Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types of extremal dependence in the time series such as asymptotic dependence, or Markov time series of finite order.\ In this paper, we develop statistical methodology for time series extremes based on recent probabilistic results that allow us to flexibly model the decay of a stationary time series after witnessing an extreme event.\ While Markov sequences of finite order are naturally accommodated by our approach, we consider a broader setup, based on the conditional extreme value model, which allows for a wide range of possible dependence structures in the time series.\ We consider inference based on Monte Carlo simulation and derive an upper bound for the variance of a commonly used importance sampler.\ Our methodology is illustrated via estimation of cluster functionals in simulated data and in a time series of daily maximum temperatures from Orleans, France.
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…
Recent extreme value theory literature has seen significant emphasis on the modelling of spatial extremes, with comparatively little consideration of spatio-temporal extensions. This neglects an important feature of extreme events: their evolution over time. Many existing models for the spatial case are limited by the number of locations they can handle; this impedes extension to space-time settings, where models for higher dimensions are required. Moreover, the spatio-temporal models that do exist are restrictive in terms of the range of extremal dependence types they can capture. Recently, c…
One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time series. However, in many applications one often encounters conditional heteroskedasticity. In this paper we propose a new class of models, referred to as GARMA-GARCH models, that jointly specify both the conditional mean and conditional variance processes of a general non-Gaussian time series. Under the general modeling framework, we propose three specific mod…
We consider $α$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of the estimator. A useful and typical application to functional times series prediction is given.
This paper is concerned with modeling the dependence structure of two (or more) time-series in the presence of a (possible multivariate) covariate which may include past values of the time series. We assume that the covariate influences only the conditional mean and the conditional variance of each of the time series but the distribution of the standardized innovations is not influenced by the covariate and is stable in time. The joint distribution of the time series is then determined by the conditional means, the conditional variances and the marginal distributions of the innovations, which …
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
We introduce the decision-aware time-series conditional generative adversarial network (DAT-CGAN) as a method for time-series generation. The framework adopts a multi-Wasserstein loss on structured decision-related quantities, capturing the heterogeneity of decision-related data and providing new effectiveness in supporting the decision processes of end users. We improve sample efficiency through an overlapped block-sampling method, and provide a theoretical characterization of the generalization properties of DAT-CGAN. The framework is demonstrated on financial time series for a multi-time-st…
We present a method for conditional time series forecasting based on an adaptation of the recent deep convolutional WaveNet architecture. The proposed network contains stacks of dilated convolutions that allow it to access a broad range of history when forecasting, a ReLU activation function and conditioning is performed by applying multiple convolutional filters in parallel to separate time series which allows for the fast processing of data and the exploitation of the correlation structure between the multivariate time series. We test and analyze the performance of the convolutional network …
Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact the cumulative residual process no longer admits, under the null hypothesis, a distribution-free limit. To obtain a practical solution one either transforms the process in order to achieve a distribution-free limit or approximates the non-distribution free limit using a numerical or a re-sampling technique. Here the three solutions will be considered.It is …
In this work we introduce a class of dynamic models for time series taking values on the unit interval. The proposed model follows a generalized linear model approach where the random component, conditioned on the past information, follows a beta distribution, while the conditional mean specification may include covariates and also an extra additive term given by the iteration of a map that can present chaotic behavior. The resulting model is very flexible and its systematic component can accommodate short and long range dependence, periodic behavior, laminar phases, etc. We derive easily veri…
Stanford University（斯坦福大学）；Mitsubishi UFJ Trust Investment Technology Institute（三菱日联信托投资技术研究所）；Japan Digital Design（日本数字设计公司）
The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion models for Imputation (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Un…
