Cut-off frequencies and noise power law model of spectral density: adaptation of the multi-variance method for irregularly spaced timing data using the lowest mode estimator approach

The concept of structure functions, which is an extension of the variance approach, is useful to determine the variance (the structure function) which is optimized for a type of noise and for an order of drift. The multi-variance method was developed to use different variances over the same signal. It is then possible to select a set of variances in which each variance is optimized to the determination of one parameter (of one noise level, drift, or cut-off frequency). Recently, we adapted this method to irregularly spaced timing data. In this connection, we replaced the structure functions by another method of spectral density estimation: the lowest mode estimator, introduced by J.E. Deeter and P.E. Boynton (1982, 1984) for the analysis of pulsar timing data. Different lowest mode estimators can be constructed according to two priorities: the order of drifts that must be removed and the type of noise for which the sensitivity must be maximum. Thus, a multivariance system is developed using a set of different estimators. The details of this method are described and the results for different signals are discussed in this paper