A Hierarchical Model for Aggregated Functional Data

Dias, Ronaldo; Garcia, Nancy L.; Schmidt, Alexandra M.

doi:10.1080/00401706.2013.765316

Cited by 10 publications

(14 citation statements)

References 28 publications

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“…Special attention has been devoted to the functional data analysis. A hierarchical model for aggregated functional data is introduced by Dias et al , with an application to the distribution of energy among different types of consumers. Other fashionable techniques often used are neural networks and the Gaussian process .…”

Section: A Review Of Alternative Modelsmentioning

confidence: 99%

Multivariate dynamic regression: modeling and forecasting for intraday electricity load

Migon

Alves

2013

Appl Stoch Models Bus & Ind

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This paper introduces electricity load curve models for short-term forecasting purposes. A broad class of multivariate dynamic regression models is proposed to model hourly electricity load. Alternative forecasting models, special cases of our general model, include separate time series regressions for each hour and week day. All the models developed include components that represent trends, seasons at different levels (yearly, weekly, etc.), dummies to take into account weekends/holidays and other special days, and short-term dynamics and weather regression effects, discussing the necessity of nonlinx ear functions for cooling effects. Our developments explore the facilities of dynamic linear models such as the use of discount factors, subjective intervention, variance learning and smoothing/filtering. The elicitation of the load curve is considered in the context of subjective intervention analysis, which is especially useful to take into account the adjustments for daylight savings time. The theme of combination of probabilistic forecasting is also briefly addressed.variance learning, is a novelty, as far as we know, in the area of electricity load forecasting. All the models developed include components that represent trends, seasons at different levels (yearly, weekly etc.), dummies to take into account weekends/holidays and other special days, and short-term dynamics and weather regression effects, including nonlinear functions for cooling effects. A comparison between multivariate and univariate models shows that they mainly differ in computational cost. From the point of view of the distribution network operator, this is relevant information, especially because the univariate models takes less time to be fitted.Special care is taken with the role played by weekends/holidays and their effect on the estimated coefficients. In particular, we explore the similarities between the shapes of load curves occurring on the day just before and just after weekends/holidays. Our developments explore the facilities of dynamic linear models such as the use of discount factors, subjective intervention, variance learning and smoothing. The elicitation of the load curve is considered in the context of subjective intervention analysis, which is especially useful to take into account the adjustments for daylight savings time.More precisely, we model a suitable transformation of the electricity load at hour and day t as a linear combination of the transformed load at the same hour on the previous day and appropriate functions of the prevailing temperatures on day t . The coefficients depend on the pair . ; t / in a continuous nonlinear manner. The paper ends by briefly addressing the theme of combination of probabilistic forecasting.The remainder of the paper is organized as follows. A review of alternative models is presented in Section 2. In Section 3, we explore the data set analyzed. Some stylized facts always presented in the load electricity data are also reviewed. Our application to Brazilian southeast hourly electrici...

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Section: A Review Of Alternative Modelsmentioning

confidence: 99%

Multivariate dynamic regression: modeling and forecasting for intraday electricity load

Migon

Alves

2013

Appl Stoch Models Bus & Ind

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“…The estimation of typical load curves of electrical consumption using aggregated functional data was first done by Dias, Garcia, and Martarelli () and revisited in the Bayesian framework by Dias, Garcia, and Schmidt (). However, these authors assumed that the reported classes were equal to the true classes.…”

Section: Introductionmentioning

confidence: 99%

Analysis of aggregated functional data from mixed populations with application to energy consumption

et al. 2016

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Understanding the energy consumption patterns of different types of consumers is essential in any planning of energy distribution. However, obtaining consumption information for single individuals is often either not possible or too expensive. Therefore, we consider data from aggregations of energy use, that is, from sums of individuals' energy use, where each individual falls into one of C consumer classes. Unfortunately, the exact number of individuals of each class may be unknown: consumers do not always report the appropriate class, due to various factors including differential energy rates for different consumer classes. We develop a methodology to estimate the expected energy use of each class as a function of time and the true number of consumers in each class. We also provide some measure of uncertainty of the resulting estimates. To accomplish this, we assume that the expected consumption is a function of time that can be well approximated by a linear combination of B-splines. Individual consumer perturbations from this baseline are modeled as B-splines with random coefficients. We treat the reported numbers of consumers in each category as random variables with distribution depending on the true number of consumers in each class and on the probabilities of a consumer in one class reporting as another class. We obtain maximum likelihood estimates of all parameters via a maximization algorithm. We introduce a special numerical trick for calculating the maximum likelihood estimates of the true number of consumers in each class. We apply our method to a data set and study our method via simulation.

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“…However, the high dimensionality of the problem and the fact that there is no replication of the data results in poor aggregated covariance estimates, with sample covariance matrices having high condition numbers and therefore often being numerically singular. To overcome this problem, we model the covariance function as suggested by Dias et al (2012), we assumed that the covariance of each ǫ i (t) in model (2.4) is homogeneous and given by…”

Section: Artificial Datasetsmentioning

confidence: 99%

“…This is an interesting sample to analyze since it was designed to achieve an orthogonal design in the calibration step. It was also analyzed, using a Bayesian perspective, but only for the calibration step, by Dias, Garcia and Schmidt (2012). The other one is the so-called Tecator Data which is used by several authors to compare the techniques in terms of prediction tool, for example in the works by Borggaard and Thodberg (1992), Eilers, Li andMarx (2009), Ferraty and, Aneiros-Pérez and Vieu (2006).…”

Section: Introductionmentioning

confidence: 99%

Aggregated functional data model for near-infrared spectroscopy calibration and prediction

Dias

Garcia

Ludwig

et al. 2014

Journal of Applied Statistics

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Calibration and prediction for NIR spectroscopy data are performed based on a functional interpretation of the Beer-Lambert formula. Considering that, for each chemical sample, the resulting spectrum is a continuous curve obtained as the summation of overlapped absorption spectra from each analyte plus a Gaussian error, we assume that each individual spectrum can be expanded as a linear combination of B-splines basis. Calibration is then performed using two procedures for estimating the individual analytes curves: basis smoothing and smoothing splines.Prediction is done by minimizing the square error of prediction. To assess the variance of the predicted values, we use a leave-one-out jackknife technique. Departures from the standard error models are discussed through a simulation study, in particular, how correlated errors impact on the calibration step and consequently on the analytes' concentration prediction. Finally, the performance of our methodology is demonstrated through the analysis of two publicly available datasets.

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A Hierarchical Model for Aggregated Functional Data

Cited by 10 publications

References 28 publications

Multivariate dynamic regression: modeling and forecasting for intraday electricity load

Multivariate dynamic regression: modeling and forecasting for intraday electricity load

Analysis of aggregated functional data from mixed populations with application to energy consumption

Aggregated functional data model for near-infrared spectroscopy calibration and prediction

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