Properties of batch means from stationary ARMA time series |
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| Institution: | 1. Dokuz Eylul University, The Graduate School of Natural and Applied Sciences, Izmir, Turkey;2. Dokuz Eylul University, Department of Computer Engineering, Izmir, Turkey;1. Department of Industrial and Materials Science, Chalmers University of Technology, Gothenburg, 41296, Sweden;2. Department of Computer Science and Engineering, Chalmers University of Technology, Gothenburg, 41296, Sweden;3. School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai, 519070, China;4. Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, 22904, USA;5. Department of Engineering Systems and Environment, University of Virginia, Charlottesville, VA, 22904, USA;1. Wageningen University & Research, Information Technology Group, Wageningen, the Netherlands;2. Bahcesehir University, Department of Computer Engineering, Istanbul, Turkey;1. Institute for Frontier Materials, Carbon Nexus, VIC3216, Deakin University, Australia;2. Composites Research Network, School of Engineering, University of British Columbia, Canada;3. School of Engineering, RMIT University, Melbourne, Australia |
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| Abstract: | The batch-means process arising from an arbitary autoregressive moving-average (ARMA) process time series is derived. As side results, the variance and correlation structures of the batch-means process as functions of the batch size and parameters of the original process are obtained. Except for the first-order ARMA process, for which a closed-form expression is obtained, the parameters of the batch-means process are determined numerically. |
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