My Own favourite:
How Important is Variable Selection?
Overfitting is strongly related to variable selection. It is a common problem and a tough one, best explained by way of example.
When you are busy with a lengthy project, like writing a paper, you create many objects along the way. Every time you log into the project, you need to remember what is what. In the past, each new working session I used to rerun the script anew and follow what each line is doing until I get back the objects I need and continue working. Apart from helping you remember what you are doing, it is very useful for reproducibility, at least given your data, in the sense that you are sure nothing is overrun using the console and it is all there. Those days are over.
Presenting properly is important. Here is how I think it should look like,
Frequently, we see the term ‘control variables’. The researcher introduces dozens of explanatory variables she has no interest in. This is done in order to avoid the so-called ‘Omitted Variable Bias’.
What is Omitted Variable Bias?
In general, OLS estimator has great properties, not the least important is the fact that for a finite number of observations you can faithfully retrieve the marginal effect of X on Y, that is . This is very much not the case when you have a variable that should be included in the model but is left out. As in my previous posts about Multicollinearity and heteroskedasticity, I only try to provide the intuition since you are probably familiar with the result itself.
Few weeks back I simulated a model and made the point that in practice, the difference between Bayesian and Frequentist is not large. Here I apply the code to some real data; a model for Industrial Production (IP).
THIS IS NOT INVESTMENT ADVICE. ACTING BASED ON THIS POST MAY, AND IN ALL PROBABILITY WILL, CAUSE MONETARY LOSS.
Quantile regression is now established as an important econometric tool. Unlike mean regression (OLS), the target is not the mean given x but some quantile given x. You can use it to find stocks that present good upside potential. You may think it has to do with the beta of a stock, but the beta is OLS-related, and is symmetric. High-beta stock rewards with an upside swing if the market spikes but symmetrically, you can suffer a large draw-down when the market drops. This is not an upside potential.
Rivers of ink have been spilled over the ‘Bayesian vs. Frequentist’ dispute. Most of us were trained as Frequentists. Probably because the computational power needed for Bayesian analysis was not around when the syllabus of your statistical/econometric courses was formed. In this age of tablets and fast internet connection, your training does not matter much, you can easily transform between the two approaches, engaging the right webpages/communities. I will not talk about the ideological differences between the two, or which approach is more appealing and why. Larry Wasserman already gave an excellent review.
Roughly speaking, Multicollinearity occurs when two or more regressors are highly correlated. As with heteroskedasticity, students often know what does it mean, how to detect it and are taught how to cope with it, but not why is it so. From Wikipedia: “In this situation (Multicollinearity) the coefficient estimates may change erratically in response to small changes in the model or the data.” The Wikipedia entry continues to discuss detection, implications and remedies. Here I try to provide the intuition.
If you have 10 possible independent regressors, and none of which matter, you have a good chance to find at least one is important.
Slides 18 and 30 are especially nice:
Numbers are useful (I think we can all agree on that..). If you own a smart phone, you can install this runmeter app. When you run, you can take the smartphone with you and activate this app to collect interesting numbers like distance, pace, fastest pace, heart rate*, calories etc. Now we can load the statistics collected over the past months into R and have a quantified look at the progress.
A vector autoregression (VAR) process can be represented in a couple of ways. The usual form is as follows: