- ScilabGuru
**Posts:**297**Joined:**

Being mathematician and econometrist for many years I see the same problem when mathematicians and physists work with data and derive results without any reference to statsitical significance and confidence interval. The general attitude to statitics is quite arrogant. This is extremely dangerous when one tries to forecast, not just calibrate a model. Veru often I see in papers and reports the estimated values of parameters without any references to estimation of confidence intervals these parameters are from. When you work with data from physical experiment - this is justified since you can repeat your experiment many many times and the data seem be staionary in some sense. In finance this is not the case.

QuoteOriginally 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.

Last edited by rcohen on July 12th, 2004, 10:00 pm, edited 1 time in total.

- ScilabGuru
**Posts:**297**Joined:**

QuoteOriginally posted by: rcohenQuoteOriginally posted by: zqhomeIn engineering, you don't use optimisation to get the parameters. I don't know where you get this idea from. what should go in these equations.I am sorry,rcohen but I am also have degree in Mechanics. It seems you never really estimated parameters in physical systemslike gravitation constant or eigen frequencyes mechanical systems. If you ahve an object with unknown mass and whatever, but you have trajectory of this object - then plugging parameters into the equation you can fit them. ALL physical results are based on the experiments. When you try to find some constant like graviation constant - you have to make measurments - experiments. You plug your experiments in your equations and try to fit them via say least squares or maximum likelihood approach. Why? Because your experiments also have an ERROR. So you also have certain assumptions both for model (Newton or relativistic ) and for your noise. The greatnesss of physcis that you can repeat your experiments as many times as you want and then via STATISTICAL LAW your error of estimate of your constant will tends to zero.There is no estimation of parameters without optimization of something - (your emperical believe or quantitative measueof fit) This is why generally speaking we don't need advance econometric /statistical methods in mechanics/physics - the basic laws and equations are derived already and seem reflect reality pretty well in certain bounds. Assuming that one can find TRUE laws in finance we then will significanlt simplify econometric part into the research. Nobody islooking for other than Newton Euler equation in mechanics today. Regards

- DogonMatrix
**Posts:**242**Joined:**

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)

I have some experience in engineering. There are exact laws (conservation laws, parity, etc.) and constituitive laws and effects one neglects. A pretty good example is spinoidal decomposition in alloys.Normally, conservation of species leads to the absolute law dc/dt = -grad*Flux = -J_xTheFourier law of diffusion says that Flux = -D*c_x.This is a modeling assumption, which is usually pretty good. Together they give you the heat equation, dc/dt = [D*c_x]_xBut in some alloys, diffusion does not cause the concentrations to go towards constant concentrations c; instead they go towards an equilibrium profile that looks like a distorted sine wave. A deeper analysis models the flux as the mobilitiy times the gradient of the chemical protential, which is the first variation of the free energy with concentration. The appropriate constituitive law then yields dc/dt = [D(c)*c_x]_xOne then finds that some free energy profiles (which are actually quite common in alloys), the diffusion coefficient D(c) is negative for a range of c's. This is a disaster mathematically, causing concentration profiles to become arbitrarily rugged. If one re-examines the physics, one sees that one should have included a 0.5*[c_x]^2 term in the free energy. This leads to dc/dt = [D(c)*c_x]_x - const * c_xxxxand the fourth order term stabilizes the short wavelength concentration fluctuations. This leads to stable predictions which match experiment quite closely.I guess the bottom line, regardless of one's methodology is what did one learn? If the physics or econometrics, or I Ching session didn't produce useabe information, then it's a waste.

- hedgeQuant
**Posts:**99**Joined:**

Ok. I just went through this thread and realized not many were paying much attention to the underlying tool everybody was using: Mathematics. Though many problems had their origin in Physics, math was the driving force that led to the refinement of many concepts. (Surely Measure Theory was not a contribution from Physics or Engineering). As far as the Physics vs. Econometrics debate goes, all that matters in the end is the tools you have; it does not matter where you picked them. I have a Bachelors in Physics, Masters in Eelectrical Engineering (Telecommunication), PhD in EE (Signal Processing) and now working in Finance. I picked up my tools from all branches of Science and Engineering (including Physics and Econometrics) and in the end it is very very difficult to point to one particular subject and say that I got my knowledge from there. (By the way, what is my field ? As of now I dont have an answer!). All through my education and (as of now, brief) career, I have remembered once piece of wisdom that I gto from my mentor (during my Masters): Never get into a position where you are considered too practical to be a mathematician and too theoretical to be an engineer. Best,hedgeQ.

