Properties of point forecast reconciliation approaches

by   Shanika L Wickramasuriya, et al.

Point forecast reconciliation of collection of time series with linear aggregation constraints has evolved substantially over the last decade. A few commonly used methods are GLS (generalized least squares), OLS (ordinary least squares), WLS (weighted least squares), and MinT (minimum trace). GLS and MinT have similar mathematical expressions, but they differ by the covariance matrix used. OLS and WLS can be considered as special cases of MinT where they differ by the assumptions made about the structure of the covariance matrix. All these methods ensure that the reconciled forecasts are unbiased, provided that the base forecasts are unbiased. The ERM (empirical risk minimizer) approach was proposed to relax the assumption of unbiasedness. This paper proves that (a) GLS and MinT reduce to the same solution; (b) on average, a method similar to ERM (which we refer to as MinT-U) can produce better forecasts than MinT (lowest total mean squared error) which is then followed by OLS and then by base; and (c) the mean squared error of each series in the structure for MinT-U is smaller than that for MinT which is then followed by that for either OLS or base forecasts. We show these theoretical results using a set of simulation studies. We also evaluate them using the Australian domestic tourism data set.



There are no comments yet.


page 20

page 21

page 22

page 28


Probabilistic forecast reconciliation under the Gaussian framework

Forecast reconciliation of multivariate time series is the process of ma...

Linear pooling of sample covariance matrices

We consider covariance matrix estimation in a setting, where there are m...

On Measuring the Variability of Small Area Estimators in a Multivariate Fay-Herriot Model

This paper is concerned with the small area estimation in the multivaria...

Reconciling Hierarchical Forecasts via Bayes' Rule

When time series are organized into hierarchies, the forecasts have to s...

Forecast combination based forecast reconciliation: insights and extensions

In a recent paper, while elucidating the links between forecast combinat...

Optimal Combination Forecasts on Retail Multi-Dimensional Sales Data

Time series data in the retail world are particularly rich in terms of d...

Material Facts Obscured in Hansen's Modern Gauss-Markov Theorem

We show that the abstract and conclusion of Hansen's Econometrica paper,...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.