Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).
This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model, and we prove consistency and, in the short memory case, asymptotic normality of this estimator. When the underlying trawl p…
A new forecasting method based on the concept of the profile predictive the likelihood function is proposed for discrete-valued processes. In particular, generalized autoregressive and moving average (GARMA) models for Poisson distributed data are explored in details. Highest density regions are used to construct forecasting regions. The proposed forecast estimates and regions are coherent. Large sample results are derived for the forecasting distribution. Numerical studies using simulations and a real data set are used to establish the performance of the proposed forecasting method. Robustnes…
We develop a forecasting methodology for providing credible forecasts for time series that have recently undergone a shock. We achieve this by borrowing knowledge from other time series that have undergone similar shocks for which post-shock outcomes are observed. Three shock effect estimators are motivated with the aim of minimizing average forecast risk. We propose risk-reduction propositions that provide conditions that establish when our methodology works. Bootstrap and leave-one-out cross validation procedures are provided to prospectively assess the performance of our methodology. Severa…
The University of Texas at Dallas（得克萨斯大学达拉斯分校）；National Renewable Energy Laboratory (NREL)（国家可再生能源实验室）；IBM TJ Watson Research Center（IBM托马斯·J·沃森研究中心）
Solar forecasting accuracy is affected by weather conditions, and weather awareness forecasting models are expected to improve the performance. However, it may not be available and reliable to classify different forecasting tasks by using only meteorological weather categorization. In this paper, an unsupervised clustering-based (UC-based) solar forecasting methodology is developed for short-term (1-hour-ahead) global horizontal irradiance (GHI) forecasting. This methodology consists of three parts: GHI time series unsupervised clustering, pattern recognition, and UC-based forecasting. The dai…
National Technical University of Athens（雅典国家技术大学）；Hellenic Air Force（希腊空军）
Delivering useful hydrological forecasts is critical for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among others. In this work, we present and appraise a new simple and flexible methodology for hydrological time series forecasting. This methodology relies on (a) at least two individual forecasting methods and (b) the median combiner of forecasts. The appraisal is made by using a big dataset consisted of 90-year-long mean annual river flow time series from approxima…
Singular Spectrum Analysis (SSA) as a tool for analysis and forecasting of time series is considered. The main features of the Rssa package, which implements the SSA algorithms and methodology in R, are described and examples of its use are presented. Analysis, forecasting and parameter estimation are demonstrated by means of case study with an accompanying code in R.
We introduce a novel functional time series methodology for short-term load forecasting. The prediction is performed by means of a weighted average of past daily load segments, the shape of which is similar to the expected shape of the load segment to be predicted. The past load segments are identified from the available history of the observed load segments by means of their closeness to a so-called reference load segment, the later being selected in a manner that captures the expected qualitative and quantitative characteristics of the load segment to be predicted. Weak consistency of the su…
This is a case study discussing the supervised artificial neural network for the purpose of forecasting with comparison of the Box-Jenkins methodology by using the data of well known emergency service Rescue 1122. We fits a variety of neural network (NN) models and many problems were revealed while fitting the ANNs model to achieve the local minima. Moreover ANNs model is giving much better out of sample forecasts as compare to the ARIMA model. However we use diagnostic checks for the comparison of models.
Dynamic model averaging (DMA) combines the forecasts of a large number of dynamic linear models (DLMs) to predict the future value of a time series. The performance of DMA critically depends on the appropriate choice of two forgetting factors. The first of these controls the speed of adaptation of the coefficient vector of each DLM, while the second enables time variation in the model averaging stage. In this paper we develop a novel, adaptive dynamic model averaging (ADMA) methodology. The proposed methodology employs a stochastic optimisation algorithm that sequentially updates the forgettin…
In this work we propose a new class of long-memory models with time-varying fractional parameter. In particular, the dynamics of the long-memory coefficient, $d$, is specified through a stochastic recurrence equation driven by the score of the predictive likelihood, as suggested by Creal et al. (2013) and Harvey (2013). We demonstrate the validity of the proposed model by a Monte Carlo experiment and an application to two real time series.
