TL;DR: In this paper, Naidu et al. showed that the reversal intervals of the geomagnetic field for the period 0-76 m.y. are not independent and proposed a first-order autoregressive moving average model to compute the autocorrelation function.
Abstract: In a recent paper, Naidu [1975] has proposed that the reversal intervals of the geomagnetic field for the period 0-76 m.y. are not independent. In fact, the author has fitted a firstorder autoregressive moving average model to the data published by Heirtzler et. al. [1968]. This conclusion, if true, is of ;importance because it suggests that the mechanism governing the reversals of the geomagnetic dynamo possesses a memory. Naidu [1975] has developed his model on the basis of the exponential nature of the autocorrelation function calculated for the entire 76-m.y. data set. Implicit in this model is the assumption of stationarity during this time interval. However, Naidu [ 1971 ] himself has shown very clearly that the statistical ,,:;structure of the polarity intervals underwent a marked transition about 48 m.y. ago. This fact has a pronounced effect on the computed autocorrelation function as demonstrated in Figure 1. It can clearly be seen that whereas the autocorrelation of the whole data set does exhibit an exponential form, the autocorrelation computed for the first 48-m.y. ._ reversal history is impulsive at zero lag and demonstrates conclusively the independence of the intervals in this time
TL;DR: Criteria for the detection of parameter changes in ARIMA models is derived and an alternative approach is investigated in which they attempt to continually estimate or update the parameters as each new observation becomes available.
Abstract: : In this paper we derive criteria for the detection of parameter changes in ARIMA models. An alternative approach is investigated in which we attempt to continually estimate or update the parameters as each new observation becomes available. Furthermore, we discuss how a step change in the parameters can affect the autocorrelation function. (Autor)