Long-term forecasting of multivariate time series in industrial furnaces with dynamic Gaussian Bayesian networks

2021 ◽  
Vol 103 ◽  
pp. 104301
Author(s):  
David Quesada ◽  
Gabriel Valverde ◽  
Pedro Larrañaga ◽  
Concha Bielza
Keyword(s):  
Time Series ◽  
Bayesian Networks ◽  
Multivariate Time Series ◽  
Long Term Forecasting

scholarly journals Gaussian processes with skewed Laplace spectral mixture kernels for long-term forecasting

2021 ◽  
Author(s):  
Kai Chen ◽  
Twan van Laarhoven ◽  
Elena Marchiori
Keyword(s):  
Gaussian Processes ◽  
Multivariate Time Series ◽  
Heavy Tail ◽  
Lottery Ticket ◽  
Spectral Densities ◽  
Heavy Tailed ◽  
Long Term Forecasting ◽  
The Time Domain ◽  
Spectral Mixture

AbstractLong-term forecasting involves predicting a horizon that is far ahead of the last observation. It is a problem of high practical relevance, for instance for companies in order to decide upon expensive long-term investments. Despite the recent progress and success of Gaussian processes (GPs) based on spectral mixture kernels, long-term forecasting remains a challenging problem for these kernels because they decay exponentially at large horizons. This is mainly due to their use of a mixture of Gaussians to model spectral densities. Characteristics of the signal important for long-term forecasting can be unravelled by investigating the distribution of the Fourier coefficients of (the training part of) the signal, which is non-smooth, heavy-tailed, sparse, and skewed. The heavy tail and skewness characteristics of such distributions in the spectral domain allow to capture long-range covariance of the signal in the time domain. Motivated by these observations, we propose to model spectral densities using a skewed Laplace spectral mixture (SLSM) due to the skewness of its peaks, sparsity, non-smoothness, and heavy tail characteristics. By applying the inverse Fourier Transform to this spectral density we obtain a new GP kernel for long-term forecasting. In addition, we adapt the lottery ticket method, originally developed to prune weights of a neural network, to GPs in order to automatically select the number of kernel components. Results of extensive experiments, including a multivariate time series, show the beneficial effect of the proposed SLSM kernel for long-term extrapolation and robustness to the choice of the number of mixture components.

Short, medium and long term forecasting of time series using the L-Co-R algorithm

2014 ◽  
Vol 128 ◽  
pp. 433-446 ◽  
Author(s):  
E. Parras-Gutierrez ◽  
V.M. Rivas ◽  
M. Garcia-Arenas ◽  
M.J. del Jesus
Keyword(s):  
Time Series ◽  
Long Term Forecasting

scholarly journals A Multivariate Forecasting Model for the COVID-19 Hospital Census Based on Local Infection Incidence

2021 ◽  
Author(s):  
Hieu M. Nguyen ◽  
Philip Turk ◽  
Andrew McWilliams
Keyword(s):  
Time Series ◽  
Multivariate Time Series ◽  
Healthcare Systems ◽  
Leading Indicators ◽  
Short Term ◽  
Correction Model ◽  
Vector Error Correction ◽  
Infection Incidence ◽  
Vector Error

AbstractCOVID-19 has been one of the most serious global health crises in world history. During the pandemic, healthcare systems require accurate forecasts for key resources to guide preparation for patient surges. Fore-casting the COVID-19 hospital census is among the most important planning decisions to ensure adequate staffing, number of beds, intensive care units, and vital equipment. In the literature, only a few papers have approached this problem from a multivariate time-series approach incorporating leading indicators for the hospital census. In this paper, we propose to use a leading indicator, the local COVID-19 infection incidence, together with the COVID-19 hospital census in a multivariate framework using a Vector Error Correction model (VECM) and aim to forecast the COVID-19 hospital census for the next 7 days. The model is also applied to produce scenario-based 60-day forecasts based on different trajectories of the pandemic. With several hypothesis tests and model diagnostics, we confirm that the two time-series have a cointegration relationship, which serves as an important predictor. Other diagnostics demonstrate the goodness-of-fit of the model. Using time-series cross-validation, we can estimate the out-of-sample Mean Absolute Percentage Error (MAPE). The model has a median MAPE of 5.9%, which is lower than the 6.6% median MAPE from a univariate Autoregressive Integrated Moving Average model. In the application of scenario-based long-term forecasting, future census exhibits concave trajectories with peaks lagging 2-3 weeks later than the peak infection incidence. Our findings show that the local COVID-19 infection incidence can be successfully in-corporated into a VECM with the COVID-19 hospital census to improve upon existing forecast models, and to deliver accurate short-term forecasts and realistic scenario-based long-term trajectories to help healthcare systems leaders in their decision making.Author summaryDuring the COVID-19 pandemic, healthcare systems need to have adequate resources to accommodate demand from COVID-19 cases. One of the most important metrics for planning is the COVID-19 hospital census. Only a few papers make use of leading indicators within multivariate time-series models for this problem. We incorporated a leading indicator, the local COVID-19 infection incidence, together with the COVID-19 hospital census in a multivariate framework called the Vector Error Correction model to make 7-day-ahead forecasts. This model is also applied to produce 60-day scenario forecasts based on different trajectories of the pandemic. We find that the two time-series have a stable long-run relationship. The model has a good fit to the data and good forecast performance in comparison with a more traditional model using the census data alone. When applied to different 60-day scenarios of the pandemic, the census forecasts show concave trajectories that peak 2-3 weeks later than the infection incidence. Our paper presents this new model for accurate short-term forecasts and realistic scenario-based long-term forecasts of the COVID-19 hospital census to help healthcare systems in their decision making. Our findings suggest using the local COVID-19 infection incidence data can improve and extend more traditional forecasting models.

