The covariance matrix of a vector-valued time series is a very important indicator which lends itself to several useful interpretations - as a leading example, it may represent the risk of a portfolio of assets in applications in finance. This paper investigates whether the covariance matrix - and, therefore, the risk or volatility - change over time. In particular, this is not done ex-post, i.e. using data from the past and thereby realising that there was a change: the paper proposes an on-line monitoring procedure, where changes are detected as new data come in, in real time.
More specifically, in this Nottingham School of Economics working paper Matteo Barigozzi and Lorenzo Trapani develop a monitoring procedure to detect changes in a large approximate factor model. Letting r be the number of common factors, the main test statistics are based on the fact that the (r + 1)-th eigenvalue of the sample covariance matrix is bounded if there is no change, whereas it diverges to infinity in the presence of changes. Given that sample eigenvalues cannot be estimated consistently under the null, the authors randomise the test statistic, obtaining a sequence of i.i.d statistics, which are used for the monitoring scheme.
GC discussion paper 18/04: Sequential testing for structural stability in approximate factor models, by Matteo Barigozzi and Lorenzo Trapani.
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Matteo Barigozzi and Lorenzo Trapani
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Posted on Wednesday 28th November 2018