Influence diagnostics in log-linear integer-valued GARCH models

Fukang Zhu, Lei Shi, Shuangzhe LIU

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    Integer-valued generalized autoregressive conditional heteroscedasticity (GARCH) models have played an important role in time series analysis of count data. To model negatively autocorrelated time series and to accommodate covariates without restrictions, the log-linear integer-valued GARCH model has recently been proposed as an alternative to the existing models. In this paper, we study a local influence diagnostic analysis in the log-linear integer-valued GARCH models. The slope-based diagnostic and stepwise curvature-based diagnostics in a framework of the modified likelihood displacement are proposed. Under five perturbation schemes the corresponding local influence measures are derived. Two simulated data sets and a real-world example are analyzed to illustrate our method. In addition, the fitted model for this example has a negative coefficient for one of the two covariates, which is particularly illustrative of the extra flexibility of the considered model.
    Original languageEnglish
    Pages (from-to)311-335
    Number of pages25
    JournalAStA Advances in Statistical Analysis
    Volume99
    Issue number3
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Influence Diagnostics
    Generalized Autoregressive Conditional Heteroscedasticity
    diagnostic
    Integer
    Local Influence
    Covariates
    Model
    Diagnostics
    Likelihood Displacement
    Modified Likelihood
    Time series analysis
    Count Data
    time series analysis
    Time Series Analysis
    Generalized autoregressive conditional heteroscedasticity
    time series
    Time series
    Slope
    flexibility
    Flexibility

    Cite this

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    abstract = "Integer-valued generalized autoregressive conditional heteroscedasticity (GARCH) models have played an important role in time series analysis of count data. To model negatively autocorrelated time series and to accommodate covariates without restrictions, the log-linear integer-valued GARCH model has recently been proposed as an alternative to the existing models. In this paper, we study a local influence diagnostic analysis in the log-linear integer-valued GARCH models. The slope-based diagnostic and stepwise curvature-based diagnostics in a framework of the modified likelihood displacement are proposed. Under five perturbation schemes the corresponding local influence measures are derived. Two simulated data sets and a real-world example are analyzed to illustrate our method. In addition, the fitted model for this example has a negative coefficient for one of the two covariates, which is particularly illustrative of the extra flexibility of the considered model.",
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    Influence diagnostics in log-linear integer-valued GARCH models. / Zhu, Fukang; Shi, Lei; LIU, Shuangzhe.

    In: AStA Advances in Statistical Analysis, Vol. 99, No. 3, 2014, p. 311-335.

    Research output: Contribution to journalArticle

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