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14

There is some research that directly bears upon the issue of estimating covariance in the presence of unequal return histories and regime change. Wharton professor Robert Stambaugh (of liquidity premia fame) wrote a paper in '97 called "Analyzing Investments Whose Histories Differ in Length". Prior to the paper, most academics and practitioners would use ...


13

Quant Guy's list is really impressive! However, I am not sure they will readily solve your specific problem? I think there is one missing piece. Please note that imputing missing data is a very broad topic. There are many recipes to impute missings but that's for their specific 'assumptions' and purposes. They do not necessarily intend to well address your ...


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 ...


8

There are two functions for estimating variance matrices with missing values (and aimed at finance, by the way) in the R package BurStFin. Available via: install.packages('BurStFin', repos="http://www.burns-stat.com/R") but not yet for 2.14.x. You can of course get a correlation matrix from the variance matrix. One function estimates a statistical ...


6

High VIX arguably leads to less predictability of the market factor (i.e. market timing), but high volatility does lead to greater predictability of the cross-section of returns. Indeed, linear risk factor models have higher explanatory power during bear markets. However, your goal is to build a better market timing model where the forecasts (and perhaps ...


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 ...


3

Windham Capital Management is using hidden markov models for their Risk Regime Strategies. Mark Kritzman, who is also CEO, has published an article about the general outline of the strategy (with source code so you can replicate the results!): Regime Shifts: Implications for Dynamic Strategies (corrected August 2012) by M. Kritzman, S. Page, D. ...


3

How about adapting Ledoit-Wolf shrinkage to average correlation? You calculate the ratio of average correlations in two regimes to get a sense of the magnitude of regime shift. Use this ratio to adjust the correlations of short-lived stock with others. The method is simple and result will definitely make sense to you.


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} = ...


2

I'd use a Hidden Markov Model. Develop a statistical model of how the variables behave in different regime and establish transition probabilities between the regimes. Solve with the Viterbi Algorithm.



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