Keywords

Composite, The main rule - the sufficient amount of price history, Stability (split) criterion, Predictable zones, Correlation criterion - forecast ability,  Correlation, Walk Forward Analysis (WFA) criterion, Annual, Moon position, Moon phase, Mercury phase, Venus phase, Jupiter cycles, Composite Box, Triplicity, Cardinality charts, Smoothing a projection line, Target

Making a forecast based on astronomical cycles

Timing Solution software is focused on creating a reliable forecast of the markets. We do that by modeling the market situation for existing data. Depending on the model's type and the amount of data used to create that model, we can have different projection lines.

The models applied in this forecast are based on the assumption that planetary positions or angles between the planets are in some way related to the stock market movements. I would not say that the market moves because of the Sun in Libra or because of the Mercury - Mars trine. We do not know yet how the links between the planets and the market actually work. However, we can state that some connection exists between market's ups and downs and the mutual disposition of the planets in the sky above. The statistics is behind this statement. 

There is one more interesting thing about astronomical cycles. They are different type of cycles compared to fixed cycles. Fixed cycles are even in time. They make the same phase in the same period of time. Astronomical cycles are not even in time. They have a different nature. They are cycles of some object's move around a center. In regards to that center, each astronomical object (a planet) goes again and again on the same orbit. They are not even in time, though every object makes the full circle around the center for the same amount of time. And it makes a good part: we always know where the object is. Having observations of what happens to the market in regards to that movement, we can do projections to the future.

However, it is a subject for the scientists to explore. For us, it is enough to know that there is a connection, and we can work with it. So, we can use it to make a forecast. It is very simple to do with Timing Solution software.

Before doing any forecast, you have to choose the financial instrument and make sure that you have a source of data for it. It is a first step, no matter what you want to use for your forecast.

So, download price history data for your financial instrument and click "Calculate" button. When it is done, you will see your data in the Main Window, and all modules of the software will be available for you. Click on  this button:

By default, the analysis will start with the Annual cycle. You will get something like this, it is called "Composite diagram for Annual cycle":

 

 

These curves show the averaged price movement while the Sun is passing through different Zodiac signs. There is no mystery here, it is a natural cycle that we all know too well - it is our YEAR formed by the Earth moving around the Sun. Making a composite diagrams of Annual cycle for some financial instruments, you see the works of the Annual cycle as a seasonal portrait of your financial instrument. You can use it as hints of future movements of its price. However, this is not the exact forecast, these curves show only some tendencies, the most typical for your financial instrument movements, in regards to the movement of the Sun. Going back to our example, you can see here a September drop (when the Sun passes Scorpio sign), Christmas rally (the Sun leaves Scorpio and goes through Sagittarius): 

Now look at the Main screen:

This green curve shows how the Annual cycle works in time. To display this curve together with the price chart (instead of separate panels for each one), click this button:

To change the color and thickness of this projection line, you need to highlight "Current Composite" item and click button:

 

 

Play with this Annual cycle. Try it for the same financial instrument, for different data sets (selecting data intervals by mouse). Watch the changes. Then try it for different financial instruments. Annual cycle is one of the most important ones.

Timing Solution makes possible for you to work with any astronomical cycle.

As an example, analyze the angle between the Moon and the Sun and its relation to the price moves, i.e. the Moon phase cycle:

 

This is the composite diagram for the Moon phases:

 

It shows that in average the price (DJIA is analyzed) reaches its high around the New Moon, then it goes down till the moment when the Moon - the Sun angle separation reaches 290 degrees (i.e. one week before the next New Moon), and after that it moves up till the next New Moon. This information  can serve as a base for the forecast. On the Main screen you can see how the Moon phases cycle works in time: 

 

Astronomy gives so many options for this type of analysis. In addition to different astronomical objects and their combinations, it is possible to use different Zodiacs (why not? they are nothing else but different coordinate systems where we can observe the same planetary movement). See the cycle related to changes in a heliocentric position of Mercury:

 

"Mercury-Mercury" here means that the position of Mercury is being analyzed. Thus you can see how Mercury heliocentric cycle works (this is approximately 88 days cycle):

 

 

And, as with the previous examples, the good part is: you can prolong the astro cycle's curve into the future, therefore, creating a projection line.

