Abstract
In addition to the autoregressive models described above, which are used for instance in the form of GARCH models when modeling volatility, a further technique of time series analysis, called principal component analysis (abbreviated as PCA), is widely applied in the financial world.
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Notes
- 1.
An introduction in the technique of Lagrange multipliers for solving extreme value problems with boundary conditions can be found, for example, in [34].
- 2.
Since the Lagrange function differs only by zero from the value to be maximized (the variance), this equals the maximal value we are looking for. Of course, this is only true, if the difference is indeed equal to zero, i.e., if the boundary condition is fulfilled. This is the short form explanation of this method.
- 3.
The kth eigenvalue is in fact equal to the variance of the new random variable Y k.
- 4.
It has already been pointed out that principle component analysis assumes that the data in the time series are stationary. For the following investigation, this assumption is made keeping in mind that the results of the investigation should convey only a qualitative impression of term structure dynamics. Using the data directly (i.e. without a pre-treatment such as taking time differences, etc.) will simplify the interpretation of the results substantially.
References
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Deutsch, HP., Beinker, M.W. (2019). Principal Component Analysis. In: Derivatives and Internal Models. Finance and Capital Markets Series. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-22899-6_34
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DOI: https://doi.org/10.1007/978-3-030-22899-6_34
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