Journal of Credit Risk

Risk.net

Moment estimators for autocorrelated time series and their application to default correlations

Christoph Frei and Marcus Wunsch

  • Classical estimators used in credit risk modelling are based on independence assumptions.
  • However, default rate time series often exhibit autocorrelation, leading to too low estimations.
  • We propose an adjusted estimator, considering autocorrelation and shortness of time series.
  • The adjustment removes a big part of the bias observed in classical estimators.

In credit risk modeling, method-of-moment approaches are popular for estimating latent asset return correlations within and between rating buckets. However, the autocorrelation often present in time series of default rates leads to estimations that are systematically too low. We propose a new estimator that adjusts to the problems of this autocorrelation and the shortness of the time series, thus eliminating a significant portion of the bias observed with classical estimators. The adjustment is based on convergence and approximation results for general autocorrelated time series, and it is easily implementable and nonparametric.

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