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13

Short of having a 'reasonable' predictive model for expected returns and the covariance matrix, there are a couple lines of attack. Shrinkage estimators (via Bayesian inference or Stein-class of estimators) Robust portfolio optimization Michaud's Resampled Efficient Frontier Imposing norm constraints on portfolio weights Naively, shrinkage methods ...


12

You can use changepoint analysis to identify regime change. You can also look at large angle differences in the eigenvectors between your most up-to-date/recent covariance matrix and the covariance matrix from the prior window. Another way to identify regime change is using a factor model. If the returns on a particular set of factors is X standard ...


10

Both answers from Shane and Vishal Belsare make sense and detail different models. In my experience, I have never been satisfied by a unique model since the majority of papers out there can be split in two categories: Those that predict the mean component of the problem. Those that predict the variance component of the problem. The ideal (to read ...


10

I highly recommend the Maximum Entropy Bootstrap for time series, implemented by the meboot package in R. In my work, I've stopped using both the block bootstrap and residuals bootstrap in favor of meboot, and I am pleased with the results. Hrishikesh Vinod, the researcher behind meboot, described it in his talk at UseR/2010 last year. The algorithm is ...


8

Perhaps you may want to consider article by D. Levine - Modeling Tail Behavior with Extreme Value Theory who gives practicale example on how EVT can be used to calculate probabilities on returns in tails with use of the Pickands-Balkema-de Haan Theorem and generalized Pareto distribution. It also contains some criterias and points on other methods that can ...


8

One approach is Conditional Value at Risk (CVaR) a.k.a. Expected Shortfall (ES). It does, as you suggest, take into account the whole set of returns. However, instead of traditional VaR which asks "what is the worst 1% or 5% loss I can expect" in a given time frame, conditional VaR asks "assuming I sustain losses of at least 95% or 99% (and perhaps am ...


7

You raise a very important point, which unfortunately doesn't have a simple answer. Black-Litterman addresses the allocation problem by allowing you to provide a prior within a bayesian framework. It doesn't really tell you how to produce the prior itself. But more importantly, it doesn't address the fundamental problem: it's difficult to accurately ...


7

A block bootstrap makes sense to me. (If the term doesn't make sense to you, I explain it at the end.) In order to pick the block size, I would essentially do a grid search: pick the largest feasible block size pick a smallest reasonable block size pick how many block sizes you feel like testing I'd run the selected bootstraps and see if there was a ...


6

Nonlinear optimization algorithms are very susceptible to starting points, so some problems with same structure can become difficult to solve compared to others. A few suggestions: For a few instances where you are having difficulty in getting answers, try using another solver. You can try Excel, Matlab or R, all of which can be used for fitting. Try ...


6

What you refer to as the 99.5th percentile is known as the "Value-at-Risk." You are correct that you will need to make a distributional assumption, and there is a popular and well-researched approach to this problem, though I'm not certain it could be called "standard." I would recommend you use the "truncated Levy flight" distribution. James Xiong at ...


5

Estimating $MA(q)$ models is significantly harder than $AR(p)$ models. Eviews, MATLAB and R can use multiple algorithms which are all based on some form of maximum likelihood estimation. You can look at the source of MATLAB and R or the excellent Eviews documentation. However, I strongly advise against rolling your own since efficient and well tested ...


5

I would suggest a multivariate garch model as a possibility. We aren't exactly overrun with wonderful software for that, but with just bivariate data I would think that the in-sample correlation estimates would be reasonably robust over models and estimation. It would be good to try two or three ways of doing it to make sure I'm right about that. You may ...


5

I think an extremely interesting strand of research on this topic is represented by extensions of vine copulas with time-varying parameters. For vine copulas in general have a look at this site from the Technische Universit√§t M√ľnchen: Vine Copula Models One of their research projects, which is the most relevant in this context, is:Time varying vine copula ...


4

You could try measuring autocorrelation at varying lags, as described here, and then choose your optimal block size according to the results of this test, i.e. if there is significant autocorrelation up to and including lag 5, your block size should be no larger than 5.


