Analysis of Approximately Periodic Time Series

In this paper, we first define the concept of approximately periodic time series, that is, the length of their periods is not any constant. For example, the sunspot series has a period about 11 years, but the length of its periods is not just 11 years, which is approximately periodic. Then we give a method to extract approximately periodic trend and bring forward a generalized difference operator, which can eliminate not only time trend and periodicity but also approximately periodicity of time series. At last, we take the sunspot data as an example to show the application of generalized difference operator.