The T-R Periodogramm Analysis /short description/
The method , of discovering and cycle analysis in the time series which is provisionally called - 'T-R periodograme analysis', is described in details in [1]. It should be concedered not as a principally new mathod, but rather as a specific numerical a
lgorithm including the following stages .
1. The investigated time series is approximated by the least mean squares method with series of simple periodical functions of the type :
where :t=0,1,2....
The period T, varies from a set initial value to a set maximum one, with "delta-T" step . The final minimum value of T is 2. For the sake of convinience the time series is to be used as a unit of time , because of the considered time series on the ba
sis of the equivident values .
2. For each one of the so discovereded simple periodical functions a correlation coefficient R is calculated. This coefficient is between every function and the time series and the error of the latter
where N is the length of the time series . In this connection the so obtained sequence of the R values ( T - R correlation ) has local maximums round these values of the T period which correspond to the potentional cycles , existing in the inve
stigated time series. The amplitude (power) of the cycle can be determened by the following formula :
3. The statistical reliability of the discovered cycles is checked. Two criteria have been used for this purpose . In compliance with the first of them the correlation coefficient has to correspond to the condition in which R/SR>2 This criterion h
as 95% reliability level for the two - parametric relationship. The coefficient is near to the Z Fisher's test. However in its requirements very often in the series of pseudorandom numbers weak cycles satisfaying this criterion occur. These cycles are v
ery clear after applying a moving average procedure . The second more solid criterion was empirically obtained on the basis of the analysis of over 1000 series of pseudo random numbers. In compliance with it, if the correlation coefficient corresponds to
the condition
in this situation the established value near R maximum is not typical for the series of random numbers. In this case the cycle has not occasionally occured , just the opposite - it is real and causatively determined. If the local maximum R is between the
two critical limit criteria , then the question is if the so discovered weak cycle is real or no. The latter is to be solved on the basis of additional information by researcher's estimation.
The total power index for cyclies, in area with limits T1, and T2 can be calculated as
Komitov B., 1997, Bulg.Geophys.J,v.23.No1-2