Cycles in the New Zealand Economy

(originally posted 02/05/07 on Wobbly Universe blog by Ray Tomes)

Although I had been somewhat interested in cycles before 1978, that was the year when I began doing economic modelling on a computer and some cycles just jumped out at me uninvited, and a long time serious interest in cycles began. I did work at that time for a number of Corporations, both large ones and small ones that were about to become large. I developed my own techniques for doing this, and eventually became convinced that this method is better than the methods used by many economists.

This study was performed at a time when the NZ economy was not an open one and some corporations wanted to predict possible future changes in the exchange rate, changes in interest rates and in inflation. Data were gathered for the last 44 years and included anything related to the New Zealand economy:- import and export prices and volumes by various major categories; stocks of major NZ production items; terms of trade; share prices; several price and inflation indices; a variety of demographic data; births, deaths and marriages; mortgages and land and building prices and transfers; wages. The analysis used the base variables and also the annual rate of change of them because that is often what is desired to be predicted.

All these variable were processed by a method known as factor analysis. What this does is to take many variables and reduce them to a much smaller number that still contains the essence of the original, in that the original data is very largely explained as each item being affected by several of these factors, with the balance taken as being to some extent noise. In this study, 9 independent (that is uncorrelated) factors were extracted and this report shows graphs of these. When considering any of the original variables or its rate of exchange, nearly all of the variables can be well explained as the sum of a combination of the factors with various loadings.

The factors are displayed below:


Factors in the New Zealand Economy

It can be seen that the first two factors are rather slow moving ones that show the general state of the economy and it is suggested that these are related to the Kondratieff cycle which is recognised as being about 53 years. Factors 3 and 4 show a moderately regular cycle with a period varying between 3 and 4 years. These two variables are related in the same way that a sine and cosine wave are (or an electric and magnetic field for that matter) with factor 4 being a reasonable measure of the rate of change of factor 3 and factor 3 being a reasonable measure of the negative rate of change of factor 4. These two together are what is generally called the business cycle.

Factor 6 shows a quite regular cycle of close to 3 years although it shows two periods of heightened amplitude around 1957-60 and 1972-74. These two periods correspond to brief periods (3 years each) when the country had Labour governments in between longer periods of National government. However the timing allows the conclusion that the cause of the cycle was not the change in government but perhaps the other way around.

The other factors are not so clearly defined as cycles, although there is some presence of cyclical activity. They are less well defined, but have specific meanings in terms of which variables they correlate with.

In order to try and predict future economic conditions, multiple regression equations were found that use the 9 factors to predict each of the factors in turn from the previous years values for those factors. This works particularly well for factors 3 and 4 because, as mentioned, each variable is closely related to the rate of change of the other.

Before trying to predict the future, it is always best to try and predict the past to see if the method is reasonably sound.

So here are two test runs of the method compared to what actually happened. One test was started in 1960 and the other in 1973. The choice of 1973 was made because the so-called oil shock happened in 1974 and lead to major disruption in world prices and economies, and is considered to have been a random rather than a predictable event.

However the test shows that the regression equations predict the big swing in factor 3, actually slightly over-estimating it. Factor 3 is negatively correlated with many economic variables and so goes up when the economy crashes – the things related to it are terms of trade and export prices and volumes. NZ is harder hit by this factor than most countries.


Test Prediction of Factors in NZ economy

In most cases the predictions are moderately accurate for about 5 years ahead after which the forecasts become a bit sterile compared to the economic movements that actually happen.

The next step is to use the data to make real predictions about the future.

It has been said that prediction is a difficult business, especially about the future.

These forecasts were supplied to several corporations and also I gave a talk at the NZ Statistical Association Conference. It was well received, except that several economists had some criticisms. They told me that the long cycle that seemed to exist in factor 1 (and perhaps 2) was called the Kondratieff cycle and also named another cycle or two and then told me that these cycles did not exist. I was very puzzled as to why cycles that didn’t exist appeared in my data and why that had been given names! However participants other than economists said that some of the other cycles were exactly what they experienced in their own areas of study.