University of Corsica（科西嘉大学）；Castelluccio Hospital（卡斯泰卢乔医院）
The renewable energies prediction and particularly global radiation forecasting is a challenge studied by a growing number of research teams. This paper proposes an original technique to model the insolation time series based on combining Artificial Neural Network (ANN) and Auto-Regressive and Moving Average (ARMA) model. While ANN by its non-linear nature is effective to predict cloudy days, ARMA techniques are more dedicated to sunny days without cloud occurrences. Thus, three hybrids models are suggested: the first proposes simply to use ARMA for 6 months in spring and summer and to use an …
The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear estimation, we describe the theoretical framework and then we provide detailed examples of response distributions, including binomial, Poisson, negative binomial, geometric, normal, log-normal, gamma, exponential, Weibull, Pareto, beta, and inverse Gaussian. We give numerical illustrations for all distributions (except for the normal). Putting together all the…
In this paper we offer a review and bibliography of work on Hankel low-rank approximation and completion, with particular emphasis on how this methodology can be used for time series analysis and forecasting. We begin by describing possible formulations of the problem and offer commentary on related topics and challenges in obtaining globally optimal solutions. Key theorems are provided, and the paper closes with some expository examples.
Électricité de France R&D（法国电力公司研发部）；Viking Conseil（维京咨询公司）
We focus on day-ahead electricity load forecasting of substations of the distribution network in France; therefore, our problem lies between the instability of a single consumption and the stability of a countrywide total demand. Moreover, we are interested in forecasting the loads of over one thousand substations; consequently, we are in the context of forecasting multiple time series. To that end, we rely on an adaptive methodology that provided excellent results at a national scale; the idea is to combine generalized additive models with state-space representations. However, the extension o…
Qualcomm AI Research（高通AI研究院）；Qualcomm Technologies Netherlands B.V.（高通荷兰技术有限公司）；Qualcomm Technologies, Inc.（高通技术公司）；University of Amsterdam（阿姆斯特丹大学）
Autoregressive models (ARMs) currently hold state-of-the-art performance in likelihood-based modeling of image and audio data. Generally, neural network based ARMs are designed to allow fast inference, but sampling from these models is impractically slow. In this paper, we introduce the predictive sampling algorithm: a procedure that exploits the fast inference property of ARMs in order to speed up sampling, while keeping the model intact. We propose two variations of predictive sampling, namely sampling with ARM fixed-point iteration and learned forecasting modules. Their effectiveness is dem…
We present new Bayesian methodology for consumer sales forecasting. With a focus on multi-step ahead forecasting of daily sales of many supermarket items, we adapt dynamic count mixture models to forecast individual customer transactions, and introduce novel dynamic binary cascade models for predicting counts of items per transaction. These transactions-sales models can incorporate time-varying trend, seasonal, price, promotion, random effects and other outlet-specific predictors for individual items. Sequential Bayesian analysis involves fast, parallel filtering on sets of decoupled items and…
We study the estimation of the probability distribution of individual patient waiting times in an emergency department (ED). Our feature-rich modelling allows for dynamic updating and refinement of waiting time estimates as patient- and ED-specific information (e.g., patient condition, ED congestion levels) is revealed during the waiting process. Aspects relating to communicating forecast uncertainty to patients, and implementing this methodology in practice, are also discussed.
In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to put it into practice. For this purpose, we obtain the likelihood in closed form, and provide two on-line computations of this function. Then, we investigate the asymptotic behaviour of statistical estimators. Finally, we quantify the effect of a bad calibration with the continuous time mis-specified Kalman filter. Numerical examples illustrate the difficulty o…
We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model…
DoFlow: Flow-based Generative Models for Interventional and Counterfactual Forecasting on Time Series
H. Milton Stewart School of Industrial and Systems Engineering（H. Milton Stewart工业与系统工程学院）；Georgia Institute of Technology（佐治亚理工学院）；Northwestern–Argonne Institute for Scientific and Engineering Excellence（西北-阿贡科学与工程卓越研究所）
Since the beginning of the COVID-19 pandemic, many dashboards have emerged as useful tools to monitor the evolution of the pandemic, inform the public, and assist governments in decision making. Our goal is to develop a globally applicable method, integrated in a twice daily updated dashboard that provides an estimate of the trend in the evolution of the number of cases and deaths from reported data of more than 200 countries and territories, as well as a seven-day forecast. One of the significant difficulties to manage a quickly propagating epidemic is that the details of the dynamic needed t…
The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility covariance matrix of the time series is modelled via inverted Wishart and singular multivariate beta distributions allowing a fully conjugate Bayesian inference. Model performance and model comparison is done via the likelihood function, sequential Bayes factors, the mean of squared standardized forecast errors, the mean of absolute forecast errors (known al…
