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Abstract:
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Functional principal component scores play a fundamental role in functional data analysis, replacing mathematically infinitely dimensional curves by finite-dimensional vectors. A finite number of the scores for each curve encode the shape of the curve. For intraday cumulative return curves studied in finance, the first score quantifies the degree of monotonic upward or downward trend and the second score measures the degree of reversion. These scores exhibit extremal dependence for certain assets and certain periods. Such a dependence means that an extremely high monotonic trend and a pronounced reversion tend to occur simultaneously. Therefore, knowledge of the extremal dependence of the scores may enhance the management of intraday risk. The talk will focus on the study the extremal dependence measure (EDM), one of the commonly used estimators for extremal dependence. We derive conditions under which the EDM computed from the sample scores is consistent for the EDM of the unobservable population scores. We further illustrate this extremal dependence by a numerical study of Exchange Traded Funds that track the nine S&P 500 sector indexes.
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