The Conditional Cauchy-Schwarz Divergence with Applications to Time-Series Data and Sequential Decision Making
UiT - The Arctic University of Norway（挪威北极大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Florida（佛罗里达大学）；NORCE Norwegian Research Centre（NORCE挪威研究中心）；Copenhagen University（哥本哈根大学）；Norwegian Computing Center（挪威计算中心）
Universitat Autònoma de Barcelona（巴塞罗那自治大学）；Universitat de Barcelona（巴塞罗那大学）
(Conditional) Generative Adversarial Networks (GANs) have found great success in recent years, due to their ability to approximate (conditional) distributions over extremely high dimensional spaces. However, they are highly unstable and computationally expensive to train, especially in the time series setting. Recently, it has been proposed the use of a key object in rough path theory, called the signature of a path, which is able to convert the min-max formulation given by the (conditional) GAN framework into a classical minimization problem. However, this method is extremely expensive in ter…
In this paper we propose a data augmentation method for time series with irregular sampling, Time-Conditional Generative Adversarial Network (T-CGAN). Our approach is based on Conditional Generative Adversarial Networks (CGAN), where the generative step is implemented by a deconvolutional NN and the discriminative step by a convolutional NN. Both the generator and the discriminator are conditioned on the sampling timestamps, to learn the hidden relationship between data and timestamps, and consequently to generate new time series. We evaluate our model with synthetic and real-world datasets. F…
University of Southern California（南加州大学）；IBM T.J. Watson Research Center（IBM T.J. Watson研究中心）
In many applications of time series models, such as climate analysis and social media analysis, we are often interested in extreme events, such as heatwave, wind gust, and burst of topics. These time series data usually exhibit a heavy-tailed distribution rather than a Gaussian distribution. This poses great challenges to existing approaches due to the significantly different assumptions on the data distributions and the lack of sufficient past data on extreme events. In this paper, we propose the Sparse-GEV model, a latent state model based on the theory of extreme value modeling to automatic…
Neural Processes (NPs) are a family of conditional generative models that are able to model a distribution over functions, in a way that allows them to perform predictions at test time conditioned on a number of context points. A recent addition to this family, Convolutional Conditional Neural Processes (ConvCNP), have shown remarkable improvement in performance over prior art, but we find that they sometimes struggle to generalize when applied to time series data. In particular, they are not robust to distribution shifts and fail to extrapolate observed patterns into the future. By incorporat…
We introduce a new type of estimator for the spectral tail process of a regularly varying time series. The approach is based on a characterizing invariance property of the spectral tail process, which is incorporated into the new estimator via a projection technique. We show uniform asymptotic normality of this estimator, both in the case of known and of unknown index of regular variation. In a simulation study the new procedure shows a more stable performance than previously proposed estimators.
We consider the problem of modeling discrete-valued vector time series data using extensions of Chow-Liu tree models to capture both dependencies across time and dependencies across variables. Conditional Chow-Liu tree models are introduced, as an extension to standard Chow-Liu trees, for modeling conditional rather than joint densities. We describe learning algorithms for such models and show how they can be used to learn parsimonious representations for the output distributions in hidden Markov models. These models are applied to the important problem of simulating and forecasting daily prec…
Employing recent results of Robinson (2005) we consider the asymptotic properties of conditional-sum-of-squares (CSS) estimates of parametric models for stationary time series with long memory. CSS estimation has been considered as a rival to Gaussian maximum likelihood and Whittle estimation of time series models. The latter kinds of estimate have been rigorously shown to be asymptotically normally distributed in case of long memory. However, CSS estimates, which should have the same asymptotic distributional properties under similar conditions, have not received comparable treatment: the tru…
Université Gustave Eiffel（古斯塔夫·埃菲尔大学）；EDF Lab（法国电力实验室）；FiME (Laboratoire de Finance des Marchés de l’Énergie)（能源市场金融实验室）
We introduce three new generative models for time series that are based on Euler discretization of Stochastic Differential Equations (SDEs) and Wasserstein metrics. Two of these methods rely on the adaptation of generative adversarial networks (GANs) to time series. The third algorithm, called Conditional Euler Generator (CEGEN), minimizes a dedicated distance between the transition probability distributions over all time steps. In the context of Ito processes, we provide theoretical guarantees that minimizing this criterion implies accurate estimations of the drift and volatility parameters. …
