Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems

M.J. Chambers, J.R. McCrorie

    Research output: Working paperDiscussion paperOther research output

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    Abstract

    This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time.The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows.We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data.We formally establish the order of consistency and the asymptotic sampling properties of such an estimator.The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.
    Original languageEnglish
    Place of PublicationTilburg
    PublisherVakgroep CentER
    Number of pages34
    Volume2004-40
    Publication statusPublished - 2004

    Publication series

    NameCentER Discussion Paper
    Volume2004-40

    Fingerprint

    Frequency Domain
    Gaussian distribution
    Sample Size
    Converge
    Continuous-time Model
    Error Correction
    Long-run
    Limiting Distribution
    Square root
    Unknown Parameters
    Continuous Time
    Triangular
    Discrete-time
    Disturbance
    Analogue
    Estimator
    Estimate
    Form
    Model

    Keywords

    • estimation
    • aggregation
    • cointegration
    • general equilibrium

    Cite this

    Chambers, M. J., & McCrorie, J. R. (2004). Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems. (CentER Discussion Paper; Vol. 2004-40). Tilburg: Vakgroep CentER.
    Chambers, M.J. ; McCrorie, J.R. / Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems. Tilburg : Vakgroep CentER, 2004. (CentER Discussion Paper).
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    abstract = "This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time.The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows.We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data.We formally establish the order of consistency and the asymptotic sampling properties of such an estimator.The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.",
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    author = "M.J. Chambers and J.R. McCrorie",
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    year = "2004",
    language = "English",
    volume = "2004-40",
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    Chambers, MJ & McCrorie, JR 2004 'Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems' CentER Discussion Paper, vol. 2004-40, Vakgroep CentER, Tilburg.

    Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems. / Chambers, M.J.; McCrorie, J.R.

    Tilburg : Vakgroep CentER, 2004. (CentER Discussion Paper; Vol. 2004-40).

    Research output: Working paperDiscussion paperOther research output

    TY - UNPB

    T1 - Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems

    AU - Chambers, M.J.

    AU - McCrorie, J.R.

    N1 - Pagination: 34

    PY - 2004

    Y1 - 2004

    N2 - This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time.The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows.We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data.We formally establish the order of consistency and the asymptotic sampling properties of such an estimator.The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.

    AB - This paper discusses the joint estimation of the long run equilibrium coe cients and the parameters governing the short run dynamics of a fully parametric cointegrated system formulated in continuous time.The model allows the stationary disturbances to be generated by a stochastic di erential equation system and for the variables to be a mixture of stocks and flows.We derive a precise form for the exact discrete analogue of the continuous time model in triangular error correction form, which acts as the basis for frequency domain Gaussian estimation of the unknown parameters using discrete time data.We formally establish the order of consistency and the asymptotic sampling properties of such an estimator.The function of the data that estimates the cointegrating parameters is shown to converge at the rate of the sample size to a mixed normal distribution, while that estimating the short run parameters converges at the rate of the square root of the sample size to a limiting normal distribution.

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    KW - aggregation

    KW - cointegration

    KW - general equilibrium

    M3 - Discussion paper

    VL - 2004-40

    T3 - CentER Discussion Paper

    BT - Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems

    PB - Vakgroep CentER

    CY - Tilburg

    ER -

    Chambers MJ, McCrorie JR. Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems. Tilburg: Vakgroep CentER. 2004. (CentER Discussion Paper).