# Tag Info

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Just about every introductory Econometrics class teaches that the violations of BLUE ("Best Linear Unbiased Estimator" -- the properties of linear least squares) are invalid standard errors in the case in the heteroscedasticity, so while your parameter estimates are still valid ("unbiased") your inference may be off invalid estimates (!!) in the presence ...

6

W.l.o.g we use the initial condition $S(0)=1$ and define $\gamma:=\mu-\frac{\sigma^2}{2}$. Hence we have the dynamics $$S_t=e^{\gamma t +\sigma W_t}$$ By definition $Cov(X,Y)=E((X-E(X))(Y-E(Y))=E(XY)-E(X)E(Y)$, where the last equality follows from the linearity of the expectation. Note $\gamma t+\sigma W_t$ is normal distributed with mean $\gamma t$ and ...

5

Apparently yes, (I haven't verified the math but have no reason to doubt it). For this simple case you can find a closed form in the following paper: Jeff A. BILMES: What HMM can do The closed form is given on part 4.4 of the paper but the whole thing is worth reading as it clearly shows the main properties of these models. You can also note that ...

4

Generally we use models that go so far out in a comparative sense, not as an absolute decision. You are definitely do some good reading but I believe you are thinking about these models in the wrong way. I think (and correct me if I'm wrong) you are looking at creating or finding the perfect "crystal ball" model that will predict returns/risk premiums etc. ...

4

Couple points I like to make: There exists no reliable model that can even predict future price returns (risk premiums, excess returns, whatever you want to call it) beyond a year, run as fast as you can if you hear from someone who claims he can predict risk premiums 10 years out, whether reliably or not. It makes zero sense and clearly comes from either ...

4

Simple...because you are interested in deviations from a metric, and not whether it deviates above or below. The very definition of volatility is a "measure of deviation". Squaring returns or using the absolute values just eases the calculation to arrive at a deviation measure. Otherwise volatility would have to be calculated in other ways as positive and ...

4

To simplify, consider the errors rather than the returns. The variance is effectively the average of the squared errors, while absolute deviation is the average of the absolute errors. So plotting the squared errors or absolute errors over time could give an indication of whether the variance or absolute deviation is constant over time. Since variance is ...

4

Thanks gappy for your precise response. However the answer to this auto-correlation is much more important than an academic discussion of which portfolio performance ratio is best. Auto-correlation distorts max draw-down calculations raising the question of whether the (positive) auto-correlation will continue in the future producing large draw-downs, or ...

3

This is a partial explanation in that trading strategies with longer horizons have higher information ratios, t-statistics, slope coefficients, and R^2 in general. In other words, if information ratios for both strategies are identical then the longer-term trading strategy is already worse. John Cochrane illustrates how longer horizons have higher t-stats ...

3

Autocorrelation is usually a problem when you are doing the analysis of your error terms. When you build a model, you expect that the error term will have non significant autocorrelation. It is simple to understand: If your error term still have autocorrelations it certainly means that you are missing some information that could be introduced in your model. ...

3

This question was ultimately answered on Cross Validated Here are a couple of articles that deal with this subject: Britten-Jones and Neuberger, Improved inference and estimation in regression with overlapping observations Harri & Brorsen, The Overlapping Data Problem

1

Three good references are the Asymptotic theory for econometricians, H. White Stochastic Limit Theory, Davidson Asymptotic Theory of Statistical Inference for Time Series, Taniguchi and Kakizawa They are roughly in order of complexity. The crux of the matter is to balance the requirements of finiteness of higher moments of $X$ with its dependence ...

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