Replication of the Gold Forecast Findings with New Data
Copyright © 2013 All Rights Reserved by David Cochrane and Linda Berry ABSTRACT:A Gold Forecast AstroSignature developed in 2006 predicted gold prices over 3-month periods with an average correlation r value = 0.057 for 126 3-month periods. Because the AstroSignature had not been tested with new data and the AstroSignature was not completely elegant, a mean correlation value of .03 to .035 with the new data would be considered a positive result. The obtained correlation value of .0375 was slightly above this expected range, the likelihood of this result was p = .14 and was not statistically significant but suggests that predictors for short-term gold prices may have been identified. Note that the statistically significant result in the 2006 study was influenced by the higher power of the statistical test with N = 126 correlations in the 2006 study and N = 26 correlations in the present study. A simplified and more consistent AstroSignature produced slightly improved mean correlation and p values, and the simplified AstroSignature is recommended for future studies. This study presents one of the strongest validations of astrology to date because a hypothesis was confirmed using new data and with an effect size (as estimated by the correlation coefficient) slightly above the expected effect size. TERMINOLOGYIn this paper "astrological" refers to a celestial event which is proposed to correlate with some behavior. In this paper the behavior is the price of gold. AstroSignature,br> An AstroSignature is a combination of astrological variables which are hypothesized to correlate with a behavior. The AstroSignature score is calculated by simply adding the number of points assigned to each astrological variable contained in the AstroSignature that occurs at the time of a given behavior. Conjunction Oppostion Conjunctions and oppositions are two kinds of astrological aspects. Harmonic
In other contexts, the 2/14 aspect can be considered both a 7th and 14th harmonic aspect, but in this paper it is regarded as only a 14th harmonic aspect. Orb IsoTrap Harmonic IsoTrap LITERATURE REVIEWIn 2006 Cochrane developed an AstroSignature for predicting gold prices.1,2 The AstroSignature was developed by using research features in the Sirius astrology software (copyright ©Cosmic Patterns Software). Cochrane developed two variations of the AstroSignature:
The above shall be referred to in this paper as the "Low Risk" and the 'High Risk" AstroSignatures. In this study 126 quarterly (i.e., 3-month) periods of gold prices were correlated with the predicted gold prices based on the AstroSignatures to produce 126 correlation values for each AstroSignature. These 126 correlation values were re-analyzed in 2010 with the DerSimonian-Laird meta-analysis of correlation values using the metacor of the R statistical software package.4 The DerSimonian-Laird analysis determines the statistical significance of correlation values (typically Pearson correlation coefficients, r) and the number of subjects (N) in each correlation. In the study by Cochrane there were 90 to 92 correlation values (daily values for 3 months) because imputed values based on a linear change in prices were used on days when market trading is not conducted (weekends and holidays). The mean correlation (mean r) for the Low Risk AstroSignature was .057 and mean r for the High Risk AstroSignature was .086.2 The High Risk correlation had greater variability in correlation scores across the 126 correlations and thus was given the name "High Risk, High Yield" to indicate the greater risk involved with higher variability but also a higher mean r value indicating a potential for higher profit for an investor. The components of the Low Risk AstroSignature were: Sun and Jupiter in harmonics 1, 7, 14, 21, 28, and 35 The components of the High Risk AstroSignature were: Sun and Jupiter in harmonics 7 and 14 The two AstroSignatures differ as follows:
Also, there are the weights assigned to each aspect. The Sun-Jupiter 7th and 14th harmonic aspects were weighted more heavily than most other astrological aspects so they contribute the most to the predicted prices. DATAThe gold price data that was used in the study in 2006 spanned the years 1975 to 2006. Co-author Linda Berry identified a website that contains gold prices for dates from 1973 to the current time. A feature to download the data was not provided at this website so she copied and pasted this data into a file. The data from 2006 to the present time (May, 2013) was imported into Sirius. The years 1973 to 1974 were not included because Sirius analyzes financial data in blocks of time and two years of data is not sufficient to draw conclusions. The data from 2006 to 2013 spanned 7 ½ years, allowing 26 quarterly correlations to be produced. Although this is less than the 126 correlations in the original study, this amount of data is likely to be sufficient to obtain meaningful results. CONSIDERATIONS IN DEVELOPING A HYPOTHESISBecause there are 26 correlations in the current study and the 