Predictions of NZ economic factors

These predicted values for the factors are then used to work backwards to the original variables and give the clients what they wanted to know. My prediction of inflation continuing at a level of around 15% for at least 5 years was very markedly different from NZ Reserve Bank and other economists who were predicting a rapid decline towards 5% in 3 or 4 years time. My prediction was the one that was right.

In my report to my client, I was able to make quite an accurate prediction of the share market for the next few years and to state that there would be no more devaluations of the NZ$ as there had been several in the previous few years. There were no errors in my forecasts.


This method of reducing economic variables to a small number of factors that still contains the essence of the data is a valuable method that overcomes several serious problems in economic modelling. Firstly, there is usually insufficient historical data and models become over specified and mathematically are not sound. The use of factors also removes noise and the factors are much crisper and cleaner data.

There are other methods that are also better than traditional modelling methods, such as Box-Jenkins ARIMA models etc. These methods are mathematically based and assume no economic knowledge and they work. The economic understanding models are generally less accurate. I have not compared my method to Box-Jenkins, which uses only one variable to,predict any variable — itself! I suspect that this method would allow an improvement on Box-Jenkins, because in the case of factors like 3 and 4, they do show that there is momentum in the economy that moves from one variable to another.

For 4 years from early 2007 until late 2010, Ray Tomes ran a blog called “Wobbly Universe” on his personal web site. With software changes that blog stopped working. Over the coming weeks or months these old articles will be reposted to CRI blog.

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The Historical Process – Cycles of War

(originally posted 17/05/07 on Wobbly Universe blog by Ray Tomes)

In the early 1900s, Alexander Chizhevsky (sometimes spelled Tchijevsky or various other ways) made very comprehensive investigations in historical processes, especially wars, to try and determine the causes of the processes. He found that existing methods of analysis could not predict major events that were about to happen.

Unfortunately for us in the English speaking world, most of Chizhevsky’s writing is in Russian or French and has never been translated into English. Some parts have been, and the investigation into war has been reported in English. Some of this material has also been reported by Raymond Wheeler in America, but I think that Chizhevsky was the originator. It would be good to know the full story on any links between these two.

Chizhevsky first began to observe that conflicts in Russia tended to be cyclic. After publishing several papers on this he expanded his study to world wide conflicts and made an index of battles for the last 2500 years. It showed clearly that there were 9 fairly regular peaks in conflicts each century, or averaging 11.1 years apart. There were other fluctuations, great sweeping rises and falls over longer periods, but this one cycle stood out.

It so happens that the sunspot cycle also has an average period of 11.1 years, so it was natural to begin to look at the connection. He found that the peak in human aggression fairly much coincided with the peak in sunspots. It is natural to wonder as to whether the Sun is somehow causing or contributing to human behaviour.

There are some additional facts available to us now that help to understand this process. I have never seen this fully laid out exactly like this before (excluding things that I have written), but here are a collection of facts that we can connect the dots on:

1. The quantity of different types of radiation vary over the sunspot cycle.

2. There is a continuous stream of radiation of various types, called the “Solar Wind” that arrives at the Earth.

3. Fluctuations in the stream of radiation at the Earth affects the earth’s geomagnetic field.

4. There is an oscillation of the Earth’s entire electromagnetic field, called the “Schumann Resonance” which oscillates about 7.5 times per second because that is how fast electromagnetic waves travel around the Earth.

5. Bursts of Solar radiation can get the Schumann resonance really ringing. Although the 7.5 Hz mode is the main one, there are also oscillations at near multiples of this: 15, 22.5, 30 Hz and sometimes at lower frequencies such as 3 Hz.

