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Bounds for the probability distribution function of the linear ACD process. (English) Zbl 1097.62080
Summary: This paper derives both lower and upper bounds for the probability distribution function of stationary Autoregressive Conditional Duration, ACD($$p,q$$) processes. For the purpose of illustration, the author specializes the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.
MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B28 Finance etc. (MSC2000)
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References:
 [1] Bauwens, L.; Giot, P., The logarithmic ACD modelan application to the bid-ask quote process of three NYSE stocks, Ann. d’economie et de statistique, 60, 117-150, (2000) [2] Carrasco, M.; Chen, X., Mixing and moment properties of various GARCH and stochastic volatility models, Econom. theory, 18, 17-39, (2002) · Zbl 1181.62125 [3] Drost, F., Werker, B.J.M., 2001. Semiparametric duration models, Journal of Business and Economic Statistics, forthcoming. [4] Engle, R.F.; Russell, J.R., Autoregressive conditional duration: A new model for irregularly-spaced transaction data, Econometrica, 66, 1127-1162, (1998) · Zbl 1055.62571 [5] Fernandes, M., Grammig, J., 2002. A family of autoregressive conditional duration models. Ensaios Econômicos 404, Fundação Getulio Vargas. · Zbl 1337.62259 [6] Focardi, S.M., 2001. An actuarial model of credit risk contagion. Discussion Paper, Intertek Group. [7] Glaser, R.E., Bathtub and related failure rate characterizations, J. amer. statist. assoc., 75, 667-672, (1980) · Zbl 0497.62017 [8] Gouriéroux, C.; Jasiak, J.; Le Fol, G., Intra-day market activity, J. financial markets, 2, 193-226, (1999) [9] Grammig, J.; Maurer, K.-O., Non-monotonic hazard functions and the autoregressive conditional duration model, Econom. J., 3, 16-38, (2000) · Zbl 1038.91523 [10] Lunde, A., 1999. A generalized gamma autoregressive conditional duration model. University of Aarhus. [11] Pawlak, M.; Schmid, W., On the distributional properties of GARCH processes, J. time ser. anal., 22, 339-352, (2001) · Zbl 0978.62084
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