# Timing Solution Glossary

## Permanent versus Dominant cycles

Permanent cycles are the cycles that work in the same manner all the time. So, if we want to deal with the permanent cycle, we will look for a permanent pattern inside the data. In Timing Solution, we can do that in Composite module. To find such pattern, we should use ALL AVAILABLE price history. A good example of permanent cycle is Annual cycle. It works in the same manner all the time: now, in 1950, 1975, 1900, etc. - in any year of the available data.

Here is how the Annual cycle can be done in Composite module. To calculate the Annual cycle shown below, ALL price history is used, this is permanent cycles because we are looking for a permanent Annual pattern:

Permanent cycles are helpful in understanding long-term tendencies on the market. However, we should be careful relying only on these cycles in our trading. We all know by experience that patterns that worked so well for many years may be not that good in a certain year.

That is why the market research moved to Dominant cycles. Dominant cycles also work in the same manner, but for a limited period of time.

Let us build a dominant Annual cycle. We start with the assumption that there is an Annual cycle (we have seen it in Composite module example above). Suppose we want to know how actually this Annual cycle has worked for THE LAST 7 years, not for all available price history. It is quite possible that some permanent pattern is not so strong now. Instead of general outlook of the cycle, we are looking at the latest tendencies in Annual cycle. Do it this way:

The chart shows how the Annual cycle works for the last 7 years. Clearly, it works a bit differently than in the previous chart: for example, Christmas rally is not so certain now as it used to be.

Similarly we can calculate any dominant astro cycle. Please look at this example of Moon synodic cycle based on the last 12 months (to be precise, 12 full Moon synodic cycles i.e. 12*29.5=354 last days):

Please pay attention to this parameter, 7 for Annual cycle and 12 for Moon synodic cycle. It is called Stock Memory (SM), and it will be explained later.

There is no fixed, working forever cycles in finance. The only exceptions are cycles used by economists - Kitchen 5 years and Juglar 10-11years cycles. All modules that reveal fixed math cycles (like Spectrum, Q-Spectrum) are oriented to catch dominant cycles. So in all these modules SM parameter is present:

## Stock Memory (SM)

This is a very important parameter. As I have already mentioned, you can find it in Q-Spectrum, Spectrum and other modules that work with cycles. Here are the examples -  in Spectrum, Q-Spectrum, Composite and Trading Spectrum modules:

Stock memory (SM) parameter shows how much price history is needed to reveal the presence of some cycle. It indicates a number of periods when cycle manifests itself. As an example, if we analyze 100-days cycle and use SM=12, it means that we use to calculate the importance of this cycle not all available price history, but only its portion: 12x100=1200 days of price history.

We believe that the optimal value is between 5 and 20. Let us consider two extreme cases of too big and too small values of SM:

Case #1. SM is too high: we set SM to 100 and work with the Spectrum module calculating there a periodogram:

In the statistics it is a sutuation called "white noise": here all (or almost all) cycles have equal (almost equal) intensity. It is practically impossible to figure out what cycle is less or more important here. We can say with equal assurance that "Anything is working" and "Nothing is working". (To be precise, this is not exactly a white noise, but a gray noise (noise with some structure). Though it does not make a big difference for us.)

Case #2. SM is too small, we set SM=3 and have calculated a periodogram with the same Spectrum module. And we have got another face of Chaos:

Now we can see two  cycles that could be taken as the most important ones. But - their peaks are too wide here, it may be some cycle with the period between 215 and 250 days. To get a more certain picture we have to apply the bigger value of SM, i.e. use more price history.

Let us set SM=5. The peaks become more narrow, i.e. more certain peaks:

Setting SM=7, we can see two peaks that correspond to 202 and 251 days cycles:

Now we got something to work with.

## Forecast Stock Memory (FSM)

FSM is related to forecast ability of some cycle. It shows how much price history we need to use to get the best forecast based on this cycle. This is not the same as Stock Memory (SM).

Consider the difference between SM and FSM this way: to reveal a cycle, we need to use the last 12 cycles (SM=12), while to get the best forecast based on this cycle we need only the last 5 cycles (FSM=5). The stock memory parameter (SM) is not the same due to the difference of the goals: to find a cycle, the amount of data is important while to get a forecast based on that cycle only the latest price history is relevant.

If you work with Spectrum, you can modify FSM here:

In this example, Spectrum module has revealed a presence of 78 calendar days cycle for S&P500 index (analyzing 12 completed cycles). Then we will try to build a projection line based on that 78-days cycle.

We  begin with setting FSM=1, i.e. we try to interpolate the last 78 days of price history with 78-days cycle. As you see, the coincidence is very good:

Now we try FSM=2; we try to interpolate the last 2x78=156 days of price history. The coincidence is not that good, though our projection line describes more price history:

And we continue to play with FSM. Please note that when we set FSM=15 (i.e. building a projection line that interpolates last 15 cycles), the projection line describes just major tendencies:

So, changing FSM parameter, we are looking for the balance between over-fitting problem (FSM=1) and too general projection line (FSM=15).

If you work with Q-Spectrum, set FSM here: