Aknouche, Abdelhakim and Almohaimeed, Bader and Dimitrakopoulos, Stefanos (2020): Periodic autoregressive conditional duration.
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Abstract
We propose an autoregressive conditional duration (ACD) model with periodic timevarying parameters and multiplicative error form. We name this model periodic autoregressive conditional duration (PACD). First, we study the stability properties and the moment structures of it. Second, we estimate the model parameters, using (profile and twostage) Gamma quasimaximum likelihood estimates (QMLEs), the asymptotic properties of which are examined under general regularity conditions. Our estimation method encompasses the exponential QMLE, as a particular case. The proposed methodology is illustrated with simulated data and two empirical applications on forecasting Bitcoin trading volume and realized volatility. We found that the PACD produces better insample and outofsample forecasts than the standard ACD.
Item Type:  MPRA Paper 

Original Title:  Periodic autoregressive conditional duration 
English Title:  Periodic autoregressive conditional duration 
Language:  English 
Keywords:  Positive time series, autoregressive conditional duration, periodic timevarying models, multiplicative error models, exponential QMLE, twostage Gamma QMLE. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C18  Methodological Issues: General C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C41  Duration Analysis ; Optimal Timing Strategies C  Mathematical and Quantitative Methods > C5  Econometric Modeling C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics 
Item ID:  106785 
Depositing User:  Prof. Abdelhakim Aknouche 
Date Deposited:  25 Mar 2021 09:12 
Last Modified:  25 Mar 2021 09:12 
References:  Aknouche, A. (2015). Explosive strong periodic autoregression with multiplicity one. Journal of Statistical Planning and Inference 161, 5072. Aknouche, A. and Francq, C. (2020). Count and duration time series with equal conditional stochastic and mean orders. Econometric Theory, forthcoming. Aknouche, A. and Francq, C. (2019). Twostage weighted least squares estimator of the conditional mean of observationdriven time series models. MPRA paper 97382. Aknouche, A., Demmouche, N., Dimitrakopoulos, S. and Touche, N. (2020). Bayesian analysis of periodic asymmetric power GARCH models. Studies in Nonlinear Dynamics and Econometrics, forthcoming. Ambach, D. and Croonenbroeck, C. (2015). Obtaining superior wind power predictions from a periodic and heteroscedastic wind power prediction tool. In Stochastic Models, Statistics and Their Applications, edt, 225232. Ambach, D. and Schmid, W. (2015). Periodic and long range dependent models for high frequency wind speed data. Energy 82, 277293. Andersen, T. and Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of Empirical Finance 4, 115158. BarndorffNielsen, O.E. and Shephard, N. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society B64, 253280. Baur, D., Cahill, D., Godfrey K. and Liu, Z. (2019). Bitcoin timeofday, dayofweek and monthofyear effects in returns and trading volume. Finance Research Letters 31, 7892. Bernardi M, Catania L. (2014). The model confidence set package for R. ArXiv:1410. 8504v1. Bhogal, S.K. and Variyam, R.T. (2019). Conditional duration models for highfrequency data: A review on recent developments. Journal of Economic Surveys 33, 252273. Billingsley, P. (1999). Convergence of probability measures. 2nd edition, Wiley, New York. Billingsley, P. (1995). Probability and measure. 3rd edition, Wiley, New York. Bollerslev, T. and Ghysels, E. (1996). Periodic autoregressive conditional heteroskedasticity. Journal of Business & Economic Statistics 14, 139152. Bollerslev, T., Cai, J. and Song, F.M. (2000). Intraday periodicity, long memory volatility, and macroeconomic announcement effects in the US Treasury bond market. Journal of Empirical Finance 7, 3755. Bortoluzzo, A.B., Morettin, P.A. and Toloi, C.M. (2010). Timevarying autoregressive conditional duration model. Journal of Applied Statistics 37, 847864. Boswijk, H.P. and Franses, P.H. (1995). Testing for periodic integration. Economics Letters 48, 241248. Boswijk, H.P. and Franses, P.H. (1996). Unit roots in periodic autoregressions. Journal of Time Series Analysis 17, 221245. Bougerol, P. and Picard, N. (1992a). Strict stationarity of generalised autoregressive processes. Annals of Probability 20, 17141730. Bougerol, P. and Picard, N. (1992b). Stationarity of GARCH processes and some nonnegative time series. Journal of Econometrics 52, 115127. Boynton, W., Oppenheimer, H.R. and Reid, S.F. (2009). Japanese dayoftheweek return patterns: New results. Global Finance Journal 20, 112. Bracher, J. and Held, L. (2017), Periodically stationary multivariate autoregressive models. arXiv preprint, arXiv:1707.04635. Caporin, M., Rossi, E., and Santucci De Magistris, P. (2017). Chasing volatility: a persistent multiplicative error model with jumps. Journal of Econometrics 198, 122145. Charles, A. (2010). The dayoftheweek effects on the volatility: The role of the asymmetry. European