L1 linear interpolator for missing values in time series

Zudi Lu; Y. V. Hui

doi:10.1007/BF02530494

L₁ linear interpolator for missing values in time series

Zudi Lu
, Y. V. Hui

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

8 Citations (Scopus)

Abstract

We propose a minimum mean absolute error linear interpolator (MMAELI), based on the L₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal and t distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed.

Original language	English
Pages (from-to)	197-216
Journal	Annals of the Institute of Statistical Mathematics
Volume	55
Issue number	1
DOIs	https://doi.org/10.1007/BF02530494
Publication status	Published - 2003

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Research Keywords

Autoregressive process
Innovation departure
Linear interpolation
Minimum mean absolute error
Missing values

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10.1007/BF02530494

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Cite this

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title = "L1 linear interpolator for missing values in time series",

abstract = "We propose a minimum mean absolute error linear interpolator (MMAELI), based on the L1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal and t distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed.",

keywords = "Autoregressive process, Innovation departure, Linear interpolation, Minimum mean absolute error, Missing values",

author = "Zudi Lu and Hui, \{Y. V.\}",

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T1 - L1 linear interpolator for missing values in time series

AU - Lu, Zudi

AU - Hui, Y. V.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2003

Y1 - 2003

N2 - We propose a minimum mean absolute error linear interpolator (MMAELI), based on the L1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal and t distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed.

AB - We propose a minimum mean absolute error linear interpolator (MMAELI), based on the L1 approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal and t distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed.

KW - Autoregressive process

KW - Innovation departure

KW - Linear interpolation

KW - Minimum mean absolute error

KW - Missing values

UR - https://www.scopus.com/pages/publications/12444253888

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-12444253888&origin=recordpage

U2 - 10.1007/BF02530494

DO - 10.1007/BF02530494

M3 - RGC 21 - Publication in refereed journal

SN - 0020-3157

VL - 55

SP - 197

EP - 216

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 1

ER -