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.