126 correlations in the earlier study, a statistical analysis of the data in this study has much lower power than in the previous study and thus is less likely to produce statistically significant results. In addition to the p value, the mean correlation provides a meaningful result. In the study in 2006 the r value was .057 for the Low Risk AstroSignature and .086 for the High Risk AstroSignature. We expect a positive correlation in the current study, but less than the correlation value obtained in the previous study, given that the current study analyzes new data and the earlier study was exploratory in nature rather than a hypothesis test. Also, the two AstroSignatures had not yet been evaluated in a hypothesis test. Both the High Risk AstroSignature and Low Risk AstroSignature contain a fairly consistent set of astrological influences, but there are inconsistencies, as follows:
Given the above complexities in the AstroSignatures, we can expect some degradation in the mean r obtained in the current study as compared to the study in 2006. In addition, of course, the current study is a hypothesis test and the study in 2006 was more purely exporatory in nature. The authors regard the High Risk AstroSignature as less elegant because harmonics 21, 28, and 35 are variations of the 7th harmonic, whereas the High Risk AstroSignature also includes the 5th harmonic and only one harmonic between Sun and Saturn. If one finds that related harmonics produce similar results, then the findings are consistent with harmonic theory. Finding the 3rd harmonic of Sun and Saturn is important but not the related harmonic of the 6th harmonic and possibly also the 9th, 12th, and 18th is not completely theoretically consistent. Therefore, it is more likely to be an anomaly in the research results rather than an indication of an actual predictor. With these considerations in mind it was expected that the Low Risk AstroSignature would outperform the High Risk AstroSignature. Given only a .057 mean correlation with the Low Risk AstroSignature, a correlation of .03 to .035 in the current study would suggest that the Low Risk AstroSignature may be a valid predictor of short term changes in gold prices. There is insufficient data to obtain definitive conclusions but indications of whether the theoretical framework used and previous findings obtained are worthy of additional research can be determined. HYPOTHESISThe null hypothesis is that the Low Risk AstroSignature produces a mean correlation of less than .03. Because the power of the DerSimonian-Laird meta-analysis with the amount of data analyzed is unclear, a hypothesis regarding statistical significance was not made, but a statistical significance level of less than .05 would strongly suggest that the AstroSignature is a valid predictor. The High Risk AstroSignature is expected to produce similar results but at a slightly less significant level. BASIC FINDINGSThe mean r of the 26 quarterly correlations of actual gold prices with the predicted gold prices from the Low Risk AstroSignature was .0375, with p = .14. The finding of r = .0375 was surprisingly high, but the power of the test was not sufficient to obtain statistical significance. The High Risk AstroSignature produced a mean r = .020, with p = .32. The High Risk AstroSignature, unlike the Low Risk AstroSignature, did not produce results that suggest that it is valid. The inclusion of the 5th harmonic aspects and Sun trine Saturn seriously degraded the ability of the AstroSignature to produce accurate predicted gold prices. Despite the poor performance of the High Risk AstroSignature, a detailed analysis of the results obtained from the Low Risk AstroSignature, as described below, suggests that the simpler definition of aspects for Sun-Jupiter and for Jupiter-Neptune in the High Risk AstroSignature (only 7th and 14th harmonics) may be an advantage of the High Risk AstroSignature Detailed Analysis of Results Sun-Moon 7th harmonic aspects were added to the Low Risk AstroSignature to see if they would improve the AstroSignature. Sun-Moon 7th harmonic aspects were found to be potentially important in the making of a video on the gold price forecast (http://youtu.be/EcajsPRDZNc) The results were mean r = .04, effect size of 5 =.04, p = .15. The p value did not improve with the addition of the Sun-Moon 7th harmonic aspects so it was concluded that Sun-Moon 7th harmonic aspects are not related to gold prices. To determine if IsoTraps contributed to the forecast of gold prices, they were removed from the AstroSignature and the results obtained were mean r = 0.02, effect size of r = 0.02, and p = 0.21. The mean r dropped from .04 to .02 and the p value increased from .14 to .21, suggesting that the IsoTraps included in the original Low Risk AstroSignature should be retained. Only 7th harmonic aspects of Jupiter and Neptune are included in the Low Risk AstroSignature. Related harmonics like the 14th harmonic are not included, and this is theoretically mildly inconsistent. Removing the Jupiter-Neptune 7th harmonic aspects produced these results: mean