When you change the planets/Zodiacs, the program redraws the projection line automatically; you pick up any cycle, and the program updates the projection line.

 

The main rule - the sufficient amount of price history

While working with astro cycles, you should always keep in mind the period of analyzed astro cycles. Please pay attention to this information line in the Composite module:

In this particular case it shows the period of analyzed cycle (Mercury heliocentric 88 days cycle) and the amount of full cycles that this cycle has made within the analyzed period. Here 32 years of price history data has been downloaded. Within this time span, Mercury has made 131 full cycles around the Sun.

The rule is: to analyze any cycle you should have 3 x Period of price history data at least, better more. For example, analyzing the Annual cycle you should download 3 X 1 year=3 years of price history data at least .

The more data we have, the better we can learn the effect of this astro cycle on the market. In the example above, there is enough price history data (131 full cycles) to work with Mercury astro cycle.

Let's consider another example. We have downloaded 20 years of price history data and we would like to work with Jupiter cycle: 

The period of Jupiter cycle is almost 12 years. According to the rule, the minimum amount of price history that we need for the calculation of this cycle is 3x12 = 36 years. It means that 20 years of price history data is not enough to make any conclusion regarding this cycle (the data file that we have downloaded covers only 1.68 of Jupiter's full cycle). 

 

Composite Box

You may work with just one cycle (I always start with the Annual cycle), and you can also create the projection line that is based on several astro cycles.

Click this button "+":

 

The cycle you are working with goes to "Composite Box". Thus you can add as many cycles as you need and obtain the projection line which is based on several astronomical cycles. 

Look at this picture:

The blue line represents a composite cycle which is based on heliocentric positions of three planets: Mercury, Venus and Mars.

In Composite module you can modify color/thickness of Composite Box projection line or hide it this way:

 

 

To show all cycles in Composite Box set option "Composite Terms" ON.

 

Triplicity, Cardinality etc...

Sometimes we need to know what is going with the price when the Sun moves through Fire signs of Zodiac ( Aries, Leo, Sagittarius),  Earth signs of Zodiac (Taurus, Virgo, Capricorn), Air signs of Zodiac (Gemini, Libra, Aquarius) and Water signs of Zodiac (Cancer, Scorpio, Pisces). I.e. we need to analyze triplicity. To calculate the corresponding cycle, set harmonic parameter in this window to 3:  

 

You get the composite diagram similar to this one: 

The angle scale here covers 120-degree sector. First 30 degrees here correspond to Fire signs of Zodiac, 30-60 degrees sector - Earth signs of Zodiac, 60-90 Air signs of Zodiac and 90-120 degrees sector is for Water signs of Zodiac.

We can look at parts of this diagram in more details. The diagram below shows that the price moves down when the Sun passes the sector 15-30 degrees of Earth signs of Zodiac, i.e. Taurus, Virgo, Capricorn (here we take the beginning of the Earth sector as zero, so the area of downward price movement is 15 - 30 degrees while the whole Earth sector covers 30 - 60 degrees of the previous diagram):

 

 

The same manner you can analyze cardinality effect, setting harmonic parameter to 4:

 

You will get a diagram like the one below. I believe it explains itself:

 

Smoothing a projection line

Sometimes a composite diagram and a projection line are too choppy, like on this picture:

 

To make the projection line smoother,  increase "Smoothing orb" parameter here:

 

or set "Slow" or "Very slow" oscillator here:

 

Target

What do we forecast with the projection line in the composite module? The program automatically calculates the oscillator as we must handle the trend. This oscillator is different for different planets, and the period of this oscillator is shown here:

 

For the Sun cycles, the program uses the oscillator with 73-day period  to catch Annual oscillations, while for the Moon cycle it is usually the oscillator with 6-day period to reveal monthly cycles.

