Method Of Trend Extraction For Approximately Periodic Time Series And Its Applications To Predicting Consumer Credit Balances

There are a large amount of periodic time series in people’s daily life and social activities, such as the series of milk production volume, GDP and monthly highest temperature in Shanghai, etc. Some of them seem to be periodic, however their period lengths are actually not constant. Take the sunspot series as an example. Its period length is approximately 11 years, but in reality the lengths are 12,11,9,10,10,11,11, 10 and 11 in the 20th century. We call this kind of time series as approximately periodic time series.In this thesis, we first introduce the definition of approximately periodic time series. Then, an approach to extract time series period of approximately periodic time series and a so-called generalized difference operator are proposed. The generalized difference operator is an important extension of the existing difference operators because it is able to eliminate the impact of time growth trend and periodicity as well as approximately periodicity of time series. Finally, we utilize the balance data of a consumption credit product as an empirical study to further demonstrate the existence of approximately periodic time series and also the effectiveness of the proposed method to solve approximately periodic time series problems. In the empirical study, we compute each of the period lengths through linear transformation and then eliminate the time trend with generalized difference operator. As a result, the out-of-sample validation can achieve no more than 0.3% error level, which shows that approximately periodic time series can fit the balance series very well.