r = 0.03, effect size of r = 0.03, and p = 0.16. Removing Jupiter-Neptune 7th harmonic aspects slightly decreased mean r and slightly increased the p value. Therefore, Jupiter-Neptune 7th harmonic aspects were included as well as Jupiter-Neptune 14th harmonic aspects in order to have a more consistent AstroSignature in which 7th and 14th harmonic aspects of Sun-Jupiter and Jupiter-Neptune are included in the AstroSignature. The results produced by the Low Risk AstroSignature with Jupiter-Neptune 7th harmonic and 14th harmonic aspects were mean = 0.05, effect size = 0.05, and p = 0.09. The mean r went up slightly and the p value improved from .14 to .09, and the consistent use of 7th and 14th harmonic aspects with Sun-Jupiter and Jupiter-Neptune suggests that Jupiter-Neptune 7th and 14th harmonic aspects should be included in future research. Having concluded that the results suggest that Jupiter-Neptune 7th and 14th harmonic aspects should be included in the AstroSignature, an evaluation of harmonics 21, 28, and 35 was undertaken. These harmonics were included for Sun-Jupiter in the original Low Risk AstroSignature. When these harmonics were included (as well as harmonics 7 and 14), for Jupiter-Neptune, the results were mean r = 0.02, effect size of r= 0.02, and p = 0.26. Including these harmonics reduced the significance of the results. To make the Sun-Jupiter and Jupiter-Neptune harmonics consistent, an AstroSignature with harmonics 21, 28, and 35 for Sun-Jupiter removed and also Sun-Jupiter conjunction was created and the results for this AstroSignature were mean r = 0.05, effect size of r = 0.05, and p = 0.11. The p value of .11 is higher than the p value of .09 with the additional harmonics included, but the new AstroSignature is simpler and more consistent, with Sun-Jupiter and Jupiter-Neptune having the same harmonics (7 and 14), so this AstroSignature appears to be the most promising AstroSignature for predicting gold prices. Lastly, an AstroSignature of only IsoTraps was created to see how well it predicts gold prices. The results were mean r = 0.05, effect size of r = 0.07, and p = .17. Amazingly, IsoTraps predicted gold prices as well as the AstroSignature that includes Sun-Jup and Jup-Nep 7th and 14th harmonics as measured by mean r, and the effect size was even higher. However, the p value of .17 is worse.
Note that a standard IsoTrap occurs when the aspect between the midpoints is either a conjunction (0 degrees) or opposition, (180 degrees). The symmetry of the IsoTrap results in two points of symmetry at points 0 and 180. This symmetry may imply that when a trine aspect (120 degrees) is used, then the sextile (60 degrees, i.e., 180 minus 120) should also be used. Similarly, the 40, 80, and 160 degree angles of the 9th harmonic aspects may imply that the angles of 20 degrees (180 - 160), 100 degrees (180-80), and 140 degrees (180 minus 40) should also be included in order to be consistent with the harmonic properties of the Harmonic IsoTrap. For this reason, all of these angles are included in the Gold Forecast AstroSignatures. Also, there are three variations of midpoint structures that are possible between four planets. For example, for Sun, Mars, Jupiter, and Uranus, where "/" indicates the midpoint of the planets and "=" indicates conjunction or opposition, the following IsoTraps are possible:
CONCLUSIONSThe Low Risk AstroSignature performed slightly better than expected, suggesting that the Low Risk AstroSignature may be an accurate predictor of gold prices. However, given the limited amount of data and the relatively low power of the statistical analysis in the current study as compared to the study in 2006 with a larger dataset, statistically significant results were not obtained (p = .14). Therefore, we conclude that the results suggest only that the AstroSignature may be valid and is worthy of further research, but the results were not strong enough to be convincing or overwhelming, and may represent random fluctuation in the data. The detailed analysis of the data strongly suggests that a simpler AstroSignature that removes harmonics 1, 21, 28, and 35 from the Sun-Jupiter combinations and includes 14th harmonic aspects as well as 7th harmonic Jupiter-Neptune improves the ability of the AstroSignature to predict gold prices. This revised AstroSignature is also more elegant and internally consistent. Sun and Jupiter in 7th and 14th harmonic aspects are, in a sense, the central basis of the Low Risk AstroSignature, the High Risk AstroSignature, and the variations of the AstroSignatures introduced in this paper. The Sun-Jupiter 7th and 14th harmonic aspects are central because they are given the greatest weight in the AstroSignatures and therefore have the most dramatic effect on raising gold prices. The confirmation in this study that Sun-Jupiter 7th harmonic and 14th harmonic aspects suggests that the most fundamental and important components of the AstroSignature may be valid predictors of higher gold prices. A somewhat surprising finding is that Harmonic IsoTraps were retained as valid components