/PCAapplied_and_European_Yield_Curve

This paper aims to explore the time series’ proprieties of the features extracted by using the Principal Component Analysis (PCA) technique on the European AAA-rated Government Bond Yield curve. The PCA can greatly simplify the problem of modelling the yield curve by massively reducing its dimensionality to a small set of uncorrelated features. It finds several applications in finance and in the fixed income particularly from risk management to trade recommendation. After selecting a subset of Principal Components (PCs), this paper first analyzes their nature in comparison to the original rates and the implications in terms of information retained and lost. Then the time-series characteristics of each PC are studied and, when possible, Auto-Regressive Moving-Average (ARMA) models will be fitted on the data. One hundred observations of the original dataset are set aside as a test set to evaluate the predictive power of these models. Eventually, further analyses are performed on the PCs to evaluate the presence of heteroscedasticity and GARCH-ARCH models are fitted when possible. Tests are performed on the fitted coefficient to investigate the real nature of the conditional variance process.

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Principal Component Analysis applied to European Yield Curve

This paper aims to explore the time series’ proprieties of the features extracted by using the Principal Component Analysis (PCA) technique on the European AAA-rated Government Bond Yield curve. The PCA can greatly simplify the problem of modelling the yield curve by massively reducing its dimensionality to a small set of uncorrelated features. It finds several applications in finance and in the fixed income particularly from risk management to trade recommendation. After selecting a subset of Principal Components (PCs), this paper first analyzes their nature in comparison to the original rates and the implications in terms of information retained and lost. Then the time-series characteristics of each PC are studied and, when possible, Auto-Regressive Moving-Average (ARMA) models will be fitted on the data. One hundred observations of the original dataset are set aside as a test set to evaluate the predictive power of these models. Eventually, further analyses are performed on the PCs to evaluate the presence of heteroscedasticity and GARCH-ARCH models are fitted when possible. Tests are performed on the fitted coefficient to investigate the real nature of the conditional variance process.