6. Human brain wave frequencies that are commonly studied cover the range from about 0.3 to 40 Hz, and the Schumann resonance is right in the middle of that range. The brain is a largely electrical organ in its functioning.

7. Outside electromagnetic fields can affect the brain by entrainment or in other ways. For example it is known that 10 Hz waves will make human reaction times faster while 3 Hz waves will slow it down.

8. Accidents are more frequent when there are strong ELF or ULF (Extra Low Frequency or Ultra Low Frequency) waves such as 3 Hz. This can be understood as resulting from a slowing down of human reaction times – people are less able to deal with tripping up or sudden events and so more likely to have an accident.

I do not know of evidence that moods are affected by ELF / ULF waves, but would expect that to be the case. Certainly we may say that the evidence is that when the Sun gets uppity, so do people, probably because of electromagnetic waves affecting our brain operation.

My guess is that we all have stored up resentments that we are bottling up, and that when a bit of extra electrical activity is brought to bear on our brains, these then overflow just as they would when the last straw was added by events in our lives. Then all sorts of stuff bursts forth. However when this comes from the whole Earth resonating, it means that many people get agitated at the same time. That is just the recipe for international conflict or social unrest.


For further reading please see:

Chizhevsky’s paper (1.4 MB PDF file) as published by the Foundation for the Study of Cycles.

Edward Dewey’s War cycle analysis (0.1 MB PDF file). Dewey found other cycles in Chizhevsky,s data also, of which the strongest were 53.5, 23.8, 17.4, 11.2 and 6.0 years.

For 4 years from early 2007 until late 2010, Ray Tomes ran a blog called “Wobbly Universe” on his personal web site. With software changes that blog stopped working. Over the coming weeks or months these old articles will be reposted to CRI blog.

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Harmonic Cloud Patterns on Jupiter

(originally posted 28/06/07 on Wobbly Universe blog by Ray Tomes)

At the NASA web site the following description is found about a polar map of Jupiter.

This map of Jupiter is the most detailed global color map of the planet ever produced. The round map is a polar stereographic projection that shows the south pole in the center of the map and the equator at the edge. It was constructed from images taken by Cassini on Dec. 11 and 12, 2000, as the spacecraft neared Jupiter during a flyby on its way to Saturn.

The map shows a variety of colorful cloud features, including parallel reddish-brown and white bands, the Great Red Spot, multi-lobed chaotic regions, white ovals and many small vortices. Many clouds appear in streaks and waves due to continual stretching and folding by Jupiter’s winds and turbulence. The bluish-gray features along the north edge of the central bright band are equatorial “hot spots,” meteorological systems such as the one entered by NASA’s Galileo probe. Small bright spots within the orange band north of the equator are lightning-bearing thunderstorms. The polar region shown here is less clearly visible because Cassini viewed it at an angle and through thicker atmospheric haze.

Image Credit: NASA/JPL/Space Science Institute

jupiter-pole       Jupiter polar map produced by NASA from photos taken December 11-12, 2000.

It is clear that there are several types of features that repeat around that planet at fairly regular intervals. There are regular white spots about half way between the pole and equator, and much closer regular notches nearer to the equator.

Several of these features are marked on the map below, and in some places where the pattern is not clear it is continued until it links with the same pattern further around.

jupiter-pole-harmonics       Jupiter polar map showing harmonics of 12, 24, 72 and 144.

The smaller wave pattern is made clearer in the following magnification. There is a Full size image of Jupiter available at this same scale at NASA.

jupiter-72        A magnification shows the regularity of the wave identified as the 72nd harmonic.

It so happens that there is an explanation based on the harmonic formation of waves in a non-linear system that predicts that certain harmonics should be much stronger than others. It is called The Harmonics Theory and was developed by me, Ray Tomes. Here is a graphic showing the predicted relative power in various harmonics:

h1-100       Predicted Strong Harmonics from 1 to 100 according to the Harmonics Theory

Quite clearly, 12, 24 and 72 (also 144 not shown on this graph) are expected to be strong harmonics. The reason that certain harmonics are stronger than others is that they can be formed in more ways. This type of behaviour is not observed in essentially linear systems such as a guitar string, where no harmonics are especially strong relative to their neighbours. But in 2 and 3 dimensional structures, especially nearly closed systems where standing waves can last for a long time, not only do harmonics form, but harmonics of harmonics.

