## About a correlation between currency exchange rate and astronomical parameters of the Solar system’s celestial bodies## Alexander Trunev (Toronto, Canada)## Victor Okhonin (Toronto, Canada)A currency exchange rate simulation is one of the popular problems of financial astrology. There are several approaches to such a problem. The most substantial results we can reach by using intellectual systems based on neural network computer applications. We have analysed an exchange rate dependence among 20 countries (see: Table1) according to astronomical parameters of Solar system’s celestial bodies: The Sun, Moon, Mercury, Venus, Mars, Jupiter, Chiron, Saturn, Uranus, Neptune and Pluto in period from January 1, 2000 up to June 15, 2006. For the simulation we have constructed a neural network which was able to compare a relative contribution of input parameters. Among the input parameters there were following: - Astronomical parameters of celestial bodies;
- Newton’s linear time (in seconds);
- Calendar time: year, month, day of a month and day of a week.
Among astronomical parameters were used longitude sine and longitude cosine, latitude and a distance between the Earth and every celestial body. The database was prepared as a matrix where there were exchange-rate rows as well as astronomical parameters, linear time and calendar time. It has been used back-propagation neural network, with 60 outputs, 189 input, and 14940 non-linear neurones. As algorithm of optimization it was used conjugate gradients method, modified for elimination of effect of conversion training. On an output neural network reproduced daily trends on 20 hard currencies, for three next days, on an input there were daily trends on the same currencies for seven last days, and the block of 49 time parameters, including time under the physical standard, calendar day, day of week, month and year, and actually astronomical 44 parameters. Other variants of neural networks were approved also. All entrance and target parameters were preliminary shifted on zero average on sample and normalized on an individual root-mean-square deviation on sample that excluded dependence of neural network parameters from scale of a signal. As a parameter of the importance of an entrance signal the sum of squares of weights of communications with an input corresponding to this signal was used. During neural network training "useless" communications for successful approximation decreased, and "useful” grew. A forecast power of such a model is greatly flexible according to different countries (see Data: Table 1). Thus by any forecast for the next day the model gives an opportunity to determine a sign of any exchange-rate change for 14 currencies of 20 shown in Table 1. Moreover a forecast rate varies for different values from 37% (New Zealand) up to 76% (China) of true forecasts. In other words not all exchange-rate series are able to be predicted to the right degree. It is possible to find a group of countries with a forecast rate of 2/3 and higher, but at the same time there is another one with maximum forecast degree ½. It is obvious that: - The input parameter set is not complete;
- In real case we should analyse a market players’ behaviour influencing on market prices.
Nevertheless this model allows us to compare a relative role of the input parameters that gives an example of independent scientific interest. On Diagram 1 and in Tables 2 we can see a relative role of all the input parameters in percent equivalent. As it was revealed the most important parameter for all analysed series is a calendar month. Its relative contribution is about 14%. Obviously, that a calendar month is the best parameter to describe seasonal fluctuations of currency exchange rate series. It is remarkable that 12 calendar months of a year are equal to 12 zodiac singes in astrology. The most interesting intriguing is that the summary contribution of planet parameters exceeds four times a calendar and hundred times – contribution of linear time which is usually used for a simulation of natural as well as economical processes. And such a factor, that linear time is less important than astronomical parameters of celestial bodies, is in favour of astrology as an adequate model of some economical processes. Moreover among all astronomical parameters the summary contribution of the distance is only 22.68% whereas a quota of angular parameters and time is summary 77.32% - see: Table3. In other words ancient astronomers and astrologers who had constructed astrology based on only angular positions of celestial bodies (so long as they could not measure distances to celestial bodies) had intuitively suggested that the angular parameters contribution is the most considerable. Among all the planets the most important contribution in value trends gives the Jupiter (9.59%), then come the Mercury (9.05%), Moon (8.63%) and Venus (8.55%) – see: Table 2. Note, that a contribution of asteroid Chiron (8.44%) is higher than Saturn’s contribution (8.09%). The Sun (6.14%) gives the smallest contribution among the planets of classical astrology. Contributions of invisible planets Uranus (4.07%) und Neptune (3.97%) are twice less than, for example, Saturn’s. At the same time a contribution of relatively small celestial body Pluto (5.07%) excels Uranus’s and Neptune’s. The Mars – a symbolical Lord of the 8-th “business” House – contributes 7.84%. Over more a pair Mars – Pluto (both – Lord of Scorpion sign) takes almost 12.91%. The fulfilled analysis gives us an opportunity to take a new look at classical astrology as a forecast model. First of all it is clear that astrology could be used as a real instrument in description of economic processes. Secondly it is obvious that a prognosis degree is variable from case to case and never reaches 100%. That is why it has no sense to require a high accuracy of the model’s prognosis anyway, but it is better to pay a close attention on processes with the forecast degree of 2/3 or higher. Table 1: A forecast level of currency exchange-rate for the next day
Table 2: A relative contribution of input parameters of celestial bodies
Diagram 1: A relative contribution of celestial bodies parameters Table 3: A contribution of angular parameters, distance and time
Most the general feature in all approbation the established small weight of time under the physical standard was. Thus the weight of astronomical parameters was essentially higher. The given circumstance can be counted the basic result of the lead researches. It well-known that astronomical parameters with high accuracy can be considered as functions of time under the physical standard. Essentially neural network as mathematical realization of non-linear regression algorithm can reproduce corresponding dependence. Nevertheless, neural network "prefers" to use given to it astronomical parameters. Thus astronomical parameters and time of the physical standard “are topologically non equivalent”, because there is a continuous mapping of the physical standard time to the set of astronomical parameters, but there is no inverse continuous mapping. And as approximating abilities of neural network connected with properties of the continuity, observable "preferences" of neural network are not so paradoxical. Observable “elimination of the physical standard of time at a competition to astronomical parameters” is not certainly "proof" of primacy of astronomical parameters. Moreover, now even it is not clear, how it is correctly to set such problem of “a demonstrative choice of the best variant of representation of time”. At the same time, it is possible to assert, that in a considered case astronomical parameters look as “more natural and convenient”, than time of the physical standard. At last we should say that according on following data asteroids could introduce a remarkable distribution equal with planets’ distribution. We cannot find the best explanation than to suggest that every celestial body has got its certain topological “charge” which does not depend on its mass and other physical parameters. This “charge” spreads its power on “charges” of other celestial bodies interacting with their “charges” and creating specific astral field. This astral field is obviously a matter of research in astrology. Acknowledgements The authors are gratitude to Vladimir Shashin (St-Petersburg, Russia) and Ludmila Gavrilova (Cologne, Germany) for technical support. |