4

The blog post http://www.portfolioprobe.com/2011/11/21/asynchrony-in-market-data/ explains a bit more about the problem and it also points to a paper that shows that a moving average model is the way to make the adjustment that Tal is seeking. The paper is presented in the context of a multivariate garch model. That is gratuitous, really -- the MA estimate ...


4

The use of kernels to estimate volatility using intraday data is "nothing more" than combining: intraday volatility estimation kernel smoothing Thus you have to take care about the "usual pits" of these two approaches. Intraday volatility estimation. I hope you know the "signature plot" effect. Of course if you use the proper estimation method, it ...


3

One approach would be Engle (2002) dynamic conditional correlations. Taking your $Y_t$ and $X_t$, I will make the simplifying assumption that the mean equation of these is: $$\boxed{Y_t = \mu_y + \varepsilon_{y,t}}$$ $$\boxed{X_t = \mu_x + \varepsilon_{x,t}}$$ with $\varepsilon_{y,t} = z_{y,t} \sigma_{y,t} \sim N(0,\sigma_{y,t})$, $\varepsilon_{x,t} = ...


3

The answer to the original question is simple: the Chopra-Ziemba paper is highly flawed and unreliable. Note that the framework is in-sample and based on a utility function. It has nothing to do with out-of-sample behavior of the mean vs. the covariance in an optimization. Estimation error grows linearly in the mean but quadratically in the covariance. At ...


3

The pdfs of Student-t distributions have asymptotically Paretian tails, and the tail shape parameter (aka the maximal moment exponent) is equal to the distribution's degrees of freedom parameter. Assuming you have enough observations, you could estimate the Pareto parameter using the so-called Hill method (named after Bruce Hill, 1975). A word of caution: ...


3

There are many techniques, but I would begin with Stambaugh Analyzing Investments Whose Histories Differ in Lengths. The full information maximum likelihood approach he describes basically involves regressing the short history series against the long history series to obtain the covariance with the longer history securities and adding back the covariance of ...


3

Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...


2

I like the function b.star in the np package for R to select the block size and pass it to tsboot although I don't have the math background to determine whether this is the best method.


2

Here's an answer from a purely statistical point of view: http://www.duke.edu/~rnau/regnotes.htm#constant And another from Cross Validated: http://stats.stackexchange.com/questions/7948/when-is-it-ok-to-remove-the-intercept-in-lm The lean in both cases is to include the intercept unless there is a strong theoretical reason. A more satisfying answer would ...


2

Unless it is due to random chance, there seems to be a bias in your estimation method for $\kappa$, and this bias appears to depend on the size of the sample. This may be revealing a deeper underlying problem with your technique that will ultimately make it clearer what the tradeoff is between accuracy and sample size. I do not believe it should be the ...


2

Once we start building time-varying copulas like Lopes suggests in that paper, I think we are better off venturing into the world of state space models. When viewed in a bayesian context, the similarities between the approaches are striking to me. The advantage of the copula, as I understand it, is that it is a quick and dirty way to understand the ...


2

$dF(t,T)$ describes the dynamics of the rate of a particular forward contract as time $t$ moves forward to a fixed expiration $T$. $d\bar F(t,\tau)$ describes the dynamics of the rate at a particular point on the yield curve as time moves forward. The differential $\frac{\partial F}{\partial T}dt$ is simply the difference between holding the expiration ...


2

You need to know timezone for each instrument. Then for each instrument convert its time data from local to UTC (or to any other timezone that is convenient to you). Implementation hint: use the freely available Olson database. Timezone conversion routines are easy to find for every serious programming language.


2

I would recommend to use simple standard deviation (among the 2 options you offered). You are performing time series analysis of historical data points, you are not forecasting. Thus, why exposing yourself to a much more computationally intensive method? May I also point you to a related (not duplicate) thread: Why are GARCH models used to forecast ...


2

1.Is it correct, that the coefficients are now different to the coefficients of the arima output? It seems right that the ARMA coefficients are different. Indeed, in the second model, the GARCH component will capture fluctuations that the ARMA component will not have to capture, resulting in different ARMA parameter estimates. 2.This is the acf of ...



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