This means that a wave that divides the planets circumference in 2 for example will itself have divisions which will therefore divide the planets circumference in 4, 6, 8, 10, 12 and so on. Likewise a wave that divides the planet into 3 will form harmonics that divide it into 6, 9, 12 and so on. Because some numbers can be factorised in many more ways than others, these strong harmonics will be more evident when we see pictures of Jupiter or any other nearly closed system which can sustain standing waves for long periods of time.

Harmonics theory also makes predictions of much smaller waves (larger order harmonics) and these predictions are also found in cloud patterns on Earth. When applied to the entire universe, the theory explains why there are certain scales of distance at which structures prefer to form and these include galaxies, stars, planets, moons as well as cells, atoms and nuclear particles. Based on the predicted and observed patterns, it can be concluded that the universe is much larger than many cosmologists currently believe.

For 4 years from early 2007 until late 2010, Ray Tomes ran a blog called “Wobbly Universe” on his personal web site. With software changes that blog stopped working. Over the coming weeks or months these old articles will be reposted to CRI blog.

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3.029 and 3.606 minute cycles in Solar Wind Speed

The ACE satellite measures the solar wind speed (among other things) of particles traveling from the Sun towards the Earth. Located at the L1 libration point it is always around 1.5 million km in the direction of the Sun and so can give about an hours warning of space weather changes. The solar wind speed is typically in the range of 300 to 700 km/s.

This 1 minute interval real time data remains available for only a short period of time. The  present analysis was done on data recorded on 11th July 2015 and there are 1440 (less about 20 or so missing) measurements at 1 minute intervals. The analysis was done using our free CATS software.

Firstly the rapidly fluctuating solar wind speed is shown.  solarwindspeed-20150711It can be seen that minute by minute there are substantial changes in solar wind speed. A spectral analysis of the solar wind speed shows a number of cycles significant at p=0.05 level as listed in this table:

no. of    Cycle period    Date of peak    Cycle            Bartell’s
cycles    minutes                                  Strength        Test (p=)

399.28    3.60649    2015.5252621    0.098406    0.00000000
475.39    3.02909    2015.5252634    0.076864    0.00000000
398          3.61809    2015.5252620    0.054579    0.00001875
400.83    3.59255    2015.5252648    0.050971    0.00014225
402.19    3.58040    2015.5252665    0.045818    0.00079066
49.32    29.19708    2015.5253121    0.070705    0.00204380
395.79    3.63829    2015.5252675    0.039579    0.00348685
217.41    6.62343    2015.5252699    0.042097    0.00369764
476.69    3.02083    2015.5252647    0.036243    0.00429099
50.53    28.49792    2015.5252634    0.060138    0.00621892
215.95    6.66821    2015.5252676    0.038759    0.00634786
474.01    3.03791    2015.5252625    0.032432    0.00820103
403.29    3.57063    2015.5252618    0.034605    0.00867797
74.88    19.23077    2015.5252801    0.046984    0.01230259
194.41    7.40703    2015.5252621    0.038716    0.01238090
32.64    44.11765    2015.5252903    0.042015    0.01393355
48.11    29.93141    2015.5253090    0.055255    0.01451557
161.24    8.93079    2015.5252751    0.043495    0.01474822
324.51    4.43746    2015.5252652    0.036788    0.01493206
482.48    2.98458    2015.5252647    0.020699    0.01656507
172.13    8.36577    2015.5252655    0.038061    0.01716400
76.21    18.89516    2015.5252839    0.050419    0.01754671
39.99    36.009    2015.5253088    0.057387    0.01863100
565.36    2.54705    2015.5252626    0.032063    0.02572346
160.07    8.99606    2015.5252717    0.03406    0.02682052
25.42    56.64831    2015.5252675    0.043156    0.02765430
120.2    11.98003    2015.5252833    0.036602    0.02871458
14.77    97.49493    2015.5253709    0.071089    0.03136794
222.09    6.48386    2015.5252709    0.035618    0.03216350
394.53    3.64991    2015.5252657    0.030707    0.03295080
230.47    6.2481    2015.5252618    0.031044    0.03326301
211.72    6.80144    2015.5252714    0.034033    0.03358752
210.13    6.8529    2015.5252671    0.031237    0.03360750
477.93    3.01299    2015.5252662    0.028155    0.03678022
274.73    5.24151    2015.5252660    0.031051    0.03685700
83.61    17.22282    2015.5252927    0.047398    0.03700348
47.23    30.4891    2015.5253041    0.057521    0.03791188
78.49    18.34629    2015.5252890    0.048698    0.03937316
23.15    62.20302    2015.5253658    0.065049    0.04028760
554.02    2.59918    2015.5252628    0.026363    0.04334227
247.27    5.82359    2015.5252616    0.029738    0.04570371
173.65    8.29254    2015.5252681    0.033344    0.04915963

