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Assume you want to forecast the correlation matrix of a stocks' basket (say 15 ~ 20 stocks from different sectors); assume you need to forecast at $T$ days because you will use the forecast ouput with options written on that basket: these options have maturity equal to $T$ days.

What would you choose between these two ways and why?

  1. Rolling window Kendall's $\tau$, with window's width $= T$ days;
  2. Generalized Orthogonal APARCH(1,1) forecasting.

Rank correlation is usually more robust than linear correlation, but ARCH family models accounts for heteroskedasticity of financial time series; in both ways mean reversion of variance and covariance does exist because of window's width in 1. and unconditional (co)variance in 2.

Which estimator would you use and why?

By the way, if you think a better estimator does exist, please tell me your opinion.

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Get a time-varying Kendall's tau from Patton's (2006) time-varying copula parameterisation. Heteroscedasticity in the univariate series can be modelled by specifying the marginal distributions as a GARCH process. Fat-tailed bivariate distributions can be handled using a time-varying SJC copula or alternative. –  Jase Aug 3 '13 at 14:42
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