Beta Stationarity and Estimation Period: Some Analytical Results
推导了解释贝塔系数平稳性如何随估计期长度变化的解析表达式，并给出了平稳性随日历期增长的条件，解释了已有实证发现。
The stationarity of beta factors has received considerable attention in the financial economics literature. One particular area of study has been to investigate how the measured stationarity of beta factors changes over data sets of varying lengths. By increasing the length of the estimation period, sampling fluctuations may be reduced; however, the probability of beta factors having changed will increase. The optimal data set length, then, involves a trade-off between these two opposing phenomena. Baesel [2] reported the empirical finding that the stationarity of beta was, indeed, dependent upon the estimation period length over which beta factors were estimated. He found, using transition matrices that beta stationarity was an increasing function of the calendar period used for beta estimation. In this paper, analytic expressions will be derived to explain how and when this empirical phenomenon arises. Conditions will be presented for beta stationarity to increase with calendar period length, and it will be demonstrated that beta stationarity will not increase indefinitely with estimation period length. An identical condition is required for beta stationarity to be an increasing function of the subsequent calendar period length. This phenomenon was empirically investigated by Roenfeldt, Griepentrog, and Pflaum [6], and the analysis presented here explains, in part, their findings.