Sometimes you do not need to handle the trend. As an example, let say we have downloaded  VIX index, here it is:

 

 We do not need to create any oscillator to remove trend here, and we can use VIX index itself when calculating the composite. In order to do that, set "Algorithm" option to "Index itself":

 

To display the target, set ON "Target for Composite" option; and it will be displayed together with projection line:

 

 

Another variant: suppose we want to make a forecast for MACD (12,26,9) index. In order to do that, click "Edit" button in "Target for composite" modules, set there MACD(12,26,9) index and choose "Index Itself":

 

 

In this case we will use MACD (12,26,9) index as the Targey, and the projection line generated by the composite will forecast MACD (12,26,9).

 

How to pick up the most important astro cycles

To pick up the most important astro cycles, two tests are recommended: forecast ability and walk forward analysis.  The first test, forecast ability, gives you a general view of the analyzed cycle; walk forward analysis provides detailed analysis on how this cycle works interval-by-interval. It means that walk forward analysis is more picky, very often we simply have not enough price history to follow strict statistical criteria.

#1 forecast ability ( correlation) criterion - the projection line provided by this cycle should be good enough (i.e. the correlation between the projection line and the price itself or the price oscillator should be high enough). The presence of stable patterns in some astro cycle does not mean that the projection line based on this cycle will always be good enough; that is why we have to look for more details and analyze the projection line, watching how well this projection line fits the price. This criterion has been developed for that reason.

  #2 walk forward analysis criterion - having enough price history, we can apply walk forward analysis (WFA) for our astro cycle. The astro cycle may work for some period of time, then it stops working and later starts working again. In other words, there are periods when astro cycles work and periods when they do not work. WFA allows to reveal the periods when the astro cycle works/does not work. The periods when the astro cycle works should be longer than the periods when it does not work.

 

Let us look closer at these techniques.

Criterion #1: Forecast ability (correlation) criterion 

This test purpose is to find out that the projection line based on the analyzed cycle is good enough, i.e. the correlation between the projection line and the price/price oscillator is high enough.

To calculate the forecast ability of any astro cycle, click this button:

Below is an example of the forecast ability report for Annual cycle calculated for S&P 500 index:

The first record means that since December 2012 till now (December 2013) the Annual cycle has worked quite well, the correlation is positive, and its value is 0.203.

The second record means that for the last three years the Annual cycle also worked very well.

The third record shows a negative correlation since 2008, for the last five years, i.e. there were some periods when the Annual cycle did not work.

These first three records shows us the recent activity of Annual cycle i.e. its activity for the last year, last three years and last five years.

The last record  shows the general activity of Annual cycle i.e. how the Annual cycle has worked within the last 10 years. Sometimes this cycle worked, sometimes it did not (a negative correlation since 2008); positive average correlation means that this cycle works in general.

So the forecast ability criterion states that majority of these values should be positive, i.e. shown in red.

Another example is the forecast ability of the Moon draconic cycle:

This cycle works well for the last 5 cycles (more than four months), i.e. the recent activity of this cycle is good - it provides a good projection line. However, the general activity based on the latest 100 cycles is not so good (a negative correlation). So this cycle can stop working any moment any time, and the fact that it has worked very well for the last four months does not matter. If we plan to use that cycle, we need to observe it for more time or apply some other technique to confirm its usefulness. 

