Sucarrat, Genaro and Grønneberg, Steffen (2016): Models of Financial Return With TimeVarying Zero Probability.
This is the latest version of this item.

PDF
MPRA_paper_77264.pdf Download (648kB)  Preview 
Abstract
The probability of an observed financial return being equal to zero is not necessarily zero. This can be due to price discreteness or rounding error, liquidity issues (e.g. low trading volume), market closures, data issues (e.g. data imputation due to missing values), characteristics specific to the market, and so on. Moreover, the zero probability may change and depend on market conditions. In standard models of return volatility, however, e.g. ARCH, SV and continuous time models, the zero probability is zero, constant or both. We propose a new class of models that allows for a timevarying zero probability, and which can be combined with standard models of return volatility: They are nested and obtained as special cases when the zero probability is constant and equal to zero. Another attraction is that the return properties of the new class (e.g. volatility, skewness, kurtosis, ValueatRisk, Expected Shortfall) are obtained as functions of the underlying volatility model. The new class allows for autoregressive conditional dynamics in both the zero probability and volatility specifications, and for additional covariates. Simulations show parameter and risk estimates are biased if zeros are not appropriately handled, and an application illustrates that riskestimates can be substantially biased in practice if the timevarying zero probability is not accommodated.
Item Type:  MPRA Paper 

Original Title:  Models of Financial Return With TimeVarying Zero Probability 
English Title:  Models of Financial Return With TimeVarying Zero Probability 
Language:  English 
Keywords:  Financial return, volatility, zeroinflated return, GARCH, logGARCH, ACL 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  77264 
Depositing User:  Dr. Genaro Sucarrat 
Date Deposited:  04 Mar 2017 09:08 
Last Modified:  04 Mar 2017 09:09 
References:  Ball, C. A. (1988). Estimation Bias Induced by Discrete Security Prices. Journal of Finance 43, 841865. Bauwens, L., C. Hafner, and S. Laurent (2012). Handbook of Volatility Models and Their Applications. New Jersey: Wiley. Bien, K., I. Nolte, and W. Pohlmeier (2011). An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics. Journal of Applied Econometrics 26, 669707. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307327. Brownlees, C., F. Cipollini, and G. Gallo (2012). Multiplicative Error Models. In L. Bauwens, C. Hafner, and S. Laurent (Eds.), Handbook of Volatility Models and Their Applications, pp. 223247. New Jersey: Wiley. Cho, D. C. and E. W. Frees (1988). Estimating the Volatility of Discrete Stock Prices. Journal of Finance 43, 451466. Creal, D., S. J. Koopmans, and A. Lucas (2013). Generalized Autoregressive Score Models with Applications. Journal of Applied Econometrics 28, 777795. Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflations. Econometrica 50, 9871008. Engle, R. F. and J. R. Russell (1998). Autoregressive Conditional Duration: A New Model of Irregularly Spaced Transaction Data. Econometrica 66, 11271162. Francq, C. and G. Sucarrat (2015). An EquationbyEquation Estimator of a Multivariate LogGARCHX Model of Financial Returns. https://mpra.ub.unimuenchen.de/67140/. Francq, C. and L. Q. Thieu (2015). Qml inference for volatility models with covariates. http://mpra.ub.unimuenchen.de/63198/. Francq, C., O. Wintenberger, and J.M. Zakoian (2013). GARCH Models Without Positivity Constraints: Exponential or LogGARCH? Forthcoming in Journal of Econometrics, http//dx.doi.org/10.1016/j.jeconom.2013.05.004. Geweke, J. (1986). Modelling the Persistence of Conditional Variance: A Comment. Econometric Reviews 5, 5761. Ghysels, E., P. SantaClara, and R. Valkanov (2006). Predicting volatility: getting the most out of return data sampled at di�erent frequencies. Journal of Econometrics 131, 5995. Gottlieb, G. and A. Kalay (1985). Implications of the Discreteness of Observed Stock prices. Journal of Finance 40, 135153. Han, H. and D. Kristensen (2014). Asymptotic theory for the QMLE in GARCHX models with stationary and nonstationary covariates. Journal of Business and Economic Statistics, ???? Harvey, A. C. (2013). Dynamic Models for Volatility and Heavy Tails. New York: Cambridge University Press. Hausman, J., A. Lo, and A. MacKinlay (1992). An ordered probit analysis of transaction stock prices. Journal of Financial economics 31, 319379. Hautsch, N., P. Malec, and M. Schienle (2013). Capturing the zero: a new class of zeroaugmented distributions and multiplicative error processes. Journal of Financial Econometrics. Forthcoming. http://jfec.oxfordjournals.org/content/early/2013/03/29/jjfinec.nbt002. Li, Y. and P. A. Mykland (2014). Rounding Errors and Volatility Estimation. Journal of Financial Econometrics . Forthcoming. Liesenfeld, R., I. Nolte, and W. Pohlmeier (2006). Modelling Financial Transaction Price Movements: A Dynamic Integer Count Data Model. Empirical Economics 30, 795825. Ljung, G. and G. Box (1979). On a Measure of Lack of Fit in Time Series Models. Biometrika 66, 265270. Milhøj, A. (1987). A Multiplicative Parametrization of ARCH Models. Research Report 101, University of Copenhagen: Institute of Statistics. Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59, 347370. Pantula, S. (1986). Modelling the Persistence of Conditional Variance: A Comment. Econometric Reviews 5, 7173. R Core Team (2014). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Russell, J. R. and R. F. Engle (2005). A DiscreteState ContinuousTime Model of Financial Transaction Prices and Times: The Autoregressive Conditional MultinomialAutoregressive Conditional Duration Model. Journal of Business and Economic Statistics 23, 166180. Rydberg, T. H. and N. Shephard (2003). Dynamics of TradebyTrade Price Movements: Decomposition and Models. Journal of Financial Econometrics 1, 225. Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics 6, 461464. Shephard, N. (2005). Stochastic Volatility: Selected Readings. Oxford: Oxford University Press. Sucarrat, G., S. Grønneberg, and A. Escribano (2015). Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. Computational Statistics and Data Analysis. Forthcoming. DOI: http://dx.doi.org/10.1016/j.csda.2015.12.005. Working Paper version: http://mpra.ub.unimuenchen.de/62352/. Wintenberger, O. (2013). Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) model. Scandinavian Journal of Statistics 40, 846867. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/77264 
Available Versions of this Item

Models of Financial Return With TimeVarying Zero Probability. (deposited 21 Jan 2016 14:32)
 Models of Financial Return With TimeVarying Zero Probability. (deposited 04 Mar 2017 09:08) [Currently Displayed]