Comparing Kendall Rank Correlation and APARCH for Basket Forecasts

Summary

The document frames a choice between forecasting a stock basket’s correlation matrix with rolling-window Kendall’s tau or a generalized orthogonal APARCH(1,1) model. The motivating use is pricing options on a basket whose maturity defines the forecast horizon. The comparison highlights a tradeoff: rank correlation can be more robust than linear correlation, while ARCH-family models represent time-varying volatility. Both approaches also embody mean reversion, through the rolling window in one case and unconditional covariance in the other.

The text poses the estimator choice but supplies no answer, comparative results, or proposed alternative. It therefore serves as a modeling question rather than evidence favoring either method. Selection would need to account for the basket, horizon, option sensitivity to dependence, robustness to outliers, and forecast performance; these considerations are not evaluated in the document.

Key ideas

• The proposed methods are rolling Kendall’s tau and generalized orthogonal APARCH(1,1) correlation forecasts.
• The intended forecast horizon matches the maturity of options written on the stock basket.
• Kendall’s tau offers rank-based robustness, while APARCH models time-varying volatility.
• Both methods incorporate mean reversion through different mechanisms.
• The document does not provide empirical comparisons or recommend an estimator.

Tags

# Rolling window Kendall's tau against APARCH(1,1) correlation


# Rolling window Kendall's tau against APARCH(1,1) correlation












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?

- Rolling window Kendall's $\tau$, with window's width $= T$ days;

- 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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.