Trading Catechism

[nitro]

It is important to note that while the power spectrum and correlation/cointegration is a useful tool to use, these methods are not an invariant property of a nonlinear time series, meaning that significant changes may appear in the power spectrum etc despite the lack of changes in the dynamics of the system. Therefore, changes in power spectrum are insufficient evidence to infer changes in dynamics.

In a later post, I will detail how modern researchers try to deal with non-linearity.

 

[nitro]

As a follow up on the above post, we often have models with several inputs, but because of the non-linearity of our model, we often have a hard time understanding which inputs have the greatest impact on predictability. To further the complication, lead-lag effects make things that much more obscure.

Enter Sensitivity Analysis

 

[Gambit]

Thanks for the follow up post.

 

[nitro]

The Wiener process is scale-invariant.

A demonstration of Brownian scaling, showing

for decreasing c. Note that the average features of the function do not change while zooming in, and note that it zooms in quadratically faster horizontally than vertically.

 

[nitro]

Being able to compute a PDF is important:

 

[Gambit]

Being able to compute a PDF is important:

This might be a noob question but aren't you assuming that the time series is stationary and normally distributed if you are computing a PDF? I guess a follow up question would be do you think spreads (butterflies, condors, butterfly vs butterfly) are stationary and normally distributed?

 

[debitspread]

> normally distributed if you are computing a PDF

Normal is only one of many PDFs. But more generally, making money in options has next to nothing to do with learning textbook probability theory.

 

[nitro]

This might be a noob question but aren't you assuming that the time series is stationary and normally distributed if you are computing a PDF? I guess a follow up question would be do you think spreads (butterflies, condors, butterfly vs butterfly) are stationary and normally distributed?

Here is an interesting answer to your question. She proves that her equation is a PDF. Plot it, and tell me it it looks "normally distributed". This will do two things, it will get you engaged in a software that allows you to do the exercise (R, Matlab, Mathematica, Python, whatever), and two it will get you thinking about these things in general.

As far as markets being non-stationary, true. But are they non-stationary at all time frames? Even if they are, what strategy could you use to adapt the changing PDFs?

A more interesting question is imo, many of these PDFs assume finite mean and co-variances (first and higher moments in general.) How do we deal with that?

 

[Gambit]

Here is an interesting answer to your question. She proves that her equation is a PDF. Plot it, and tell me it it looks "normally distributed". This will do two things, it will get you engaged in a software that allows you to do the exercise (R, Matlab, Mathematica, Python, whatever), and two it will get you thinking about these things in general.

As far as markets being non-stationary, true. But are they non-stationary at all time frames? Even if they are, what strategy could you use to adapt the the changing PDFs?

A more interesting question is imo, many of these PDFs assume finite mean and co-variances (first and higher moments in general.) How do we deal with that?

A lot of this is above my pay grade so I'll tackle what I can right now. I've always assumed that shorter time frames were more stationary based on chart reading. A 1 min chart looks very different than a daily chart for example. As for strategies to take advantage of advantage of changing pdfs? This is a guess but...assuming we can get a reliable PDF, scalp the range of a butterfly spread and switch to a trend following method if the spread starts moving out of our probability range?

 

[nitro]

A lot of this is above my pay grade so I'll tackle what I can right now. I've always assumed that shorter time frames were more stationary based on chart reading. A 1 min chart looks very different than a daily chart for example. As for strategies to take advantage of advantage of changing pdfs? This is a guess but...assuming we can get a reliable PDF, scalp the range of a butterfly spread and switch to a trend following method if the spread starts moving out of our probability range?

Good hypotheses. How do you go about testing it?

Do you see why this is so hard? Infinite hypotheses, almost infinite data sets with a finite life to live. And to make it worse, it is very expensive to set up a test harness in both time and money - no one will spoon feed you the answer. So retail traders put up pretty charts and gamble on what everyone else says works.

There used to be a guy that came here and said - "Retail traders lose. They just lose."