Journal of Operational Research 202, 143152. Chen, M. and An, H.Z. (1998). A note on the stationarity and the existence of moments of the GARCH model. Statistica Sinica 8, 505510. Chou, R.Y. (2005). Forecasting financial volatilities with extreme values: The conditional autoregressive range (CARR) Model. Journal of Money, Credit, and Banking 37, 561582. Dahlhaus, R. (1997). Fitting time series models to nonstationary Processes. Annals of Statistics 25, 137. Dahlhaus R. and Subba Rao, S. (2006). Statistical Inference for TimeVarying ARCH Processes. Annals of Statistics 34, 10751114. Diebold, F. (1986). Modeling the persistence of conditional variances: A comment. Econometric Reviews 5, 5156. Engle, R. (2002). New frontiers for Arch models. Journal of Applied Econometrics 17, 425446. Engle, R. and Russell, J. (1998). Autoregressive conditional duration: A new model for irregular spaced transaction data. Econometrica 66, 11271162. Francq, C. and Zakoian, J.M. (2019). GARCH models: structure, statistical inference and financial applications. John Wiley & Sons, 2nd edt. Francq, C., Roy, R. and Saidi, A. (2011). Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models. Journal of Time Series Analysis 32, 699723. Franses, P.H. and Paap. R. (2000). Modeling dayoftheweek seasonality in the S&P 500 Index. Applied Financial Economics 10, 483488. Franses, P.H. and Paap, R. (2004). Periodic time series models. Oxford University Press. Gallo, G.M. and Otranto, E. (2018). Combining sharp and smooth transitions in volatility dynamics: a fuzzy regime approach. Journal of the Royal Statistical Society C67: 549573. Gourieroux, C., Monfort, A. and Trognon, A. (1984). Pseudo maximum likelihood methods: Theory. Econometrica 52, 681700. Hallin, M. (1984). Spectral Factorization of Nonstationary Moving Average Processes. Annals of Statistics 12, 172192. Hautsch, N. (2012). Econometrics of Financial HighFrequency Data. Berlin, Heidelberg: Springer. Hujer, R. and Vuletic, S. (2007). Econometric analysis of financial trade processes by discrete mixture duration models. Journal of Economic Dynamics and Control 31, 635667. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1995). Continuous univariate distributions. Wiley, 2nd Edition. Lanne, M. (2006). A mixture multiplicative error model for realized volatility. Journal of Financial Econometrics 4, 594616. Li, Q. (2019). Location multiplicative error models with quasi maximum likelihood estimation. Journal of Time Series Analysis, DOI: 10.1111/jtsa.12513. Lund, R. and Basawa, I.V. (2000). Recursive prediction and likelihood evaluation for periodic ARMA models. Journal of Time Series Analysis 21, 7593. Martens, M., Van Dijk, D. and De Pooter, M. (2009). Forecasting S&P 500 volatility: Long memory, level shifts, leverage effects, dayoftheweek seasonality, and macroeconomic announcements. International Journal of Forecasting 25, 282303. Mbanga, C.L. (2019). The dayoftheweek pattern of price clustering in Bitcoin. Applied Economics Letters 26, 16. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models, 2nd edn. Chapman and Hall, London. Mikosch, T. and Starica, C. (2004). Nonstationarities in Financial Time Series, the LongRange Dependence, and the IGARCH Effects. Review of Economics and Statistics 86, 378390. Miller, K.S. (1968). Linear Difference Equations. Benjamin. Mishra, A. and Ramanathan, T.V. (2017). Nonstationary autoregressive conditional duration models. Studies in Nonlinear Dynamics and Econometrics 21, 122. Moghaddam, M.D., Liu, J. and Serota, R.A. (2019). Implied and realized volatility: A study of distributions and the distribution of difference. ArXiv:1906.02306. Pacurar, M. (2008). Autoregressive Conditional Duration (ACD) Models in Finance: A Survey of the Theoretical and Empirical Literature. Journal of Economic Surveys 22, 711751. Patton, A.J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics 160, 246256. Rossi, E. and Fantazzini, D. (2015). Long memory and periodicity in intraday volatility. Journal of Financial Econometrics 13, 922961. Tsiakas, I. (2006). Periodic stochastic volatility and fat tails. Journal of Financial Econometrics 4, 90135. Wang, J.N., Liu, H.C. and Hsu, Y.T. (2020). Timeofday periodicities of trading volume and volatility in Bitcoin exchange: Does the stock market matter?. Finance Research Letters 34, 18. Wooldridge, J.M. (1999). Quasilikelihood methods for count data. In M.H. Pesaran and P. Schmidt (ed.), Handbook of Applied Econometrics, Volume 2: Microeconomics, (pp. 35406). Oxford: Blackwell. Yang, K. and Chen, L. (2014). Realized volatility forecast: structural breaks, long memory, asymmetry, and dayoftheweek effect. International Review of Finance 14, 345392. Ziel, F., Steinert, R. and Husmann, S. (2015). Efficient modeling and forecasting of electricity spot prices. Energy Economics 47, 98111. Ziel, F., Croonenbroeck, C. and Ambach, D. (2016). Forecasting wind power Modeling periodic and nonlinear effects under conditional heteroscedasticity. Applied Energy 177, 285297. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/106785 
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