July 13th, 2004, 4:29 pm
QuoteOriginally posted by: rcohenQuoteOriginally posted by: zqhomeThe phy people I have met turn to belittle econometrics in general. They will make some assumptions to begin with, working with some SDE's, then using whatever optimization to get the parameters. No tests of any kind.... Also I notice a few replies from Phy background people here I guess , only mention econometrics has assumptions, never talk about the assumptions made by the phyisists...It looks like you've got it all wrong here. Let me first admit that I'm not talking as a physicist because I'm not one. My background is in engineering, but I think I can safely compare their methods of analyses. In engineering, you don't use optimisation to get the parameters. I don't know where you get this idea from. As I stated in an ealier reply, you have certain physical laws (i.e. gravitation, fluid motion, mass & energy transport, etc), from which governing pde or sde-type equations are derived. These equations are sometimes too complicated or even not possible to solve in closed form. Therefore, they are either solved numerically or with the aid of special simplification techniques, such as asymptotics. There is simply NO room for ad hoc assumptions, similar to how it's done in econometrics. If, for example, the governing pde in mechanics is based on F = ma, then you can't add in also the number of sun spots as a parameter just because you "think" it should appear there! THis is because the parameters are already predefined and you don't need any tests to determine what should go in these equations.***from which governing pde or sde-type equations are derived. These equations are sometimes too complicated or even not possible to solve in closed form. Therefore, they are either solved numerically or with the aid of special simplification techniques, such as asymptotics***And where do you get the parameters of that SDE before simulating then: suppose you have a simple GBM, where do you get the drift and volatility of that process ? Suppose you want to model the SP500 with a mean reverting procees, do you use 1.25 or 3 or 5 for the speed of mean reversion ?!!!***There is simply NO room for ad hoc assumptions***I am sorry but once you get out of the world of physical experiments(where you can test the same assumptions under the exact same conditions), and you apply physics to the financial world you need to start with some assumptions. Is there a governing law that will tell us whether or not the EURO/Dollar fx rate follows a jum-diffusion rather than a CEV process with no discontinuity ? In the financial world ( and for any mode that wants to capture market/human behavior) you need to start with some assumption, and then estimate the model to test if it is a good representation of reality ( the Data Generating Process)****just because you "think" it should appear there***That's not how econometrics functions. And here your really show that you have NO notion at all of how econometrics modeling works. Essentially most econometrics models (but not all) are usually estimated in what is called a reduced form ( e.g the usual GARCH returns and variance equations), as opposed to structural form. And this can obscure the fact that these equations are solutions of models of agent interaction. That why I said in a previous post " you need to go upstream" and check out the econmics model from which econometrics equations are determined ( for Garch for example you need to go up to models of market microstruture(check Dacorogna @Olsen) or agent-based models (check Santa Fe institute).There is indeed a whole branch of econometrics that is completely a-theoric ( starting with Sims VAR modeling), which aims at letting the data "speak for themselves", and do not model market participant's behavior ( from utility functions, risk aversion,etc). And this because of the complexity of social systems ( as opposed to Physical systems)