Cowles Foundation for Research in Economics, Yale University（耶鲁大学考尔斯经济学研究基金会）；Rutgers University（罗格斯大学）；The University of Hong Kong（香港大学）
General nonlinear sieve learnings are classes of nonlinear sieves that can approximate nonlinear functions of high dimensional variables much more flexibly than various linear sieves (or series). This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectation functionals of time series data, where the functionals of interest are based on some nonparametric function that satisfy conditional moment restrictions and are learned using multilayer neural networks. While the asymptotic normality of the estimated functionals depends on some unknown Riesz rep…
Conformalised Conditional Normalising Flows for Joint Prediction Regions in time series
Hasso Plattner Institute for Digital Engineering（哈索·普拉特纳数字工程学院）；University of California, Irvine（加利福尼亚大学欧文分校）；Hasso Plattner Institute for Digital Health at the Icahn School of Medicine at Mount Sinai（西奈山伊坎医学院哈索·普拉特纳数字健康研究所）
The increasing penetration of embedded renewables makes forecasting net-load, consumption less embedded generation, a significant and growing challenge. Here a framework for producing probabilistic forecasts of net-load is proposed with particular attention given to the tails of predictive distributions, which are required for managing risk associated with low-probability events. Only small volumes of data are available in the tails, by definition, so estimation of predictive models and forecast evaluation requires special attention. We propose a solution based on a best-in-class load forecast…
Conditionally Whitened Generative Models for Probabilistic Time Series Forecasting
Graduate University of Advanced Studies & The Institute of Statistical Mathematics（高级研究大学及统计数学研究所）；East China Normal University（华东师范大学）；The Institute of Statistical Mathematics（统计数学研究所）
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a parametric process model (such as, e.g., an autoregressive model) for the observed random process. Instead, we only require certain smoothness properties (in the Fourier domain) of the process. The proposed inference scheme works even for sample sizes much smaller than the number of scalar process components if the true underlying CIG is sufficiently sparse. …
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian processes. Particular focus is on clarity and ease of implementation of the estimator and the associated asymptotic results, making it easy for practitioners to apply the methods. We additionally show how measurement noise in the observations will bias the estimator, potentially resulting in the practitioner erroneously finding evidence of fractal characteristics in…
This paper provides extensions of the work on subsampling by Bertail et al. (2004) for strongly mixing case to weakly dependent case by application of the results of Doukhan and Louhichi (1999). We investigate properties of smooth and rough subsampling estimators for distributions of converging and extreme statistics when the underlying time series is η or λ-weakly dependent.
Generative Adversarial Net (GAN) has been proven to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions can be both categorical and continuous variables containing different kinds of auxiliary information. Our simulation studies show that CGAN is able to learn different kinds of normal and heavy tail distributions, as well as dependent structures of different time series and it can further generate conditional predictive distributions cons…
KTH Royal Institute of Technology（瑞典皇家理工学院）；RISE Research Institutes of Sweden（瑞典RISE研究院）
We present a representation learning framework for financial time series forecasting. One challenge of using deep learning models for finance forecasting is the shortage of available training data when using small datasets. Direct trend classification using deep neural networks trained on small datasets is susceptible to the overfitting problem. In this paper, we propose to first learn compact representations from time series data, then use the learned representations to train a simpler model for predicting time series movements. We consider a class-conditioned latent variable model. We train …
ETH Zurich（苏黎世联邦理工学院）；Tri-Institutional Training Program in Computational Biology and Medicine, Weill Cornell Medical（威尔康奈尔医学院计算生物学与医学三机构联合培养项目）
Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their application to medical data. RGANs make use of recurrent neural networks in the generator and the discriminator. In the case of RCGANs, both of these RNNs are conditioned on auxiliary information. We demonstrate our models in a set of toy datasets, where we show visually and quantitat…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and stationary time series Gaussian Graphical model (StGM), and complements existing works on parametric graphical models based on change point vector autoregressions (VAR). Analogous to StGM, the proposed framework captures conditional noncorrelations (both intertemporal and contemporaneous) in the form of an undirected graph. In addition, to describe the more n…