The first two listed cycles in particular are extremely significant and would not occur even one time in a hundred million by chance alone. The Bartell’s test shows the significance of cycles as a probability. They did occur in two different days that I analysed, with extremely similar periods.

The part of the spectrum near to these two cycles is shown because there are other significant cycles nearby:

solarwindspeed-20150711-spectrum-3-minutesA graph of the autocorrelation of the minute by minute changes of the solar wind speed up to 200 minutes lag is shown:

solarwindspeed-20150711-beats-19-minutesThis shows how the change in solar wind speed compares to the corresponding change at lags of up to 200 minutes and it can be clearly seen that there is a cycle of 3 minutes or so, and also that there is a modulation of 19 minutes in the autocorrelation. The two dominant cycles periods will produce beats of 18.92 minutes just as we observe. Note that there are two actual cycles near to 19 minutes also.

The author has often found cycles of near 3 and 6 minutes in the solar system previously. Along with 80 and 160 minutes these periods are rather common. We may note that the inner planets are roughly spaced at 3 light minutes apart in distance from the Sun, and the outer planets at 80 light minutes apart.

In my previous post to CRI Blog, I reported on Kotovs method of analysing planetary distances from the Sun gives spacings which are multiples or fractions of 0.376, 0.734, 5.01 and 10.06 AU. Light travels 1 AU in 8.317 minutes, so these distances can be converted to periods of an electromagnetic (or gravitational) standing wave of 3.13, 6.10, 41.7 and 83.7 minutes. In the solar wind speed as well as many cycles around 3 minutes or so there are a number at a little over 6 minutes.

Two periods of 3.17 and 6.34 minutes have also been found by the author in fluctuations in the rate of radioactive decay of Plutonium as measured by Biophysics laboratory at Russian Academy of Sciences in Pushchino. These periods are not perfectly steady but wander about by around 5%.


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Kotov’s Method of Commensurability

Valery Kotov and colleagues  have made much study of 160 minute oscillations in a wide variety of astronomical phenomena, but especially the Sun. In some cases he uses a commensurability measure to determine the best fit values for oscillations. The main purpose of this article is to explain Kotov’s method of commensurability and the way that I use it to produce graphs that are a type of spectrum derived from a set of discrete measurements, usually of time periods or distances.

