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Autoregressive–moving-average model

About: Autoregressive–moving-average model is a research topic. Over the lifetime, 4150 publications have been published within this topic receiving 118972 citations. The topic is also known as: ARMA & ARMA model.


Papers
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Journal ArticleDOI
TL;DR: In this article, a bias correction to the Akaike information criterion, called AICC, is derived for regression and autoregressive time series models, which is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample sample size.
Abstract: SUMMARY A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.

5,867 citations

BookDOI
04 Oct 2007
TL;DR: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series, which include vector autoregressive, cointegrated, vector Autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models.
Abstract: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated, vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.

5,244 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed a test for unit roots which is based on an approximation of an autoregressive-moving average model by an auto-gression, which has a limit distribution whose percentiles have been tabulated.
Abstract: SUMMARY Recently, methods for detecting unit roots in autoregressive and autoregressivemoving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an autoregressive-moving average model by an autoregression. The test statistic is standard output from most regression programs and has a limit distribution whose percentiles have been tabulated. An example is provided.

3,231 citations

Book ChapterDOI
TL;DR: This is a preliminary report on a newly developed simple and practical procedure of statistical identification of predictors by using autoregressive models in a stationary time series.
Abstract: This is a preliminary report on a newly developed simple and practical procedure of statistical identification of predictors by using autoregressive models. The use of autoregressive representation of a stationary time series (or the innovations approach) in the analysis of time series has recently been attracting attentions of many research workers and it is expected that this time domain approach will give answers to many problems, such as the identification of noisy feedback systems, which could not be solved by the direct application of frequency domain approach [1], [2], [3], [9].

2,436 citations

Book
01 Jan 1991
TL;DR: The choice of point and interval forecasts as well as innovation accounting are presented as tools for structural analysis within the multiple time series context.
Abstract: This graduate-level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts as well as innovation accounting are presented as tools for structural analysis within the multiple time series context.

2,136 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202354
2022125
2021125
2020141
2019141
2018122