Stochastic processes - Wolfram Language Tutorial

Today, what I'm going to talk about is stochastic processes. And if you go into our data analysis here, you will see that we cover a lot of this. Okay. So we have all the usual type of statistical analyses. So you can do location statistics, dispersion statistics, you know, look for variance, shape, the overall structure of the distribution. We've also got spatial point statistics. This won't be relevant to us now, but it is important in some aspects of finance, particularly, for instance, if you were doing risk analysis and wanted to find out which sections of the country or a state or whatever were more inclined to be risk-sensitive. The hint, of course, is that it's going to be determined very much by the zone you live in and your zip code. But we have that. And in addition, what we're going to be looking at though is some data smoothing. We'll be going to be looking at things like moving average and applying that to our data in order to get rid of small statistical variations and try to build models. And then we'll be doing hypothesis tests on the data to check what type of distribution is appropriate for them. And then later on, we're going to be doing some data fitting as well. But in addition to all of this, we also want to look at distributions. Okay. So if we've got here. Here we go. Probability and statistics. Okay. So we have, by far and away, the largest number of distributions of any program, even more about three to four times as many as in the program, and all of them have this form, they're like normal distribution, t-distribution, and so on. Now, one of the other things we're going to be looking at in this is random processes, that is, stochastic processes. And the reason for this is that you may want to look at a number of stocks together and compare their overall behavior. So you'll want to do model fitting for that. And that means that you're going to be looking at some type of process, since financial data is invariably time-stamped, we'll be looking at time series processes. As you can see from previously, there's a lot of stochastic processes here. We've got normal parametric ones that is to say, hey, there are well-defined mathematical formulas for them, ones that can be derived from them, various things like the white noise process, which is built into the error for many of the models, and other things such as Markov processes where you've got previous dependents. The time series processes we'll be looking at will be primarily things like autoregressive integrated moving average and ARCH type, ARCH and GARCH-type processes because we're interested in variance. So I'll discuss each of these as we meet them. First of all, I think this is an example I've given beforehand, but just to sort of emphasize how, you know, what the things we're going to be doing and the sort of general structure. So first, we're going to call in the data. Then, we'll have to sort of smooth the data to some effect in order to apply models to it. So we're going to be looking at the FinancialData function.