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Randomly Choosing Parameters from the Stationarity and Invertibility Region of Autoregressive–Moving Average Models

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  • M. C. Jones

Abstract

Choice of appropriate parameter configurations for time series simulations is not always easy. One possible approach when simulating from autoregressive–moving average models is to choose parameter values from a uniform distribution on the stationarity and invertibility region associated with such models. In this paper, well‐known time series results are applied to this problem to give a neat method which comprises generating partial autocorrelations independently distributed as appropriate beta variates and applying a standard transformation to obtain the parameters from these.

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  • M. C. Jones, 1987. "Randomly Choosing Parameters from the Stationarity and Invertibility Region of Autoregressive–Moving Average Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 134-138, June.
    • Handle: RePEc:bla:jorssc:v:36:y:1987:i:2:p:134-138
    DOI: 10.2307/2347544
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    Cited by:

    1. Ng, Chi Tim & Joe, Harry, 2010. "Generating random AR(p) and MA(q) Toeplitz correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1532-1545, July.
    2. Billio, M. & Monfort, A. & Robert, C. P., 1999. "Bayesian estimation of switching ARMA models," Journal of Econometrics, Elsevier, vol. 93(2), pages 229-255, December.
    3. Alexander Meyer-Gohde & Daniel Neuhoff, 2015. "Generalized Exogenous Processes in DSGE: A Bayesian Approach," SFB 649 Discussion Papers SFB649DP2015-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Luigi Spezia & Andy Vinten & Roberta Paroli & Marc Stutter, 2021. "An evolutionary Monte Carlo method for the analysis of turbidity high‐frequency time series through Markov switching autoregressive models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    5. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 2-25.
    6. Davide Ravagli & Georgi N. Boshnakov, 2022. "Bayesian analysis of mixture autoregressive models covering the complete parameter space," Computational Statistics, Springer, vol. 37(3), pages 1399-1433, July.
    7. Pötscher, Benedikt M. & Preinerstorfer, David, 2018. "Controlling the size of autocorrelation robust tests," Journal of Econometrics, Elsevier, vol. 207(2), pages 406-431.
    8. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    9. Daniel Neuhoff, 2015. "Dynamics of Real Per Capita GDP," SFB 649 Discussion Papers SFB649DP2015-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Fitzgibbon, L.J., 2006. "On sampling stationary autoregressive model parameters uniformly in r2 value," Statistics & Probability Letters, Elsevier, vol. 76(4), pages 349-352, February.
    11. Neil Shephard & Tina Hviid Rydberg, 1999. "Modelling trade-by-trade price movements of multiple assets using multivariate compount Poisson processes," Economics Series Working Papers 1999-W23, University of Oxford, Department of Economics.
    12. Paroli, Roberta & Spezia, Luigi, 2008. "Bayesian inference in non-homogeneous Markov mixtures of periodic autoregressions with state-dependent exogenous variables," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2311-2330, January.

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