Estimation and forecasting with logarithmic autoregressive conditional duration models: A comparative study with an application |
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| Affiliation: | 1. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Lembah Pantai, Kuala Lumpur 50603, Malaysia;2. School of Mathematics and Statistics F07, The University of Sydney, NSW 2006, Australia;3. Discipline of Business Analytics, The University of Sydney, Business School, NSW 2006, Australia;1. Department of Electronics Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong Special Administrative Region;2. Department of Computer Science and Technology, Soochow University, Suzhou 215006, China;1. Department of Statistics, Cheongju University, 298, Daeseong-ro Sangdang-gu, Cheongju, Chungbuk 360-764, Republic of Korea;2. Graduate School of Management of Technology, Korea University, 1, 5-Ka, Anam-dong Sungbuk-ku, Seoul 136-701, Republic of Korea;3. Division of Industrial Management Engineering, Korea University, 1, 5-Ka, Anam-dong Sungbuk-ku, Seoul 136-701, Republic of Korea;1. Department of Software Engineering, Faculty of Telecommunication and Information Engineering, University of Engineering and Technology, Taxila, Pakistan;2. School of Electronics and Computer Science, University of Southampton, Highfield Campus, Southampton SO17 1BJ, United Kingdom;1. Department of Information Management at Fortune Institute of Technology, Kaohsiung, Taiwan;2. Thecus Technology Corporation, Taiwan;3. Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan |
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| Abstract: | This paper presents a semi-parametric method of parameter estimation for the class of logarithmic ACD (Log-ACD) models using the theory of estimating functions (EF). A number of theoretical results related to the corresponding EF estimators are derived. A simulation study is conducted to compare the performance of the proposed EF estimates with corresponding ML (maximum likelihood) and QML (quasi maximum likelihood) estimates. It is argued that the EF estimates are relatively easier to evaluate and have sampling properties comparable with those of ML and QML methods. Furthermore, the suggested EF estimates can be obtained without any knowledge of the distribution of errors is known. We apply all these suggested methodology for a real financial duration dataset. Our results show that Log-ACD (1, 1) fits the data well giving relatively smaller variation in forecast errors than in Linear ACD (1, 1) regardless of the method of estimation. In addition, the Diebold–Mariano (DM) and superior predictive ability (SPA) tests have been applied to confirm the performance of the suggested methodology. It is shown that the new method is slightly better than traditional methods in practice in terms of computation; however, there is no significant difference in forecasting ability for all models and methods. |
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| Keywords: | Duration data Conditional duration Log-ACD Estimating function Maximum likelihood |
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