Probabilistic forecasting, i.e. estimating the probability distribution of a time series' future given its past, is a key enabler for optimizing business processes. In retail businesses, for example, forecasting demand is crucial for having the right inventory available at the right time at the right place. In this paper we propose DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an auto regressive recurrent network model on a large number of related time series. We demonstrate how by applying deep learning techniques to forecasting, one can overcome many…
This paper studies some temporal dependence properties and addresses the issue of parametric estimation for a class of state-dependent autoregressive models for nonlinear time series in which we assume a stochastic autoregressive coefficient depending on the first lagged value of the process itself. We call such a model state-dependent first-order autoregressive process, (SDAR). We introduce some assumptions under which this class of models is strictly stationary and uniformly ergodic and we establish consistency and asymptotic normality of the quasi-maximum likelihood estimator of the paramet…
Owing to the growing concern of global warming and over-dependence on fossil fuels, there has been a huge interest in last years in the deployment of Photovoltaic (PV) systems for generating electricity. The output power of a PV array greatly depends, among other parameters, on solar irradiation. However, solar irradiation has an intermittent nature and suffers from rapid fluctuations. This creates challenges when integrating PV systems in the electricity grid and calls for accurate forecasting methods of solar irradiance. In this paper, we propose a triple exponential-smoothing based forecast…
We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates-- sequentially and adaptively over time-- varying forecast biases and facets of miscalibration of individual forecast densities, and-- critically-- of time-varying inter-dependencies among them ov…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of historic samples is inadequate for accurately forecasting the signal of each considered in isolation. We develop a new forecasting methodology based on Gaussian process regression that is successful in doing so in examples for which the method of generalized least-squares is not. The new method employs a form of deep machine learning.
We propose a hybrid approach for the modelling and the short-term forecasting of electricity loads. Two building blocks of our approach are (i) modelling the overall trend and seasonality by fitting a generalised additive model to the weekly averages of the load, and (ii) modelling the dependence structure across consecutive daily loads via curve linear regression. For the latter, a new methodology is proposed for linear regression with both curve response and curve regressors. The key idea behind the proposed methodology is the dimension reduction based on a singular value decomposition in a …
We propose a new methodology for denoising, variance-stabilizing and normalizing signals whose both mean and variance are parameterized by a single unknown varying parameter, such as Poisson or scaled chi-squared. Key to our methodology is the observation that the signed and square-rooted generalized log-likelihood ratio test for the equality of the local means is approximately and asymptotically distributed as standard normal under the null. We use these test statistics within the Haar wavelet transform at each scale and location, referring to them as the likelihood ratio Haar (LRH) coefficie…
Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As data become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide …
Efficiently Computed Marginal Likelihoods for Multivariate Mixture Models
Laboratoire de Mathématiques Blaise Pascal, CNRS, Université Clermont Auvergne（布莱斯·帕斯卡数学实验室，法国国家科学研究中心，克莱蒙奥弗涅大学）；CNRS, MAP5, Université Paris Cité（法国国家科学研究中心，MAP5，巴黎西岱大学）；Departments of Statistics and Sociology, University of Washington（华盛顿大学统计与社会学系）
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network snapshots. The recently introduced stochastic block transition model addresses precisely this issue, by modelling the probabilities of creating a new edge and of maintaining an edge over time. Using a model-based clustering approach, this paper illustrates a methodology to fit stochastic block transition models under a Bayesian framework. The method relies on a greed…
A maximum likelihood methodology for a general class of models is presented, using an approximate Bayesian computation (ABC) approach. The typical target of ABC methods are models with intractable likelihoods, and we combine an ABC-MCMC sampler with so-called "data cloning" for maximum likelihood estimation. Accuracy of ABC methods relies on the use of a small threshold value for comparing simulations from the model and observed data. The proposed methodology shows how to use large threshold values, while the number of data-clones is increased to ease convergence towards an approximate maximum…
Maximum-likelihood regression with systematic errors for astronomy and the physical sciences: I. Methodology and goodness-of-fit statistic of Poisson data
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the value of the so-called regularisation parameters that control the amount of regularisation enforced. These parameters are notoriously difficult to set a priori, and can have a dramatic impact on the recovered estimates. In this work, we propose a general empirical Bayesian method for setting regularisation parameters in imaging problems that are convex w.r.t.…
