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Probability & Statistics/reoccuring weekly patterns

Question
I don't know if this is a probability question, but I expect you will. Below is a link that opens a pdf copy of an introduction to a paper I wrote some years back on weekly weather patterns around Washington DC. It was very hard to produce graphs for all those years looking for consecutive weeks following similar temperature patterns.

I'm guessing that in business, finding these same kinds of weekly patterns could be valuable in some industries, in particular retail sales where knowing weekly spending patterns of shoppers might help greatly in many decision making areas. If so, there might be software or an Excel function that makes this easier than producing a graph for each week for every kind of data to be analyzed. My question is do you have any advice on how to search for such a solution to this problem, or do you have an actual solution?

https://dl.dropboxusercontent.com/u/47206368/RushHourPollutioniscausingWashingtonDC.pdf

Hello, thanks for this interesting question. I think it would be difficult to address the entirety of this very open-ended inquiry, but I think it's important get you pointed in the right direction.

I'll get you started with some pointers on the web, places where you can look for more information, and you should feel free to follow up with any additional questions once you've got some more detail to work with.

First of all, there is a name for what I believe you are describing: a process that depends on previous states to predict or determine future states is called a Markov Chain or Markov Process. You can read about that here:

Wikipedia: Markov chain

The use of Markov Chains to predict the weather is very common -- so much that it is listed as an example of one application of this mathematical idea on Wikipedia in a separate article:

Wikipedia: Examples of Markov chains

Now that you know the name of the mathematical construction, you might be able to read more and formulate additional questions -- or maybe getting you pointed in the right direction will be enough of a start for you to pick it up on your own from here. Let me know if you have follow-up questions.

Probability & Statistics

Volunteer

Clyde Oliver

Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

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I am a PhD educated mathematician working in research at a major university.

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AMS

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Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

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BA mathematics & physics, PhD mathematics from a top 20 US school.

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Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

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In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.