Beyond the stationarity condition

[NYConsultant]

I was wondering if there are any models that allow distributions to evolve in time? It seems fairly obvious while analyzing any type of market data that the underlying probability distributions are anything but stationary; their statistical variables change on a fairly small time scale in many cases.

---------- Post added at 08:15 PM ---------- Previous post was at 06:36 PM ----------

Sorry if this thread seems a bit general, and not related to pricing and hedging specifically; but there isn't a general purpose math/statistics section I could find on the forum; thanks again-

 

[joel_b]

It's pretty general, I mean nearly every model attempts to account for changes in conditions. Even Simple Moving Average is exactly that and it's one of the most basic indicators. Then Exponential moving average tries to give more weight to more recent events. These are simple indicators, let alone complex models. There are entire books on the reading list on this site that can go into the construction of many models if you want to dig into it.

Anyway you say it seems fairly obvious, and you're right. Soooo....if you had a more specific question...I mean even your premise regarding stationarity is in relation to another variable :p

Things generally don't stay stationary forever, so you have to build a rule-base to handle that, and when the conditions aren't good anymore, you don't trade it. When it comes back in favour, you do.

 

[NYConsultant]

It's pretty general, I mean nearly every model attempts to account for changes in conditions. Even Simple Moving Average is exactly that and it's one of the most basic indicators. Then Exponential moving average tries to give more weight to more recent events. These are simple indicators, let alone complex models. There are entire books on the reading list on this site that can go into the construction of many models if you want to dig into it.

Anyway you say it seems fairly obvious, and you're right. Soooo....if you had a more specific question...I mean even your premise regarding stationarity is in relation to another variable :p

Things generally don't stay stationary forever, so you have to build a rule-base to handle that, and when the conditions aren't good anymore, you don't trade it. When it comes back in favour, you do.

Thanks for the reply Joel,

I agree it's not a well posed question. I come from an experimental physics background and my only exposure to probabilistic reasoning comes from either error analysis in experiments or quantum mechanics.

Thanks for the reply.