For this purpose, I am going to use the distances of the 9 traditional planets from the Sun in AU (astronomical units). Unlike the Titus Bode method where the fit is to a more or less  geometric series, this looks for something more like an arithmetic series. It does this by having a test value that is varied in tiny steps and for each value a measure of commensurability is determined. The test value is divided into each of the data values and the absolute difference from the nearest integer is found. In the case where the data value is less than the test value, the division is done the other way around so that the result is greater than one, then the difference from an integer is found. The sum of these “errors” is determined. In my method I then use the reciprocal of the sum. That then makes the graph look like a typical spectrum with peaks at the possibly interesting test values.

So with our example of the 9 traditional planet mean distances from the Sun the result is a graph that looks like this:

pladistquaThe two strongest peaks are at very close to 5 and 10 AUs. This is hardly surprising because the 4 outer planets are at rather close to 10, 20, 30 and 40 aAU from the Sun. With Jupiter at close to 5 AU we can easily understand these peaks. But we do see the arithmetic series 10, 20, 30 and 40 AU. For the inner planets there are also two peaks at around 0.35 and 0.7 AU. Again they make an approximate series at 0.35 AU intervals, but the regularity is less in this case. There is also a peak at about 120 AU. If there is meaning in this process then we might expect to find some additional matter concentration floating about at this distance from the Sun.

Here are the tables of fits to the best test values.

planets-qua-tableThe interesting thing is that although the 5 and 10 AU spacings obviously fit the 5 outer planets, they also fit 3 of the 4 inner planets. Only Mars is not near an integer fraction of 5 and 10 AU. I have also shown the 515 AU distance which commutes the best of all with the planets, having a sum of differences from integer of only 0.797.

Kotov has shown with many examples that there is a pervading 160 minute oscillation throughout the solar system, galaxy and even further afield. He has found this period in binary stars, planetary distances, and galactic cores as well as various solar phenomena. I have found further examples, and agree with him that this is a universal wave phenomenon. I refer generally to 3, 6, 80 and 160 minutes waves.

The solar system also shows a shorter wave of around 0.12 AU. If these waves are real then there should be consequences beyond the data that was feed in and indeed there is.

The asteroids density with distance show peaks at spacings of 0.12 AU. There are additional objects between and beyond the outer planets and these also favour multiples of 5 AU. So we can reasonably conclude that this method has shown us something real that is happening in the solar system (and beyond). I close with the opening graph but having added exact ratios between values showing that the waves have harmonic relationships to each other.


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The Matamak Conference on Cycles in 1931

Copley Amory invited a group of about 30 scientists to be his guests at a conference at the mouth of the Matamak river in Canada where he had a summer house. The subject was various biological cycles, as it was known that different animals had huge variations in numbers over cycles of about 4 and 10 years. These various fluctuations were important to humans because they affected agriculture in many ways. Related matters of weather and climate cycles were also discussed and, surprisingly, the 11 year sunspot cycle did not dominate matters.

This report was filed by Ellsworth Huntington of Yale University working with an editorial committee and with the approval of the conference.


Some years later, Edward R Dewey, who had been studying economic cycles, was to find out about this conference and in a short space of time had contacted the organisers and the Foundation for the Study of Cycles was born.


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Ray Tomes Speaking at NPA Conference in Baltimore

The Natural Philosophy Alliance (NPA) is an organisation that is determined to stick to sound scientific principles based in empirical research rather than sticking with some theory and ignoring the facts that disagree with it. NPA is holding a conference in Baltimore from November 19 to 21, 2014. Ray Tomes will be one of the many speakers, giving two papers about how the Harmonics Theory came about and its successful predictions and explanations.

Ray’s two talks are available here as PDF documents for download.

NPA-Harmonics Theory and how it came about

NPA-Predictions of the Harmonics Theory


Posted in Astronomy-General, astronomy-Planets, astronomy-Solar, cycles-Common, Cycles-General, Economy-General, economy-Markets, economy-Stock_Markets, Geology, Harmonics, Physics-General, physics-Geophysics, physics-Wave_Structure, Researchers-General | Tagged , , , , , , , , , , , , , , | 3 Comments