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A Smooth Transition ARCH Model for Asset Returns

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  • Hagerud, Gustaf E.

    (Department of Finance)

Abstract

In the classical ARCH model of Engle [1982] the conditional variance is a linear function of lagged squared residuals. In this paper I introduce nonlinearity, by adding a term that consists of a constant parameter multiplied by a transition function. Two different transition functions are considered, a logistic and an exponential. Furthermore, following Bollerslev [1986], I extend the model by introducing lagged conditional variances in the conditional variance equation. This specification reduces the number of parameters in the model, which proves to be important for successful estimation. The paper also describes a number of specification tests, that can determine if the smooth transition GARCH model can be the data generating process of a times series. The techniques proposed are illustrated on data from four stock index series.

Suggested Citation

  • Hagerud, Gustaf E., 1997. "A Smooth Transition ARCH Model for Asset Returns," SSE/EFI Working Paper Series in Economics and Finance 162, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0162
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    Citations

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    Cited by:

    1. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.
    2. Melike Bildirici & Özgür Ömer Ersin, 2014. "Nonlinearity, Volatility and Fractional Integration in Daily Oil Prices: Smooth Transition Autoregressive ST-FI(AP)GARCH Models," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 108-135, October.
    3. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    4. Halunga, Andreea G. & Orme, Chris D., 2009. "First-Order Asymptotic Theory For Parametric Misspecification Tests Of Garch Models," Econometric Theory, Cambridge University Press, vol. 25(2), pages 364-410, April.
    5. Srikanta Kundu & Nityananda Sarkar, 2016. "Is the Effect of Risk on Stock Returns Different in Up and Down Markets? A Multi-Country Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 53-71, September.

    More about this item

    Keywords

    GARCH; high frequency data; asymmetry; non-linear models;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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