升推断稳健性。
A semi-analytic method is proposed for the generation of realizations of a multivariate process of a given linear correlation structure and marginal distribution. This is an extension of a similar method for univariate processes, transforming the autocorrelation of the non-Gaussian process to that of a Gaussian process based on a piece-wise linear marginal transform from non-Gaussian to Gaussian marginal. The extension to multivariate processes involves the derivation of the autocorrelation matrix from the marginal transforms, which determines the generating vector autoregressive process. The …
Given observations from a stationary time series, permutation tests allow one to construct exactly level $α$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null hypothesis of interest is that the underlying process is an uncorrelated sequence, permutation tests are not necessarily level $α$, nor are they approximately level $α$ in large samples. In addition, permutation tests may have large Type 3, or directional, errors, in which a two-sided test rejects the null hypothesis and concludes that the first-order autocorrel…
Testing restrictions on regression coefficients in linear models often requires correcting the conventional F-test for potential heteroskedasticity or autocorrelation amongst the disturbances, leading to so-called heteroskedasticity and autocorrelation robust test procedures. These procedures have been developed with the purpose of attenuating size distortions and power deficiencies present for the uncorrected F-test. We develop a general theory to establish positive as well as negative finite-sample results concerning the size and power properties of a large class of heteroskedasticity and au…
Time series observations are ubiquitous in astronomy, and are generated to distinguish between different types of supernovae, to detect and characterize extrasolar planets and to classify variable stars. These time series are usually modeled using a parametric and/or physical model that assumes independent and homoscedastic errors, but in many cases these assumptions are not accurate and there remains a temporal dependency structure on the errors. This can occur, for example, when the proposed model cannot explain all the variability of the data or when the parameters of the model are not prop…
Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many of the statistical methods used to account for autocorrelation can be viewed as regression models that include basis functions. Understanding the concept of basis functions enables ecologists to modify commonly used ecological models to account for autocorrelation, which can improve inference and predictive accuracy. Understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of multicollinearity,…
Fitting ARMA Time Series Models without Identification: A Proximal Approach
针对 ARMA 模型需先识别阶数再估计参数的问题，提出基于双路径图分层稀疏惩罚的联合优化方法，并用近端块坐标下降高效求解，保证平稳性与可逆性。
Regression-based frameworks for streamflow regionalization are built around catchment attributes that traditionally originate from catchment hydrology, flood frequency analysis and their interplay. In this work, we deviated from this traditional path by formulating and extensively investigating the first regression-based streamflow regionalization frameworks that largely emerge from general-purpose time series features for data science and, more precisely, from a large variety of such features. We focused on 28 features that included (partial) autocorrelation, entropy, temporal variation, seas…
We present a novel quasi-Bayesian method to weight multiple dynamical models by their skill at capturing both potentially non-linear trends and first-order autocorrelated variability of the underlying process, and to make weighted probabilistic projections. We validate the method using a suite of one-at-a-time cross-validation experiments involving Atlantic meridional overturning circulation (AMOC), its temperature-based index, as well as Korean summer mean maximum temperature. In these experiments the method tends to exhibit superior skill over a trend-only Bayesian model averaging weighting …
We study goodness-of-fit testing for non-causal autoregressive time series with non-Gaussian stable noise. To model time series exhibiting sharp spikes or occasional bursts of outlying observations, the exponent of the non-Gaussian stable variables is assumed to be less than two. Under such conditions, the innovation variables have no finite second moment. We proved that the sample autocorrelation functions of the trimmed residuals are asymptotically normal. Nonparametric tests are also investigated. The rank correlations of the residuals or the squared residuals are shown to be asymptotically…
Fractional lower-order covariance-based measures for cyclostationary time series with heavy-tailed distributions: application to dependence testing and model order identification
本文提出基于分数低阶协方差的循环平稳时间序列分析方法，用于处理具有厚尾分布的无限方差过程，通过peFLOACF和peFLOPACF进行依赖性检验和模型阶数识别。
Bayesian identification of early warning signals for long-range dependent climatic time series
本文提出了一种贝叶斯方法，用于检测长期依赖气候时间序列中的早期预警信号，通过分析自相关和方差的变化，评估其在真实数据中的有效性。
The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI$^+$, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI$^+$ improves the reliability of CI tests …
Traditional white noise testing, for example the Ljung-Box test, studies only the autocorrelation function (ACF). Time series can be heteroscedastic and therefore not i.i.d. but still white noise (that is, with zero ACF). An example of heteroscedasticity is financial time series: times of high variance (financial crises) can alternate with times of low variance (calm times). Here, absolute values of time series terms are not white noise. We could test for white noise separately for original and absolute values, for example using Ljung-Box tests for both. In this article, we create an omnibus t…
The main goal of this work is to present a new model able to deal with potentially misreported continuous time series. The proposed model is able to handle the autocorrelation structure in continuous time series data, which might be partially or totally underreported or overreported. Its performance is illustrated through a comprehensive simulation study considering several autocorrelation structures and two real data applications on human papillomavirus incidence in Girona (Catalunya, Spain) and COVID-19 incidence in the Chinese region of Heilongjiang.
