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Hi David, do yo mind an analysis for Royal Bank ( RY on NYSE; a Canadian bank), perhaps 165 days as I am wondering when a good longer term entry long may present itself for an investment, as opposed to just a shorter term pop. Thanks.

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What I have done in this case is to add a note in the calendar to look at RY around end of the year. This is the time that the component around 250 days is due to trough. On the shorter side the component around 80 days is powerful since mid 2021 and is analogous the below component in the financial sector, via XLF. Hope that helps for now.

https://www.sigma-l.net/p/xlf-price-cycles-9th-october-2023

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Thank you for your analysis. Most helpful.

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Sure, will run it under the microscope across a sample of around 1500 days. That should encompass any 'medium' to 'long' term waves. Watch this space - no guarantee it will make it onto the site though, depends on the signals present.

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Thanks for mentioning the general process (for any asset). I was under the incorrect impression that one could find meaningful waves for the medium and long term, for all assets, but based on your reply I see that is not always the case.

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Well the question of significance is crucial and relates to the signal to noise ratio. If we are to identify periodic functions that EXIST and are correlated to actual price movements we need to be discerning. That is fundamental to using a time frequency analysis as it is one of the most sensitive methods of decomposition which not only examines correlation power but how much that power AND frequency changes over time. You can imagine if there is a powerful signal that changes frequency in a random fashion it is pretty near impossible to predict. This is what we mean when we mention stationarity - the frequency and power is relatively stable over time.

That said, there are many *similar* waves present in markets, most notably as you see from the site around 80 days. Infact this is also present in RY as you will see shortly... However, as you will also see there is very little power around 160 days and significant power around 250 days - this means that there is a higher correlation between a periodic function with a wavelength around 250 days than 160 days, shown up in the time frequency plot as brighter yellow etc..

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