Generalizing the Theta method for automatic forecasting

The Theta method attracted the attention of researchers and practitioners in recent years due to its simplicity and superior forecasting accuracy. Its performance has been confirmed by many empirical studies as well as forecasting competitions. In this article the Theta method is tested in short-term load forecasting problem. The load time series expressing multiple seasonal cycles is decomposed in different ways to simplify the forecasting problem. Four variants of input data definition are considered. The standard Theta method is uses as well as the dynamic optimised Theta model proposed recently. The performances of the Theta models are demonstrated through an empirical application using real power system data and compared with other popular forecasting methods.

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Fuzzy Prediction Intervals Using Credibility Distributions

Engineering Proceedings ◽

10.3390/engproc2021005051 ◽

2021 ◽

Vol 5 (1) ◽

pp. 51

Author(s):

Enriqueta Vercher ◽

Abel Rubio ◽

José D. Bermúdez

Keyword(s):

Time Series ◽

Time Series Data ◽

Computational Cost ◽

Expected Value ◽

Prediction Intervals ◽

Series Data ◽

Comparative Results ◽

Automatic Forecasting

We present a new forecasting scheme based on the credibility distribution of fuzzy events. This approach allows us to build prediction intervals using the first differences of the time series data. Additionally, the credibility expected value enables us to estimate the k-step-ahead pointwise forecasts. We analyze the coverage of the prediction intervals and the accuracy of pointwise forecasts using different credibility approaches based on the upper differences. The comparative results were obtained working with yearly time series from the M4 Competition. The performance and computational cost of our proposal, compared with automatic forecasting procedures, are presented.

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Goal-Oriented Error Estimation for the Fractional Step Theta Scheme

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2014-0002 ◽

2014 ◽

Vol 14 (2) ◽

pp. 203-230 ◽

Cited By ~ 11

Author(s):

Dominik Meidner ◽

Thomas Richter

Keyword(s):

Time Discretization ◽

Posteriori Error ◽

Numerical Dissipation ◽

Error Estimator ◽

Fractional Step ◽

Weighted Residual Method ◽

Time Stepping ◽

Backward Euler ◽

Galerkin Formulation ◽

Theta Method

Abstract. In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, by combining three substeps of the theta time-stepping scheme, the fractional step theta time-stepping scheme is derived. It possesses highly desired stability and numerical dissipation properties and is second order accurate. The derived error estimator is based on a Petrov–Galerkin formulation that is up to a numerical quadrature error equivalent to the theta time-stepping scheme. The error estimator is assembled as one weighted residual term given by the dual weighted residual method and one additional residual estimating the Galerkin error between time-stepping scheme and Petrov–Galerkin formulation.

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