Estimation of Scale Transformation for Approximately Periodic Time Series with Long-term Trend
Received:April 13, 2020  Revised:May 24, 2020
Key Word: Time series, approximate periodicity, scale transformation, shape-retention transformation with lengthwise compression  
Fund ProjectL:the National Natural Science Foundation of China (No. 11471120)
Author NameAffiliationE-mail
Shujin Wu East China Normal University sjwu@stat.ecnu.edu.cn 
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Abstract:
      Approximately periodic time series means it has an approximate periodic trend. The so-called approximate periodicity refers that it looks like having periodicity, however the length of each period is not constant such as sunspot data. Approximately periodic time series has a wide application prospect in modelling social economic phenomenon. As for approximately periodic time series, the key problem is to depict its approximate periodic trend because it can be dealt as an ordinary time series only if its approximate periodic trend has been depicted. However, there is little study on depicting approximate periodic trend. In the paper, the authors first establish some necessary theories, especially bring forward the concept of shape-retention transformation with lengthwise compression and obtain sufficient and necessary condition for linear shape-retention transformation with lengthwise compression, then basing on the theories the authors present a method to estimate scale transformation, which can model approximate periodic trend very clearly. At last, a simulated example and sunspot data are analyzed by this presented method. The results show that the presented method is very effective and very powerful.
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