in the AstroSignature. Harmonic IsoTraps were introduced in the study conducted in 2006 because they appeared to be good predictors using the exploratory research features in the Sirius software for analyzing harmonic IsoTraps. This finding is somewhat surprising because Harmonic IsoTraps are relatively new and there is little previous literature that refers to them. Harmonic IsoTraps are simply aspects other than conjunctions and oppositions between the midpoints of planets. The results of this study strongly suggest that aspects between midpoints are very important. Although this finding may seem unreasonable from the point of view of the theoretical framework and traditions of many astrological systems, it is consistent with the theoretical foundations of harmonic astrology and cosmic cybernetics. The IsoTrap includes a double-resonance6 so it is a fundamental and powerful harmonic pattern, and variations of the IsoTrap by taking other angular distances other than 0 degrees and 180 degrees between the symmetric points (midpoints) of the IsoTrap is a theoretically reasonable variation of the standard symmetrical IsoTrap. Nevertheless, given the lack of previous astrological literature regarding the fundamental importance of aspects between midpoints, the replication of the finding that 3rd, 6th, 9th, and 18th harmonic aspects between IsoTraps predict higher gold prices is somewhat surprising, or at least intriguing and potentially a major new insight into the manner in which planetary resonances predict behavior. One can speculate that the Harmonic IsoTraps provide a positive and optimistic background quality and the 7th and 14th harmonic aspects of Sun and Jupiter and of Jupiter and Neptune provide a motivation for long-term investment. See the ebook The First 32 Harmonics, A Qualitative Studys for evidence regarding the effects of the 7th harmonic. However, speculations regarding the manner in which the AstroSignature forecasts gold prices may be premature. Before speculating in any detail on these theoretical considerations, more research is needed to determine if astrological variables can produce measurable effects. The correlation of the predicted prices with actual prices of about .04 in this study is very small. According to Cohen's D, r = .1 is small and the effect size obtained in this study is even smaller. Consequently, a large sample size is needed to obtain statistical significance. INDICATIONS FOR FUTURE RESEARCHHarmonic aspects and IsoTraps can be evaluated in further research on commodity prices and any other area of astrological research. The current study was conducted by two individuals who have limited time and resources for conducting research. The participation of more people in sophisticated quantitative research can accelerate the pace at which discoveries are made. Rather than producing correlations for time periods and statistically analyzing the correlations with a meta-analysis like the DerSimonian-Laird meta-analysis, a percent deviation from a moving average over 3 months (or any other duration) could be computed and a correlation for the entire dataset produced and the statistical significance obtained. Given the large N, this analysis might have more power. The authors plan to do this analysis in the near future, and results will be reported. This study was conducted by independent researchers with very limited time. Increasing the effect size in future studies could be achieved by improving the AstroSignature. Experimenting with different orbs and variations of aspects used may produce higher correlations with AstroSignatures that are also simple and elegant. However, creating these variations is time-consuming and there are also other research designs and datasets that the authors of this study are interested in pursuing. As time permits or as other researchers become engaged in quantitative astrological research, additional variations of the Gold Forecast AstroSignatures may be developed and also more intensive exploratory research and application of the theoretical framework employed in this study to other datasets can be pursued. The findings in this study are particularly important and worthy of future research considering the limitations of time and resources available. Appendix 1.R Code Given below is the R code that analyzed the results produced by Sirius 1.3. # Run only 1 of the following, depending on which AstroSig is to be evaluated: # sort by correlation to make plot look nicer # DerSimonian-Laird method with plot " p = ",GoldRes$p," count=", dim(GoldCorrDat)[1],"\n",hist(GoldCorrDat$Corr) Appendix 2Summary of Results Given below are the results produced by the R code Gold Forecast 1: Lower Yield, Lower Risk
Gold Forecast 2: Higher Yield, Higher Risk
Lo Risk With Sun-Moon,br>
"AstSigCorrelationsLoRiskWithSunMoon.txt"
Lo Risk, No IsoTraps
Lo Risk, No Ju-Ne
Lo Risk,with Ju-Ne 14th h.
Lo Risk, with Ju-Nep 14 28 21 35 h.
Lo Risk, Su-Ju and Ju-Ne 7 and 14 H Only
Lo Risk, Su-Ju and Ju-Ne 7 and 14H Only and No Su-Ju Conj
Lo Risk, IsoTraps Only
References:
AUTHOR: David Cochrane |