Computation of the exact likelihood function of an arima process

Dent, Warren T.

doi:10.1080/00949657708810151

Cited by 43 publications

(24 citation statements)

References 7 publications

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“…Before describing our algorithm, we briefly show the equivalence of the methods published independently by Newbold (1974) and Dent (1977), and note a modification to their approach due to Ali (1977). Newbold (1974) has derived the exact likelihood for a mixed process using a generalization of the approach used by Box & Jenkins for pure moving average processes.…”

Section: Existing Procedures For the Exact Likelihoodmentioning

confidence: 99%

“…Exact expressions for (1.2) that are more suitable for computation have been given by a number of authors. Box & Jenkins (1976, p. 271) give an expression for the pure moving average case, and this approach has been extended to mixed processes independently by Newbold (1974), Dent (1977) and Ali (1977). The same approach has been generalized for multivariate moving averages by Osborne (1977) and S. C. Hillmer and G. C. Tiao, in an unpublished report.…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process

Ansley¹

1979

Biometrika

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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe likelihood function for an autoregressive-moving average process is obtained by transforming the process to obtain a band covariance matrix whose Cholesky decomposition can be readily computed. Refinements are given for pure autoregressive and multiplicative seasonal processes. Evidence is presented to show that this approach allows more efficient computation than other methods proposed in the literature.Some key words: Autoregressive-moving average model; Exact likelihood function; Multiplicative seasonal model; Time series. ARMA(1, 0)

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Section: Existing Procedures For the Exact Likelihoodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process

Ansley¹

1979

Biometrika

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“…A convenient explicit formula for :i;-I is given in Dent (1977); see also the discussion in Ansley (1979). Ansley's (1979) Cholesky method also provides the inverse :i;-l very simply, and the same result can be achieved by ML algorithms based on the Kalman filter.…”

Section: General Casementioning

confidence: 92%

Testing for a Moving Average Unit Root in Autoregressive Integrated Moving Average Models

Saikkonen

Luukkonen

1993

Journal of the American Statistical Association

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Test procedures for detecting overdifferencing or a moving average unit root in Gaussian autoregressive integrated moving average (ARIMA) models are proposed. The tests can be used when an autoregressive unit root is a serious alternative but the hypothesis of primary interest implies stationarity of the observed time series. This is the case, for example, if one wishes to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical cointegration vector. A priori knowledge of the mean value of the observations turns out to be crucial for the derivation of our tests. In the special case where the differenced series follows a firstorder moving average process, the proposed tests are exact and can be motivated by local optimality arguments. Specifically, when the mean value of the series is a priori known, we can obtain a locally best invariant (LBI) test that is identical to a one-sided version of the Lagrange multiplier test. But when the mean value is a priori not known, this test breaks down and we derive a locally best invariant unbiased (LBIU) test. After having tests in this special case, we develop extensions to general ARIMA models. These tests are asymptotic, but under the null hypothesis they have the same limiting distributions as in the just-mentioned special case. When the mean value is a priori known, an asymptotic XI distribution is obtained, when it is unknown, the limiting distribution agrees with that of the Cramer-von Mises goodness-of-fit test statistic.

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“…where Q(8) = C(8)ZC (8) example, Dent, 1977). When this functional dependence needs to be emphasized we use the notation Z(t) in place of 2.…”

Section: (22)mentioning

confidence: 99%

Testing the Order of Differencing in Time Series Regression

Saikkonen

Luukkonen

1996

Journal Time Series Analysis

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In this paper we develop a test procedure for detecting overdifferencing or a moving-average unit root in time series regression models with Gaussian autoregressive moving-average errors. In addition to an intercept term the regressors consist of stable or asymptotically stationary variables and non-stationary trending variables generated by an integrated process of order 1. The test of the paper is based on the theory of locally best invariant unbiased tests. Its limiting distribution is derived under the null hypothesis and found to be non-standard but free of unknown nuisance parameters. Asymptotic critical values, which depend on the number of integrated regressors, are obtained by simulation. A limited simulation study is carried out to illustrate the finite sample properties of the test.

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Computation of the exact likelihood function of an arima process

Cited by 43 publications

References 7 publications

An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process

An Algorithm for the Exact Likelihood of a Mixed Autoregressive-Moving Average Process

Testing for a Moving Average Unit Root in Autoregressive Integrated Moving Average Models

Testing the Order of Differencing in Time Series Regression

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