On the Auto-Correlation Coefficients of the Difference Stationary Time Series

[摘要] The auto-correlation coefficient for the purely random sequence was already studied by G. U. Yule and S. Moriguti, but by auto-correlation coefficient for the difference stationary time series is scarcely studied. The author treats them statistically, inducing the correlation coefficient, and investigates their property for some special cases.The auto-correlation coefficient of the 1st difference is given by in general, the auto-correlation coefficient of the r-th difference is given by where (2r/r-τ-p)=2rCτ-p-p (equals to combination). For random sequence, we have the following relations. and finally, we referred to the relation for the sinusoidal limit theorem we obtained the following result.The necessary and sufficient conditions that the difference stationary time series is to be a simple Markoff process are that the difference sequence is a singular stationary process.

[学科分类] 大气科学