Is bitcoin a bubble? I don’t know. What defines a bubble? The price should drastically overestimate the underlying fundamentals. I simply don’t know much about blockchain to have an opinion there. A related characteristic is a run-away price. Going up fast just because it is going up fast.
Density estimation using regression? Yes we can!
I like regression. It is one of those simple yet powerful statistical methods. You always know exactly what you are doing. This post is about density estimation, and how to get an estimate of the density using (Poisson) regression.
A few words about outliers
In statistics, outliers are as thorny topic as it gets. Is it legitimate to treat the observations seen during global financial crisis as outliers? or are those simply a feature of the system, and as such are integral part of a very fat tail distribution?
We often see statements like “linear regression makes the assumption that the data is normally distributed”, “Data has no or little multicollinearity”, or other such blunders (you know who you are..).
Let’s set the whole thing straight.
Linear regression assumes nothing about your data
It has to be said. Linear regression does not even assume linearity for that matter, I argue. It is simply an estimator, a function. We don’t need to ask anything from a function.
Consider that linear regression has an additional somewhat esoteric, geometric interpretation. When we perform a linear regression you simply find the best possible, closest possible, linear projection we can. A linear combination in your X space that is as close as possible in a Euclidean sense (squared distance) to some other vector y.
That is IT! a simple geometric relation. No assumptions needed whatsoever.
You don’t ask anything from the average when you use it as an estimate for the mean do you? So why do that when you use regression? We only need to ask more if we do something more.
In the post pairs trading issues one of the problems raised was the unstable estimates of the stock’s beta with respect to the market. Here is a suggestion for a possible solution, which is not really a solution but more stuff to do to make you feel less stupid when trading based on your fragile estimates.