- DogonMatrix
**Posts:**242**Joined:**

QuoteOriginally posted by: PatI have some experience in engineering. There are exact laws (conservation laws, parity, etc.) and constituitive laws and effects one neglects. A pretty good example is spinoidal decomposition in alloys.Normally, conservation of species leads to the absolute law dc/dt = -grad*Flux = -J_xTheFourier law of diffusion says that Flux = -D*c_x.This is a modeling assumption, which is usually pretty good. Together they give you the heat equation, dc/dt = [D*c_x]_xBut in some alloys, diffusion does not cause the concentrations to go towards constant concentrations c; instead they go towards an equilibrium profile that looks like a distorted sine wave. A deeper analysis models the flux as the mobilitiy times the gradient of the chemical protential, which is the first variation of the free energy with concentration. The appropriate constituitive law then yields dc/dt = [D(c)*c_x]_xOne then finds that some free energy profiles (which are actually quite common in alloys), the diffusion coefficient D(c) is negative for a range of c's. This is a disaster mathematically, causing concentration profiles to become arbitrarily rugged. If one re-examines the physics, one sees that one should have included a 0.5*[c_x]^2 term in the free energy. This leads to dc/dt = [D(c)*c_x]_x - const * c_xxxxand the fourth order term stabilizes the short wavelength concentration fluctuations. This leads to stable predictions which match experiment quite closely.I guess the bottom line, regardless of one's methodology is what did one learn? If the physics or econometrics, or I Ching session didn't produce useabe information, then it's a waste.Once again how do you get your parameters for any of these processes? It looks to me that it doesn't matter how much sophisticated the process you use to model the market, you will still need a "tool" to tie down this process to market data. And I will claim that econometrics offers the most robust and rich set of tools to do just that: that is, econometrics is crucial to applied physics in finance.

I don't think there is an answer to the question. To me the two approaches seem justcompletely different. Typical I find Econometrics an empirical approach and Physics a model approach. The two can be useful in finance, and even complementary.When a simple model can be put together to describe markets, then using thetoolbox of Physicists can be a plus in particular when the finance problemmaps onto a problem of the physicist's domain with known solution. BS optionequation is the most obvious example. Econometrics tends to take a model as the starting point and check whether it fits with the "reality" of price series. A number of eleborate statistical tests come with the toolbox of the Econometritian. They calculate levels of confidence of approval or rejection of the model. It is then down to the Econometritianto try to come up with the model that makes most sense and passes thestatistical tests.

QuoteOriginally posted by: carvalhorEconometrics tends to take a model as the starting point and check whether it fits with the "reality" of price series. A number of eleborate statistical tests come with the toolbox of the Econometritian. They calculate levels of confidence of approval or rejection of the model. It is then down to the Econometritianto try to come up with the model that makes most sense and passes thestatistical tests.You are confirming my earlier assertion that econometrics is nothing but a testing tool. There is a problem, however, when one relies fully on econometrics to come up with new "models" or "theories". The problem, in my opinion, is that with no underlying theory, you can always find (or devise) a test that can either accept or reject a hypothesis. So, where does the testing stop?

Absolutely! I am from a Science background myself, Physics, and was at the beginning rather unconfortable with Econometric methods and the way they tend to be used. However, one must recognise that there are in Finance plenty of problems that can be easily and effectively addressed by Econometrics. For example, I use these methods to test very simple assumptions made from theoretical backgrounds. But it is true that you find plenty of econometritians and statisticians doing the most crazy things with these methods. As with everything, there are bad econometritians and there are good ones. It is just important to distinguish the good work from the bulk of rubbish.

Part of the problem however as has been noted is that whereas in physics there are pretty well nailed down 'facts' about whats going on Econometrics is a toolkit devised to test the ultimatly untestable - what are people doing? Once we realise that all economics and finance are derived from social interactions, the argument collapses. People are fundementally unamenable to modelling - all we can do is make reasonable guesses and then test whether these guesses are borne out in fact. Asking etrics to do more is asking for the moon.

- DogonMatrix
**Posts:**242**Joined:**

More importantly I think statistics in general, and econometrics in general (which is nothing else than applied statistics) helps you think in terms of probability rather than certainty. In the "Engeneering World" you are dealing with laws that will repeat themselves with certainty under the same conditions, in the "Finance World" or wherever human interaction is involved you are in the probabilistic world where you can only assign a likelihood to the occurence of events. That's the gist of books like "Fooled like Randomness" ( incidently the author as a PhD in Econometrics)....

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