Discrete time-series models when counts are unobservable
Count data in economics have traditionally been modeled by means of integer-valued autoregressive models. Consequently, the estimation of the parameters of these models and their asymptotic properties have been well documented in the literature. The models comprise a description of the survival of counts generally in terms of a binomial thinning process and an independent arrivals process usually specified in terms of a Poisson distribution. This paper extends the existing class of models to encompass situations in which counts are latent and all that is observed is the presence or absence of counts. This is a potentially important modification as many interesting economic phenomena may have a natural interpretation as a series of 'events' that are driven by an underlying count process which is unobserved. Arrivals of the latent counts are modeled either in terms of the Poisson distribution, where multiple counts may arrive in the sampling interval, or in terms of the Bernoulli distribution, where only one new arrival is allowed in the same sampling interval. The models with latent counts are then applied in two practical illustrations, namely, modeling volatility in financial markets as a function of unobservable 'news' and abnormal price spikes in electricity markets being driven by latent 'stress'.
|Date of creation:||15 Sep 2008|
|Date of revision:|
|Contact details of provider:|| Phone: 07 3138 5066|
Fax: 07 3138 1500
Web page: http://www.ncer.edu.au
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Bystrom, Hans N. E., 2005.
"Extreme value theory and extremely large electricity price changes,"
International Review of Economics & Finance,
Elsevier, vol. 14(1), pages 41-55.
- Byström, Hans, 2001. "Extreme Value Theory and Extremely Large Electricity Price Changes," Working Papers 2001:19, Lund University, Department of Economics.
- Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
- R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, 09.
- Markus Burger & Bernhard Klar & Alfred Muller & Gero Schindlmayr, 2004. "A spot market model for pricing derivatives in electricity markets," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 109-122.
- Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
- Alvaro Cartea & Marcelo Figueroa, 2005.
"Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality,"
Applied Mathematical Finance,
Taylor & Francis Journals, vol. 12(4), pages 313-335.
- Alvaro Cartea & Marcelo_Gustavo Figueroa, 2005. "Pricing in Electricity Markets: a Mean Reverting Jump Diffusion Model with Seasonality," Finance 0501011, EconWPA, revised 10 Sep 2005.
- Alvaro Cartea & Marcelo Gustavo Figueroa, 2005. "Pricing in Electricity Markets: a Mean Reverting Jump Diffusion Model with Seasonality," Birkbeck Working Papers in Economics and Finance 0507, Birkbeck, Department of Economics, Mathematics & Statistics.
- repec:dau:papers:123456789/1433 is not listed on IDEAS
- Gray, Stephen F., 1996.
"Modeling the conditional distribution of interest rates as a regime-switching process,"
Journal of Financial Economics,
Elsevier, vol. 42(1), pages 27-62, September.
- Tom Doan, . "RATS programs to replicate Gray's 1996 Regime Switching GARCH paper," Statistical Software Components RTZ00080, Boston College Department of Economics.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
- Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
- Benjamin M. Friedman & David I. Laibson, 1989. "Economic Implications of Extraordinary Movements in Stock Prices," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 20(2), pages 137-190.
- Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011.
"Modelling Electricity Prices: International Evidence,"
Oxford Bulletin of Economics and Statistics,
Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
- Peña Sánchez de Rivera, Juan Ignacio & Escribano, Álvaro & Villaplana, Pablo, 2002. "Modeling electricity prices: international evidence," UC3M Working papers. Economics we022708, Universidad Carlos III de Madrid. Departamento de Economía.
- M. T. Barlow, 2002. "A Diffusion Model For Electricity Prices," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 287-298.
When requesting a correction, please mention this item's handle: RePEc:qut:auncer:2008-24. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (School of Economics and Finance)
If references are entirely missing, you can add them using this form.