Benchmark Forecast and Error Modeling

• DOI: http://doi.org/10.1002/for.2439
• Published date: 01 July 2017
• Author: Ka Ho Wu,Zhao‐Guo Chen
• Date: 01 July 2017

Journal of Forecasting,J. Forecast. 36, 382–394 (2017)

Published online 18 September 2016 in Wiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/for.2439

Benchmark Forecast and Error Modeling

ZHAO-GUO CHEN1AND KA HO WU2

1

Statistics Canada, Ottawa, Ontario, Canada

2

Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong

ABSTRACT

For a target socioeconomic variable with data from two sources, benchmarking is a process which uses less frequent

and more reliable data, called benchmarks, to adjust more frequent and less reliable data. Consequently, forecasts of

unknown benchmarks are obtained. The regression method of benchmarking may lead to better results than widely

used numerical methods, but the model for the error of the more frequent data is supposed to be known. By properly

choosing a first-order autoregressive model as ‘working model’ for the error, the regressionmethod may work well in

reality. We present two new error modeling procedures via inside-data-period benchmark forecasts. The performance

of several modeling procedures is compared. These results may provide analysts with guidelines for choosing working

models for the error in developing and applying benchmarking software. Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS ARMA model; autocorrelation; benchmarking prediction; regression; standard deviation

INTRODUCTION

Benchmarking prediction and benchmark forecasts

Two sources of data with different degrees of precision and collecting frequency may be available for a target socioe-

conomic variable. The more frequent data (e.g. repeated monthly surveys) may reflect the immediate economic

situation, but is usually less reliable. The less frequent data (e.g. annual reports or censuses) are usually much more

accurate and can be considered as a benchmark. A process of using benchmarks to adjust for more frequent and less

reliable data is called benchmarking. The results of benchmarking are called benchmarking predictions or bench-

marked values. Here, we focus primarily on the situation in which an annual benchmark is the sum of the monthly

values of the target series in that year (the so-called flow series, such as manufacturing or retail sales), and the

error of the annual measurement, the so-called binding benchmark, can be ignored (see, for example, Dagum and

Cholette, 2006).

The set-up of the benchmarking problem in this paper is as follows. The data at month tare denoted by y.t/,

which is the sum of target variable .t/ and error e.t/.¹e.t/ºis assumed to be a stationary series and, without losing

much generality, to be mean zero (otherwise, it can be corrected by the estimated mean), i.e.

y.t/ D.t/ Ce.t/; t D1;:::;n; EŒe.t/D0(1)

The annual binding benchmarks are

´.T / DX

t2T

.t/; T D1;:::;N; n12N (2)

The notation t2Tmeans that month tis in year T. For non-binding benchmarks, an error term should be added

to the right-hand side of equation (2). Benchmarking procedures provide predictions of .t/ using the datasets of both

y.t/ and ´.T /, which should be superior to y.t/ alone.

Usually, the procedures to produce annual benchmarks ´.T/ are more expensive and complicated than those used

to obtain monthly data y.t/. They also involve reporting and/or data-processing delays. In the early part of the

current year, the monthly data for the previous year have been published but the benchmark for the previous year is

still unavailable. Simply adding up monthly data y.t/ for the previous year to obtain the total value of that year is

insufficient for representing the situation and analyzing recent economic performance. A better estimate for the total

of the previous year is required before the benchmark for that year becomes available. This is the problem of the

benchmark forecast.

Fortunately, benchmarking prediction can be obtained not only for the months covered by known benchmarks, but

also for the months in the period for which benchmarks are not yet available. If benchmarking is carried out properly,

Correspondence to: Ka Ho Wu, Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong. E-mail:

khwu@sta.cuhk.edu.hk

Copyright © 2016 John Wiley & Sons, Ltd