Nonstationary Stochastic Modelling of Multivariate Long-Term Wind and Wave Data

2005 ◽  
Author(s):  
Christos N. Stefanakos ◽  
Konstandinos A. Belibassakis
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Multivariate Time Series ◽  
Stochastic Modelling ◽  
Mean Value ◽  
Wave Data ◽  
Available Information ◽  
Periodic Components ◽  
Box Cox Transformation

In the present work, a nonstationary stochastic model, which is suitable for the analysis and simulation of multivariate time series of wind and wave data, is being presented and validated. This model belongs to the class of periodically correlated stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First, the time series is appropriately transformed to become Gaussian using the Box-Cox transformation. Then, the series is decomposed, using an appropriate seasonal standardization procedure, to a periodic (deterministic) mean value and a (stochastic) residual time series multiplied by a periodic (deterministic) standard deviation. The periodic components are estimated using appropriate time series of monthly data. The residual stochastic part, which is proved to be stationary, is modelled as a VARMA process. This way the initial process can be given the structure of a multivariate periodically correlated process. The present methodology permits a reliable reproduction of available information about wind and wave conditions, which is required for a number of applications.

An integrated deterministic–stochastic approach for forecasting the long-term trajectories of COVID-19

2021 ◽  
pp. 2141001
Author(s):  
Indrajit Ghosh ◽  
Tanujit Chakraborty
Keyword(s):  
Time Series ◽  
Stochastic Approach ◽  
World Population ◽  
Data Sets ◽  
Univariate Time Series ◽  
Reproduction Numbers ◽  
The World ◽  
Long Term Forecasting ◽  
Ar Models

The ongoing coronavirus disease 2019 (COVID-19) pandemic is one of the major health emergencies in decades that affected almost every country in the world. As of June 30, 2020, it has caused an outbreak with more than 10 million confirmed infections, and more than 500,000 reported deaths globally. Due to the unavailability of an effective treatment (or vaccine) and insufficient evidence regarding the transmission mechanism of the epidemic, the world population is currently in a vulnerable position. The daily cases data sets of COVID-19 for profoundly affected countries represent a stochastic process comprised of deterministic and stochastic components. This study proposes an integrated deterministic–stochastic approach to forecast the long-term trajectories of the COVID-19 cases for Italy and Spain. The deterministic component of the daily-cases univariate time series is assessed by an extended version of the SIR [Susceptible–Infected–Recovered–Protected–Isolated (SIRCX)] model, whereas its stochastic component is modeled using an autoregressive (AR) time series model. The proposed integrated SIRCX-AR (ISA) approach based on two operationally distinct modeling paradigms utilizes the superiority of both the deterministic SIRCX and stochastic AR models to find the long-term trajectories of the epidemic curves. Experimental analysis based on the proposed ISA model shows significant improvement in the long-term forecasting of COVID-19 cases for Italy and Spain in comparison to the ODE-based SIRCX model. The estimated Basic reproduction numbers for Italy and Spain based on SIRCX model are found to be [Formula: see text] and [Formula: see text], respectively. ISA model-based results reveal that the number of cases in Italy and Spain between 11 May, 2020–9 June, 2020 will be 10,982 (6383–15,582) and 13,731 (3395–29,013), respectively. Additionally, the expected number of daily cases on 9 July, 2020 for Italy and Spain is estimated to be 30 (0–183) and 92 (0–602), respectively.

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