zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A nonlinear autoregressive conditional duration model with applications to financial transaction data. (English) Zbl 1108.62336
Summary: This paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration (ACD) model considered by {\it R. F. Engle} and {\it J. R. Russell} [Econometrica 66, No. 5, 1127--1162 (1998; Zbl 1055.62571)]. We propose a threshold autoregressive conditional duration (TACD) model to allow the expected duration to depend nonlinearly on past information variables. Conditions for the TACD process to be ergodic and existence of moments are established. Strong evidence is provided to suggest that fast transacting periods and slow transacting periods of NYSE stocks have quite different dynamics. Based on the improved model, we identify multiple structural breaks in the transaction duration data considered, and those break points match nicely with real economic events.

62P20Applications of statistics to economics
91B62Growth models in economics
62M10Time series, auto-correlation, regression, etc. (statistics)
Full Text: DOI
[1] Andersen, T. G.; Bollerslev, T.: Answering the skeptics: yes, standard volatility models do provide accurate forecasts. International economic review 39, 885-905 (1998)
[2] Andrews, D. W. K.: Tests for parametric instability and structural change with unknown change point. Econometrica 61, No. 4, 821-856 (1993) · Zbl 0795.62012
[3] Andrews, D. W. K.; Ploberger, W.: Optimal tests when a nuisance parameters is present only under the alternative. Econometrica 62, No. 6, 1383-1414 (1994) · Zbl 0815.62033
[4] Bai, X., Russell, J.R., Tiao, G.C., 1999. Beyond Merton’s Utopia; effects of non-normality and dependence on the precision of variance estimates using high-frequency financial data. Working Paper, Graduate School of Business, University of Chicago.
[5] Berndt, E.; Hall, B.; Hall, R.; Hausman, J.: Estimation and inference in nonlinear structural models. Annals of economic and social measurement 3, 653-665 (1974)
[6] Bollerslev, T.: Generalized autoregressive conditional heteroskedasticity. Journal of econometrics 31, 307-327 (1986) · Zbl 0616.62119
[7] Bougerol, P.; Picard, N.: Stationarity of GARCH processes and of some nonnegative time series. Journal of econometrics 52, 115-127 (1992) · Zbl 0746.62087
[8] Brockwell, P. J.; Liu, J.; Tweedie, R. L.: On the existence of stationary threshold autoregressive moving-average processes. Journal of time series analysis 13, No. 2, 95-107 (1992) · Zbl 0755.62064
[9] Chan, K. S.; Petruccelli, J. D.; Tong, H.; Woolford, S. W.: A multiple-threshold $AR(1)$ model. Journal of applied probability 22, 267-279 (1985) · Zbl 0579.62074
[10] Chen, R.; Tsay, R. S.: On the ergodocity of $TAR(1)$ processes. Annals of applied probability 1, No. 4, 613-634 (1991) · Zbl 0795.93099
[11] Easley, D.; O’hara, M.: Price, trade size, and information in securities markets. Journal of financial economics 19, No. 1, 69-90 (1987)
[12] Easley, D.; O’hara, M.: Adverse selection and large trade volume. Journal of financial and quantitative analysis 27, No. 2, 185-208 (1992)
[13] Easley, D.; O’hara, M.: Time and the process of security price adjustment. Journal of finance 47, 577-606 (1992)
[14] Engle, R. F.: Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica 50, No. 4, 987-1006 (1982) · Zbl 0491.62099
[15] Engle, R. F.: The econometrics of ultra-high frequency data. Econometrica 68, No. 1, 1-22 (2000) · Zbl 1056.91535
[16] Engle, R.F., Russell, J.R., 1995. Autoregressive conditional duration: A new model for irregular spaced data. Unpublished manuscript, University of California, San Diego.
[17] Engle, R. F.; Russell, J. R.: Autoregressive conditional duration: A new model for irregular spaced transaction data. Econometrica 66, No. 5, 1127-1162 (1998) · Zbl 1055.62571
[18] Friedman, J.H., 1984. A variable span smoother. Technical Report No. 5, Laboratory for Computational Statistics, Department of Statistics, Stanford University.
[19] Glosten, L. R.; Jagannathan, R.; Runkle, D. E.: On the relation between the expected value and volatility of the nominal excess return on stocks. Journal of finance 48, 1779-1801 (1993)
[20] Glosten, L. R.; Milgrom, P. R.: Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of financial economics 14, 71-100 (1985)
[21] Goodhart, C. A. E.; O’hara, M.: High frequency data in financial markets: issues and applications. Journal of empirical finance 4, 73-114 (1997)
[22] Grammig, J., Maurer, K.-O., 2000. Non-monotonic hazard functions and the autoregressive conditional duration model. Econometric Journal 3(1), 16--38. · Zbl 1038.91523
[23] Koop, G., Potter, S., 1997. Nonlinearity, structural breaks or outliers in economic time series. Working Paper, University of Edinburgh. · Zbl 1062.91591
[24] Lancaster, T.: The econometric analysis of transition data. (1990) · Zbl 0717.62106
[25] Lee, C. M. C.; Mucklow, B.; Ready, M. J.: Spreads, depths and the impact of earnings information: an intraday analysis. Review of financial studies 6, No. 2, 345-374 (1993)
[26] Lunde, A., 1999. A generalized Gamma autoregressive conditional duration model. Working Paper, Department of Economics, Politics and Public Administration, Aalborg University, Denmark.
[27] Meyn, S.; Tweedie, R. L.: Markov chains and stochastic stability. (1993) · Zbl 0925.60001
[28] Moeanaddin, R.; Tong, H.: Numerical evaluation of distributions in non-linear autoregression. Journal of time series analysis 11, No. 1, 33-48 (1990) · Zbl 0691.62084
[29] Olsen and Associates, 1995. First International Conference on High Frequency Data in Finance (HFDF-I). Olsen and Associates, Zurich, Switzerland.
[30] Olsen and Associates, 1998. Second International Conference on High Frequency Data in Finance (HFDF-II). Olsen and Associates, Zurich, Switzerland.
[31] Petruccelli, J.; Woolford, S. W.: A threshold $AR(1)$ model. Journal of applied probability 21, 270-286 (1984) · Zbl 0541.62073
[32] Rabemananjara, R.; Zakoian, J. M.: Threshod ARCH models and asymmetries in volatility. Journal of applied econometrics 8, 31-49 (1993)
[33] Tong, H.: Non-linear time series: A dynamical system approach. (1990) · Zbl 0716.62085
[34] Tsay, R. S.: Testing and modeling threshold autoregressive processes. Journal of American statistical association 84, No. 405, 231-240 (1989) · Zbl 0683.62050
[35] Tsay, R. S.: Model checking via parametric bootstraps in time series analysis. Applied statistics 41, No. 1, 1-15 (1992) · Zbl 0825.62698
[36] Tsay, R. S.: Testing and modeling multivariate threshold models. Journal of American statistical association 93, No. 442, 478-493 (1998) · Zbl 1063.62578
[37] Zakoian, J. -M.: Threshold heteroskedastic models. Journal of economic dynamics and control 18, 931-955 (1994) · Zbl 0806.90018