 

Criterion #2: Walk Forward Analysis (WFA)

Clicking on WFA button you get the detailed statistical information regarding the analyzed astro cycle: 

 

When you click this button, the program asks you about sample's size to be used for WFA:

Set it to 50.  After the calculation the program will display the table with detailed statistical information regarding your cycle, like this one:

 

The red bars here correspond to the periods when the projection line based on this cycle provides a good projection line while blue - means that the projection line here is not good, may be inverted. The digits inside these bars show the correlation between the projection line and the price. See this record:

 

It means that in 2014 the Annual cycle has forecasted price movements with accuracy of 0.237 in terms of correlation. The correlation 0.2 and higher means a good coincidence between the projection line and the price (more about correlation coefficient you can read here: http://www.timingsolution.com/TS/Mini/38/index.htm )

We recommend four rules that should be fulfilled for a good cycle,  two of them are mandatory and two are optional. Thus you can see easily what rules are satisfied and what are not.

In the picture below you can find the explanation regarding these statistical parameters: 

 

 

Tuning astro cycles

Sometimes it is possible to improve the forecast ability of astro cycles varying some options. Her are the parameters we recommend to vary:

Stock Market memory - try to vary this parameter and conduct walk forward analysis for this cycle with the stock memory (sm)=10:

 

 

It means that we use last 10 years of price history only to calculate this cycle, and the price history over those 10 years is not considered. This way we assume that Annual (or any other cycle) works the same way/keeps the same pattern within 10 full cycles and after that this pattern is changing. You can read more about stock memory (sm) here: http://www.timingsolution.com/TS/Mini/47/index.htm

We recommend to set stock memory to 5, 10, 20 and 50 ( for fast cycles, like Moon based cycles) and conduct walk forward analysis for cycles with different SM.

Pay attention, Rule #4 in WFA results window is disabled for these cycles where the stock memory is applied; this is how this reports looks in this case:

Smoothing orb - also we recommend to vary smoothing orb, it is here:

 

 

It allows to generate more detailed (small smoothing orb, like 25%) and more smooth (like 200% orb) projection line.

 

The most important astro cycles

 

Based on our own research and experience of Timing Solution software users, we can say that the cycles shown below are the most important ones, se we recommend to start your analysis with these cycles. First of all, we recommend to work with the Annual cycle, then consider three Moon based cycles. These cycles involve the Sun and the Moon, the brightest and biggest celestial bodies from Earthly point of view, and scientific research shows that these bodies affect our Earth life.  After that we recommend to research the cycles based on planetary phases and the cycles based on the heliocentric movement of inferior planets (Mercury and Venus). Then you can research other astro cycles. Below are notes on the most important cycles, together with the cycle's terms used: 

Seasonal, Quarterly, Monthly cycles

Sun cycle seasonal/Annual cycle, period 365.25 days 

The first one to consider and the most important object in the sky is the Sun. The Earth makes the full cycle around the Sun within 365.25 days; this is the seasonal or Annual cycle, a very important cycle that we always recommend to consider first.

Quarterly cycle, period 3 months

Somehow this cycle is strong since 2010. Pay attention, to calculate quarterly we apply 4H harmonic for Solar cycle.

Solar month cycle, period one month

We apply here 12H harmonic for Solar cycle.

 

Moon based cycles  

There are three variants of the Moon cycle that worth of your attention:

Moon synodic cycle (Moon phases),  period 29.53 days

This is another very important cycle. Everybody knows this cycle as the cycle between two New Moons (or two Full Moons). It shows how the price is changed between two New Moons. Technically this cycle is calculated as an angle separation between ecliptic longitudes of the Moon and the Sun. When these objects have the same longitude (it is called conjunction), the New Moon takes place. When this angle separation reaches 180 degrees, the Full Moon takes place.

Moon Tropical  cycle, period 27.32 days

This is the cycle that reflects the Moon movement through Ecliptic.

