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Souhaib Ben Taieb, James W. Taylor, Rob J. Hyndman

Abstract:
Many applications require forecasts for a hierarchy comprising a set of time series along with aggregates of subsets of these series. Although forecasts can be produced independently for each series in the hierarchy, typically this does not lead to coherent forecasts — the property that forecasts add up appropriately across the hierarchy. State-of-the-art hierarchical forecasting methods usually reconcile these independently generated forecasts to satisfy the aggregation constraints. A fundamental limitation of prior research is that it has looked only at the problem of forecasting the mean of each time series. We consider the situation where probabilistic forecasts are needed for each series in the hierarchy. We define forecast coherency in this setting, and propose an algorithm to compute predictive distributions for each series in the hierarchy. Our algorithm has the advantage of synthesizing information from different levels in the hierarchy through a sparse forecast combination and a probabilistic hierarchical aggregation. We evaluate the accuracy of our forecasting algorithm on both simulated data and large-scale electricity smart meter data. The results show consistent performance gains compared to state-of-the art methods

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  Tag: density estimation

7 posts
March 7th, 2017

Coherent Probabilistic Forecasts for Hierarchical Time Series

Souhaib Ben Taieb, James W. Taylor, Rob J. Hyndman Abstract: Many applications require forecasts for a hierarchy comprising a set […]

June 4th, 2015

Probabilistic time series forecasting with boosted additive models: an application to smart meter data

By Souhaib Ben Taieb, Raphael Huser, Rob J Hyndman and Marc G Genton

October 19th, 2013

hdrcde package for R

The hdrcde package provides tools for computation of highest density regions in one and two dimensions, kernel estimation of univariate […]

March 10th, 2011

Improved interval estimation of long run response from a dynamic linear model: a highest density region approach

Jae H. Kim1 , Iain Fraser2 and Rob J. Hyndman1 Department of Econometrics and Business Statistics, Monash University, VIC 3800, […]

January 3rd, 2010

Density forecasting for long-term peak electricity demand

Rob J Hyndman and Shu Fan IEEE Transactions on Power Systems, 2010, 25(2), 1142-1153 Abstract: Long-term electricity demand forecasting plays […]

September 17th, 2006

Projection pursuit estimator for multivariate conditional densities

Azhong Ye and Rob J. Hyndman (2006) J. Fuzhou Univ. Nat. Sci. Ed. 34(6), 794–797. (Chinese).

July 20th, 2006

A Bayesian approach to bandwidth selection for multivariate kernel density estimation

Computational Statistics & Data Analysis (2006), 50(11), 3009-3031. Xibin Zhang, Maxwell L King and Rob J. Hyndman Abstract: Kernel density […]

July 16th, 2002

Nonparametric estimation and symmetry tests for conditional density functions

Journal of Nonparametric Statistics (2002), 14(3), 259-278. Rob J Hyndman1 and  Qiwei Yao2 Department of Econometrics and Business Statistics, Monash University, […]

June 16th, 2001

Bandwidth selection for kernel conditional density estimation

Computational Statistics and Data Analysis (2001), 36(3), 279-298. David Bashtannyk and Rob J Hyndman Abstract: We consider bandwidth selection for […]

July 16th, 1996

Estimating and visualizing conditional densities

Journal of Computational and Graphical Statistics (1996), 5 315-336. Rob J Hyndman1 and David Bashtannyk1 Abstract: We consider the kernel […]

July 16th, 1996

Computing and graphing highest density regions

American Statistician (1996),50, 120-126. Rob J Hyndman1 Abstract: Many statistical methods involve summarizing a probability distribution by a region of […]

July 15th, 1996

Wand and Jones. Kernel smoothing

July 16th, 1995

Highest density forecast regions for non-linear and non-normal time series models

Journal of Forecasting (1995),14, 431-441. Rob J Hyndman Abstract: Many modern time series methods, such as those involving non-linear models […]

July 5th, 1995

The problem with Sturges’ rule for constructing histograms

Hyndman, R.J. Abstract Most statistical packages use Sturges’ rule (or an extension of it) for selecting the number of classes […]