Natural coordinates for constrained correlation functions: Partial autocorrelations and the geometry of positive power spectra
本文证明约束相关函数的仿射变量等价于偏自相关系数，提供自然坐标，简化区间计算并赋予准高斯似然变换经典统计解释。
Multiple-group (Controlled) Interrupted Time Series Analysis with Higher-Order Autoregressive Errors: A Simulation Study Comparing Newey-West and Prais-Winsten Methods
通过蒙特卡洛模拟首次系统评估了在AR(2)和AR(3)误差结构下，Newey-West与Prais-Winsten方法在多组中断时间序列分析中的表现，发现Prais-Winsten在大多数条件下具有更好的推断校准性。
Semiparametric mean and variance joint models with Laplace link functions for count time series
针对计数时间序列条件方差难以独立建模的局限，提出 RRC-GARCH 半参数均值与方差联合模型，利用 Laplace 链接函数灵活捕捉均值-方差结构，证明了其理论性质，并通过模拟与真实数据验证了其预测准确性。
In many industrial manufacturing processes, the quality of products depends on the relation between two main ingredients or characteristics. Often, this calls for monitoring the ratio of two normal random variables with statistical process control (SPC) techniques. A large number of studies related to designing control charts monitoring this ratio have been published. However, these studies are based purely on the assumption of independent observations. In practice, autocorrelation between observations can exist and should be modeled to protect against the false alarm rate inflation when imple…
Wind farms can be regarded as complex systems that are, on the one hand, coupled to the nonlinear, stochastic characteristics of weather and, on the other hand, strongly influenced by supervisory control mechanisms. One crucial problem in this context today is the predictability of wind energy as an intermittent renewable resource with additional non-stationary nature. In this context, we analyze the power time series measured in an offshore wind farm for a total period of one year with a time resolution of 10 min. Applying detrended fluctuation analysis, we characterize the autocorrelation of…
Discovering Causal Relationships Between Time Series With Spatial Structure
本文提出一种扩展时间序列因果发现的方法，以处理具有空间结构的系统，解决空间自相关和复杂混杂问题，同时指出未来研究方向。
Beta Regression with Autoregressive Errors for Interrupted Time Series Analysis of Proportion and Rate Outcomes: A Simulation Study
研究针对比例和速率结果的中断时间序列分析，介绍了betark方法，它是具有AR(k)误差的贝塔回归的联合条件最大似然估计器，通过递归替换实现。蒙特卡罗研究表明其在多数情况校准更好，能直接考虑自相关，相比其他方法有优势，但在特定条件下自身I型错误仍较高。
Stylized Facts of High-Frequency Bitcoin Time Series
本文分析2019-2022年高频比特币数据，发现收益率呈异常扩散、重尾和多重分形特征，且市场效率随时间提升。
New tools for network time series with an application to COVID-19 hospitalisations
本文基于GNAR框架提出网络自相关函数、偏网络自相关函数及Corbit图和Wagner图等新工具，用于网络时间序列的可视化、模型选择与节点影响力分析，并在英格兰和威尔士140个NHS信托机构的COVID-19住院数据上验证了方法的有效性和预测优势。
We propose a specification test for conditional location--scale models based on extremal dependence properties of the standardized residuals. We do so comparing the left-over serial extremal dependence -- as measured by the pre-asymptotic tail copula -- with that arising under serial independence at different lags. Our main theoretical results show that the proposed Portmanteau-type test statistics have nuisance parameter-free asymptotic limits. The test statistics are easy to compute, as they only depend on the standardized residuals, and critical values are likewise easily obtained from the …