Moon Draconic cycle,  period 27.21 days

This cycle reflects the Moon movement regarding the Moon North Node (which  is the intersection of Ecliptic and the Moon's orbit). This cycle correlates with eclipses. You can find out more regarding this subject on the website http://en.wikipedia.org/wiki/Month:

Because the moon's orbit is inclined with respect to the ecliptic, the sun, moon, and earth are in line only when the moon is at one of the nodes. Whenever this happens a solar or lunar eclipse is possible. The name "draconic" refers to a mythical dragon, said to live in the nodes and eat the sun or moon during an eclipse.[1]

 

 Planetary phases.  

Inner planets (Mercury and Venus) have phases similar to the Moon phases. These cycles are called also synodic cycles; so, when you read "Mercury phases cycle", this is the same thing as Mercury synodic cycle.

As an example, let us consider Venus synodic cycle. Technically speaking, this is a cycle between two inferior conjunctions (heliocentric system). Look at this picture from Cornell University's website (   http://www.astro.cornell.edu/academics/courses/astro201/planet_view.htm ):

 

 

Inferior conjunction here is like the New Moon - New Venus. Superior conjunction is like the Full Moon - Full Venus (maximum illuminated by the Sun).

I believe that for the stock market forecasting Venus synodic cycle is quite important, especially for currencies:

Venus phase cycle (period is 584 days):

Remember that Venus phases are angles between Venus and the Earth in heliocentric system, and in the program when we work with the heliocentric system we use the Sun glyph to designate the Earth.

Mercury phases (period is 116 days):

 

Heliocentric system

In our research, we often use the cycles in Heliocentric system.

Mercury heliocentric cycle,  period 87.97 days

This cycle shows the movement of Mercury around the Sun. Mercury is the closest to the Sun planet, so the period of this cycle is the smallest - 88 days only.

 

Venus cycle,  period 224.70 days

Jupiter cycle (12 years):

This cycle is recommended if you have enough price history (36 years and more). It is suitable for long term forecast. This cycle is very close to Juglar economical cycle.

 

There is a way to calculate these cycles (the most important ones) quickly. Please click on this button and choose the cycle you need:

 

 

Archive

Some time ago we applied one more criterion. Now we do not use it due to new techniques developed. Its description is below, just in case you may want to learn about it.

#1 stability (split) criterion - the cycle should be stable, i.e.  it should work the same way now as it used to worked one year ago or ten years ago. It  means that there are some relatively stable patterns in the price movement. Examples of a stable cycle are: the price tends to go up when the Sun goes through the Zodiac sign of Sagittarius (this pattern is known as Christmas rally) or the price tends to be higher around the New Moon, etc.  The presence of these stable patterns gives us some hope that this cycle may work in the same manner for some time in the future. 

 

Criterion #1: Stability (split) criterion  Look at the composite diagram below. There is the major bold red line there that shows the summary effect and there are three different thin lines as well - red, purple and green. Here they are:

 

 

These thin lines represent the composite diagram calculated for our financial instrument though for different time intervals. In our example, red is a composite diagram calculated for the price history data of our financial instrument (DJIA) from 1991 until 2012; purple - 1969-1991 and blue - 1948-1969 years.

We need to watch the periods where ALL THREE THIN CURVES SHOW THE SAME PRICE MOVEMENT. It means that this cycle has worked the same way in different historical periods, so we can expect that it will work in the same manner in the future.

These periods are marked by red stripes at the bottom of the composite diagram; we call them PREDICTABLE ZONES. Here they are:

 

Any other area outside predictable zones cannot be used for the forecast; so, if you see that composite curves provide different (not similar) signals - these are UNCERTAIN ZONES, do not use them for the forecast.

Look at the picture below. We have marked there predictable zones for Annual cycle, and the arrows point at the most typical price movements within these predictable zones:

The stability (split) criterion states: predictable zones should occupy a significant part of the composite diagram (at least 30%). In our example red stripes occupy almost 8 signs of Zodiac.

 

Just for your information, a composite below is an example of some not working cycle:

 

A red stripe occupies there less than two signs of Zodiac. This is a random fact, we cannot trust this cycle.