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HY-A-PARCH: A stationary A-PARCH model with long memory

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  • Schoffer, Olaf

Abstract

The FI-A-PARCH process has been developed by Tse (1998) to model essential characteristics of financial market returns. However, due to the nonstationarity described by Níguez (2002) the process exhibits infinite conditional second moments and no statements about the autocovariance function can be derived. Thus, the new Hyperbolic A-PARCH model is considered, first introduced in Schoffer (2003). Subsequently the characteristics of this extension of the FI-A-PARCH process are inspected. It can be shown, that under certain parameter restrictions the intrinsic process as well as the process of conditional volatilities is stationary. Furthermore, for an asymmetric transformation of the conditional volatilities the presence of long memory is proven. Thus, the introduced model is able to reproduce the main characteristics of financial market returns such as volatility clustering, leptokurtosis, asymmetry and long memory.

Suggested Citation

  • Schoffer, Olaf, 2003. "HY-A-PARCH: A stationary A-PARCH model with long memory," Technical Reports 2003,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200340
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    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    2. Masato Ubukata & Toshiaki Watanabe, 2011. "Pricing Nikkei 225 Options Using Realized Volatility," IMES Discussion Paper Series 11-E-18, Institute for Monetary and Economic Studies, Bank of Japan.
    3. Heni Boubaker & Giorgio Canarella & Rangan Gupta & Stephen M. Miller, 2023. "A Hybrid ARFIMA Wavelet Artificial Neural Network Model for DJIA Index Forecasting," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1801-1843, December.
    4. repec:awi:wpaper:0472 is not listed on IDEAS
    5. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
    6. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.
    7. Masato Ubukata & Toshiaki Watanabe, 2014. "Pricing Nikkei 225 Options Using Realized Volatility," The Japanese Economic Review, Japanese Economic Association, vol. 65(4), pages 431-467, December.
    8. Cecilia Maya & Karoll Gómez, 2008. "What Exactly is "Bad News" in Foreign Exchange Markets? Evidence from Latin American Markets," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 45(132), pages 161-183.
    9. M. Karanasos & S. Yfanti & A. Christopoulos, 2021. "The long memory HEAVY process: modeling and forecasting financial volatility," Annals of Operations Research, Springer, vol. 306(1), pages 111-130, November.

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