The brief introduction of Essential Cycle Analyst

  

  The earth atmosphere or the weather system's moving and transformation, bring all kind of weather phenomena and it essential's evolvement. We record that in timing, that is time list, for example the list of air temperature day by day, the list of precipitation rain fall day by day and so on. Expect all kind of time list in weather, the other things innumerability, especially is the largest system that human still haven't to control its regular, that produce all kind of time list waiting me analyst and investigate. All appearance, if have a certain regularity in these time list, it must be periodicity. Because impersonality exist is moving with regular. Haven't exception, even if it is the largest system that human difficult to influence and can't to control. Although can't to control, or before to control, human should to research it and to realize it, first did that can forecast it. That we ought to research, can to realize is the cycle of time list, only to depend on this cycle for to forecast.

 

  The kinds of cycle analyst had appeared have more thousand, I believe the superlatively of science credibility is harmonic analyst. As mathematic theorem of Fourier transform, the harmonic analyst is: Anyone cycle function all is can spread to the sum of a series sine function. If it is discrete time list, so can spread become to triangle function progression. But the method of harmonic analyst is not better to used on weather, the forecast isn't will be success, it is not more availability than other ways. By all appearances, here have two experiences that it was incorrect and illogical: The long of time list use to analyst can not overlong, the number of periodicity can choose is not too many. More the time list long, more the data have, should to supply more information, more can we to open out the character of that thing's, why instead it short? According to mathematics theorem, the time list should be spread to triangle function progression was endless. Why the number of cycle can choose must is little?

  Because, the system of weather is very complex, any kind Of the time list all will have had cycle is innumerable, the shortest may be is several hours, the longest may is several years or several million years, so that how long it's total cycle had, not by a long sight to known, and that Fourier transform only fit to that function the how long of total cycle have had known, it can spread this function to a sum of sine function which have all multiple frequency, but face to the list that the total cycle is unknown, it is helplessly.

  I had to raise the "Essential Cycle Analyst" method in 1977, not only count very simple, but can conquer the two disadvantage that in upwards, and in virtual also on basis of harmonic analyst, or have equivalence with. Can to validating, the cycle gene that got from the phase stat I alleged, actually is the sum of all sine function from according to cycle for basis frequency. Otherwise, if we want to got the sine function of that integer cycle, only need to process this cycle gene to some time slippage average so it okay, it's result is same with harmonic analyst.

I often use this method to do harmonic analyst. Only the sine cycle is not integer (that request in "the exactitude harmonic analyst" that as I so-called), just need the complex calculation to solve equation.

  Now let's to illustrate what is called "phase stat" and "essential cycle gene", if have a time list that only had 18ths data:

F={3,15,21,6,6,27,18,-33,15,0,-6,-9,6,18,9,3,0,9}.

The "phase stat” according to the cycle T=6 that I called is:

 

              3   15   21   6   6   27

             18  -33   15   0  -6   -9

      Add     6   18   9    3   0    9

    -------------------------------- 

      Sum    27   0   45   9    0   27

  Average    9   0   15   3    0   9    this is Stat gene S6（F）

 

  This Stat gene S6（F）={9,0,15,3,0,9}  length  is 6. It contain gene of cycle T=2, cycle T=3 and average numerical value (that is gene of cycle T=1). Now minus them from  Stat gene S6（F）, so that became to the essential cycle gene S6ο（F）.

  Must notice:  while process on this step operation “essentialism” must don't have repeat.  For example in the list, if each other to process by phase stat of S6（F）on T=2 and T=3 got S2[S6（F）] and S3[S6（F）], then subtract the both from S6（F）, so it has  subtracted twice average numerical value S1[S6（F）], because S2 and S3 all is contain average numerical value S1, the correct essentialism operate can have different way. This example can take use follow standard process (but some time the normal isn't the best of all):

 

  The first step: aim at original phase stat gene to got the average numerical value S1=(9+0+15+3+0+9)/6=6, then from the original phase stat gene S6（F） subtract this the average 6 , become to {3,-6,9,-3,-6,3}.

 

  The second step:  aim at the result of the first step to do phase stat by T=2:

             3  -6

                     9  -3

             Add   -6   3

    ----------------- 

       Sum    6  -6

        Average    2  -2               this is S2

Subtract S2={2,-2} from the result of first step, can got:

 

     The result of the first step:  3  -6  9  -3  -6  3

                                    S2:  2  -2  2  -2   2 -2

      -----------------------------------------------------

To subtract got difference: -1 -4   7   1  -8  5

  This is result of the second step

 

 The third step:  aim at the result of the third step to do phase stat by T=3:

               -1  -4   7

               Add     1  -8   5

             ------------------

               Sum     0 -12  12

          Average     0  -6   6         this is S3

 

  From the result of second step subtract S3={0,-6,6}, at last will got essential gene S6ο（F）:

  

  The result of second step:  -1  -4  7  1  -8  5

                              S3:   0  -6  6  0  -6  6

 ---------------------------------------------------

          Subtract each other:  -1   2  1  1  -2 -1   this is essential gene S6ο（F）

 

  "Stat gene" through "essentialism" become to "essential gene". While the cycle T of "stat gene" is prime number, "essentialism operate" only need to subtract average numerical value S1, otherwise must to eliminate all cycle that it contained equal to the essential cycle function of verily gene, inverse it, any stat gene, or time list of this total cycle is known, must equal all sum of its essential cycle gene: the cycle Ti of essential cycle gene which said in there, is gene of integer T, contain T itself and T1=1. You can use instance to validate this conclusion, and discover without difficult, the list of cycle which have had known don't equal with the sum of the common stat gene.

   So, aim at the time list don't know the length of total cycle as weather data, how can we do? In there, I raise rule in following for everybody can to validate. If the list's length is L, so only need to ask for all essential gene from the cycle Ti=2 to Ti=Sqr(2L), then added each other, namely is the fact list's all-right simulate, if in this fact list the contributing cycle all is between 2 to Sqr(2L)

, so we can use the sum of this cycle gene to make forecast. If there is contributing cycles have beyond this bound, so must to found out all essential gene of this cycle. In the case, need choose how many plenty of essential cycle gene? The chances are reach bound that till the sum of length cycle of these essential genes have had equal with L.

                           Shizhao Zhang   2002-8-11