Financial Signal Processing and Multiresolution Analysis Or:

Woof.  A Primer.

“You may learn something, and whether what you see be fair or evil, that may be profitable, and yet it may not. Seeing is both good and perilous.

I was very excited to be chosen for my top choice capstone project this quarter.  The project focuses on short term algorithmic trading strategies.  Definitely an interest for me.  I run a small personal portfolio and have been fairly active in trading options for the last few years.  I am all self taught when it comes to the financial world, but I have done modestly well!  So I am very excited to get to grow my knowledge and skills related to my personal interests!

The first meeting with the sponsor was definitely eye-opening.  There were a lot of terms used in the context of trading that I was not familiar with.  So I made notes with the determination of looking up as much as I could up.  Two of the big ones were Signal Processing and Multiresolution Analysis.


So… I present to you a primer on that subject matter.  A high level overview that even an ex-liberal-arts major like me can understand. 

I. Sending You Those Signals

Our first task before we get into how all this applies to financial markets is to garner a basic understanding of what Signal Processing itself is.  For that we need to hop fields from Finance and Computer Science to Electrical Engineering.  

Electrical Engineers spend a lot of time working with, you guessed it, electricity.  More than just the juice that powers our cell phones, it is a very complex field.  There are lots of varying measurements to keep track of.  Some of note include current, voltage, and my blood pressure.  And much like my blood pressure, it is important to be able to work with these measurements.  You need to be able to process, understand, and utilize the information they are giving you.

But how would you process something that is constantly fluctuating?  Enter our new friend, signals.  A signal in its simplest form is a very easy concept to understand.  It is quantifiable numeric data, like a measurement of voltage or current, that changes throughout another completely independent variable, think something like time.

So a very basic signal would be the data points produced by measuring the electrical current of your cell phone every second.  Boom, you have a signal!  So what do you do with the signal?  Well that is WAY out of the scope of this blog post.  But know that there is an entire subsection to Electrical Engineering dedicated to figuring and processing these signals to get the most useful information possible out of them.

II. A Sea of Signals

The really exciting thing that came out of all this Signal Processing they were doing in Electrical Engineering is how applicable it is to so many other fields!  Everything from image processing to audio processing uses this technique.  The camera on your cell phone uses Signal Processing to interpret moving pictures even!

But we aren’t interested in those fields for this post.  No, we are interested in the world of Finance.  This seems like an odd place to find Signal Processing as we have defined it so far, until you abstract what a signal is.  A measurement over an independent variable.  Say something like, the closing price of a stock recorded every day.  You have a measurement, the closing price of the stock, defined over an independent variable, which is time.  

This was the birth of the field of Financial Signal Processing.  As a field it is attempting to leverage all the work done with Signal Processing so far, but with respect to the financial markets.  Super cool right, albeit a little nerdy.  But hey, nerds rule the world.  

Financial Signal Processing has led to all new approaches in market strategies.  It has led to the creation of many new indicators in the market, and new ways to use them.  Most of these strategies are guarded jealously by their Hedge Fund and Market Maker owners.  But as amateur investors and traders, we can see how a basic understanding of the Signal Processing field can help us translate strategies to our own portfolio management.

III. Multiresol-whoseit-what-now

Multiresolution Analysis is the last new term and idea we are going to look at in this post.  The best way to get a grasp on this (at least personally) intimidating word is to break it down into its parts.  Multi is pretty clear as a prefix, it means more than one.  Analysis is clearly referring to the act of analyzing a specific set of data.  Great!  We have the majority of this word figured out already.

But what is a resolution?  The word is (hopefully) not referring to my New Year’s promises I never keep.  I would hate anyone to analyze that!  No, a resolution in this context is more appropriately thought of as the change in the independent variable between a measurement of a signal.


So Multiresolution Analysis is just analyzing a signal over multiple resolutions.  I think maybe an example would be in order…

Let’s say I am a person who really really really likes dogs.  In fact, I usually pet multiple dogs a day.  For science purposes I decide to start tracking my average dogs petted for certain periods of time.  I keep a running average of the dogs I have petted over the last 3 days, the last 10 days, and the last 30 days.  That is to ensure that I am not slacking on how many dogs I am petting.

My grumpy boy Rocko

Now I recalculate these running averages at the end of every day.  My signals will be the measurement of those averages. At the end of each day.  So for the last 3 days, I have averaged petting 4 dogs a day, the last 10 days I have averaged petting 2 dogs a day, and for the last 30 days I have averaged petting 2.7 dogs a day (gross, .7 of a dog…).

So the running averages of petted dogs are our measurement part of the signal.  But everytime we measure these signals, we are measuring them against our independent variable (time), for different lengths (2, 10, 30 days), or… resolutions!  BOOM.  Multiresolution Analysis of petted dogs in my life!

Me and my 16 year old Kimmy (she gets carried everywhere, she deserves it)

Back on topic, we can see how if we were to utilize this technique with stock prices it could provide some valuable insight into trends and data to analyze!

IV. Conclusion and Resources

Let me start by saying that I am no Electrical Engineer, and until a week or so ago I thought Signal Processing was something my Engineer brother held over my head to make himself feel better for losing at Smash.  But it is really interesting and I know I am looking forward to learning more about it.

I hope this very very very high level overview helped you as much as it helped me writing it!  I will link some of the resources I used for research at the bottom of the post so you can read from some real professionals if you are interested in learning more!



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