The Effect of Aggregation on Prediction in the Autoregressive Model

Amemiya, Takeshi; Wu, Roland Y.

doi:10.1080/01621459.1972.10481264

“…If disaggregate data is available it was found that forecasting the disaggregate series and then aggregating the forecasts may be preferable to forecasting the aggregate series directly. Such results were found for both temporal as well as contemporaneous aggregation (e.g., Amemiya and Wu (1972), Wei (1978), Lütkepohl (1986Lütkepohl ( , 1987Lütkepohl ( , 2006, Silvestrini, Salto, Moulin and Veredas (2008)). Many of the available results relate to linear aggregation, however.…”

Section: Discussionsupporting

confidence: 49%

The Role of Log Transformation in Forecasting Economic Variables

Luetkepohl

¹

,

Xu

²

2009

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. It is found that it depends on the data generation process whether the former or the latter are preferable. For a range of economic variables substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved. Terms of use: Documents in EconStor mayJEL Code: C22.

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“…If disaggregate data is available it was found that forecasting the disaggregate series and then aggregating the forecasts may be preferable to forecasting the aggregate series directly. Such results were found for both temporal as well as contemporaneous aggregation (e.g., Amemiya and Wu (1972), Wei (1978), Lütkepohl (1986Lütkepohl ( , 1987Lütkepohl ( , 2006, Silvestrini, Salto, Moulin and Veredas (2008)). Many of the available results relate to linear aggregation, however.…”

Section: Discussionmentioning

confidence: 54%

The role of the log transformation in forecasting economic variables

Lütkepohl

¹

,

Xu

²

2010

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. For forecasting and economic analysis many variables are used in logarithms (logs). In time series analysis this transformation is often considered to stabilize the variance of a series. We investigate under which conditions taking logs is beneficial for forecasting. Forecasts based on the original series are compared to forecasts based on logs. It is found that it depends on the data generation process whether the former or the latter are preferable. For a range of economic variables substantial forecasting improvements from taking logs are found if the log transformation actually stabilizes the variance of the underlying series. Using logs can be damaging for the forecast precision if a stable variance is not achieved. Terms of use: Documents in EconStor mayJEL Code: C22.

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“…Studying its effects on univariate time series models goes back to the seminal work of Amemiya and Wu (1972), Tiao (1972) and Brewer (1973). The theoretical results on ARIMA processes from these papers are summarised by Rossana and Seater (1995) as being threefold: (a) temporal aggregation contaminates/complicates the dynamics of the underlying ARIMA(p, d, q) process through the moving average component (they refer to this as the Brewer effect); (b) as the level of aggregation increases the process at the aggregate level is simplified and converges to an IMA(d, d) (they call this the Tiao effect); and (c) aggregation causes loss in the number of observations resulting in a loss in estimation efficiency (they call this the sample size effect).…”

Section: Introductionmentioning

confidence: 99%

Forecasting with temporal hierarchies

Athanasopoulos

¹

,

Kourentzes

²

,

Petropoulos

³

2017

European Journal of Operational Research

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This paper introduces the concept of Temporal Hierarchies for time series forecasting. A temporal hierarchy can be constructed for any time series by means of non-overlapping temporal aggregation. Predictions constructed at all aggregation levels are combined with the proposed framework to result in temporally reconciled, accurate and robust forecasts. The implied combination mitigates modelling uncertainty, while the reconciled nature of the forecasts results in a unified prediction that supports aligned decisions at different planning horizons: from shortterm operational up to long-term strategic planning. The proposed methodology is independent of forecasting models. It can embed high level managerial forecasts that incorporate complex and unstructured information with lower level statistical forecasts. Our results show that forecasting with temporal hierarchies increases accuracy over conventional forecasting, particularly under increased modelling uncertainty. We discuss organisational implications of the temporally reconciled forecasts using a case study of Accident & Emergency departments.

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The Effect of Aggregation on Prediction in the Autoregressive Model

Cited by 132 publications

References 2 publications

The Role of Log Transformation in Forecasting Economic Variables

The Role of Log Transformation in Forecasting Economic Variables

The role of the log transformation in forecasting economic variables

Forecasting with temporal hierarchies

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