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual series. Furthermore, our algorithm is extended to take into account individual autocorrelation to provide better estimation, using a recent convex relaxation of quadratically constrained quadratic program. Extensive experiments on synthetic and real-world electricity consumption datas…
Amortized Neural Clustering of Time Series based on Statistical Features
本文提出了一种算法无关的基于特征的时间序列聚类方法，通过amortized神经推断训练神经网络近似最优划分规则，减少对传统聚类方法的依赖，并利用统计特征学习数据驱动的亲和结构，自动确定聚类数量，提升聚类准确性。
This paper develops a new time series clustering procedure allowing for heteroskedasticity, non-normality and model's non-linearity. At this aim, we follow a fuzzy approach. Specifically, considering a Dynamic Conditional Score (DCS) model, we propose to cluster time series according to their estimated conditional moments via the Autocorrelation-based fuzzy C-means (A-FCM) algorithm. The DCS parametric modelling is appealing because of its generality and computational feasibility. The usefulness of the proposed procedure is illustrated using an experiment with simulated data and several empiri…
I examine the consequences of modelling contagious influence in a social network with incomplete edge information, namely in the situation where each individual may name a limited number of friends, so that extra outbound ties are censored. In particular, I consider a prototypical time series configuration where a property of the "ego" is affected in a causal fashion by the properties of their "alters" at a previous time point, both in the total number of alters as well as the deviation from a central value. This is considered with three potential methods for naming one's friends: a strict upp…
Hydroclimatic time series analysis focuses on a few feature types (e.g., autocorrelations, trends, extremes), which describe a small portion of the entire information content of the observations. Aiming to exploit a larger part of the available information and, thus, to deliver more reliable results (e.g., in hydroclimatic time series clustering contexts), here we approach hydroclimatic time series analysis differently, i.e., by performing massive feature extraction. In this respect, we develop a big data framework for hydroclimatic variable behaviour characterization. This framework relies on…
FreDF: Learning to Forecast in the Frequency Domain
针对直接预测范式忽视未来标签自相关导致估计偏差的问题，本文提出频率增强直接预测FreDF，通过在频域学习预测来减轻标签自相关，实验表明其显著优于现有方法并兼容多种预测模型。
Count time series are widely encountered in practice. As with continuous valued data, many count series have seasonal properties. This paper uses a recent advance in stationary count time series to develop a general seasonal count time series modeling paradigm. The model permits any marginal distribution for the series and the most flexible autocorrelations possible, including those with negative dependence. Likelihood methods of inference can be conducted and covariates can be easily accommodated. The paper first develops the modeling methods, which entail a discrete transformation of a Gauss…
Semiparametric mean and variance joint models with clipped-Laplace link functions for bounded integer-valued time series
本文针对有界计数时间序列，利用方差上下界和截断拉普拉斯链接函数提出半参数均值与方差联合模型，可同时刻画欠离散、等离散和过离散现象，并建立了平稳性、遍历性及估计量渐近性质。
Depth of planning the state of a dynamic discrete system by autocorrelation function
该研究将生产系统建模为离散时间动态系统，通过自相关函数进行状态分析，并利用调节器控制分析深度，仿真揭示了循环动态，为后续多种分析方法奠定基础。
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