Can linear regression analysis really predict the future?

Labels are entirely too restrictive.

 

Good start. Now, go ahead and calculate how many steps of 1 point does the S&P make to move 100 points? It’s easy enough to calculate using historical charts. Is that number greater, equal to or significantly lower than the mean deviation calculated using the formula above?

 

I'll think this though, but I only have access to 1min data and at first glance it would be difficult to know how many 1 point steps are contained in a single OHLC candle.

 

OK, you can count 5 point moves, it really does not matter.

 

OK, I have to work the 'day job' now (NZ time), but I'll work on this tonight.

 

Without actually doing the calculation, just thinking about what it would mean logically if the measured expectation was smaller for instance, I guess this would constitute a violation of the 'p+q=1 and n1+n2=N' preconditions for deriving the equation. Quite how this could be turned into an exploitable condition, I'm not quite sure yet.

 

Maestro - very interesting thread!

So the next bar close has a normal distribution around the forecasted close using a cubic spline method?

If I am understanding correctly, this means that the fat tails seen in a regular price distribution are generally in the direction of the short term trend. (To eliminate a large upspike from the data, the forecasted center of mass would have be up large also, therefore the previous few datapoints would need to be accelerating higher).

Then the idea is to take trades at the 2 sigma levels: trend above a certain spline slope and reversion below.

If I am close, there may be a related body of work interesting (or known) to some here. The author uses a variety of polynomial fits to develop simple rules then tests out of sample with great results.


Tom

 

Also, if anyone wants to code a spline in their normal backtesting software without going to MATLAB or R, this is how to do it:

Code:

|  T  St  St2 St3 | |a0|     |Sp(t)     |
| St  St2 St3 St4 | |b0| =   |S(p(t)*t) |
| St2 St3 St4 St5 | |c0|     |S(p(t)*t2)|
| St3 St4 St5 St6 | |d0|     |S(p(t)*t3)|

(read S as summation or sigma symbol)

where
p(T) is today’s price, p(T-1) is yesterdays price and p(1) is the
price T days ago.
Sp(t) is the summation of prices from t=1 to T days
Sp(t)*t is the summation of prices times t from t=1 to T
St is the summation of the integer t from t=1 to T days
St2 is the summation of the integer squared from t=1 to T days
etc

Center of mass prediction at next time step:

Pf = a0 + b0*(T+1) + c0*(T+1)2 + d0*(T+1)3


Tom

 

This is one of the best threads I have read in a long time.

I have been looking at technical analysis for years with random success. So I figured the best way to prove to myself if the system works is to write my own market simulation software, Click here to go to Turtrades It allows me to practice my trading using real historical market data.
So far I have learned that TA does not work or I have a lot more to learn.

 

Spot ON! Good man. Congratulations! You have passed level 1! Now, the challenge is to make the decision making algorithm that has consistent positive expectations. Off to the races! May the spline be with you!