I like the idea of using linear regressions. Regarding general market trends perhaps a little heteroskedasticity–as is evident in your scatter plot–could be forgiven. You work with what you got and find the best fit possible. Do you feel comfortable with your statistical data regarding how good the fit is given the obvious heteroskedasticity?
How did you deal with the non-stationary problem with your time-series? That can make things that have no correlation whatsoever look highly correlated as you know.
Just want to know how you tested for non-stationarity and how you dealt with it.
Konstantin, I edited the post, I was in a hurry as usual when wrote it for the first time. So it sounds more clear now. You will understand the fitting problem clearly, if your question about it (actually I didn’t understand your question:)
About heteroskedasticity in MT. To check this stuff you can use Spearman test for example. But it won’t help you. The answer and the problem at the same time lay in optimization. To get lower variance (decrease stochastic deviation) you can use factor screening procedure over time and maybe ranks. You ll get not linear dependency changing over time with very high R2. But more likely it wont work in future (fitting problem again).
So the main check is macro and micro economy logic and common sense. And it should go first before any optimization (at least it sets up the limits of you optimization)
MT as far as the non-stationarity concern because to the time series. My understanding is that the problems with non-stationarity occur with time-series.
Your linear regression seemed to have some heteroskedasticity: the realized 12M return regression. You can comment for sure as to the type of data and your statistical conclusions from this data.
I didn’t chase the goal of maximizing R2 in this regression, it was shown just as example of more or less reliable MT systems in comparison to existing P123 systems.
You really just can’t use non-stationary data in a time series without adjusting. The examples in the text books show high Rs for data that in truth has no correlation whatsoever. A fairly recent Nobel Prize was awarded for techniques to deal with problem.
It has nothing to do with Maximizing R2.
I personally would not try any linear regressions for market timing or times series. I certainly would put no money into it or make any public claims. But that is just me at my level.
I like linear regressions that are similar to our rank performance test. I think this would be cross-sectional data. But I am becoming more aware that any statistical claims are questionable–including R values. This is due to the fact that the data is probably not a normal curve or i.i.d. (thanks Peter and SUpirate1081).
Market as whole is a more or less stationary process in comparison to individual stocks performance, and that’s the main difference.
As I remember Markov process deals with non-stationary time-series.
As I remember stationary means stable first and second momentums for distribution, mean and variance. It was long time ago when I studied in university
I actually like what you are doing. Personally, I would refresh my memory before going much further with any time series data.
I will be doing some of this myself but not for market timing. But again that is just me at my level. The overall market is almost certainly non-stationary even if it is not a random walk: any trending (at a minimum) must be corrected for: personally I cannot do that.
Yep, I forgot many things from that stuff. Maybe later I can say anything for sure regarding stochastic processes
Actually there is no big need to go deep in math. Models that really work are quite simple.
