Zero-Coupon Treasury Yield Curve with VIX as Stochastic Volatility

We apply Principal Component Analysis for zero-coupon Treasury bonds to get level, slope, and curvature series. We model these as autoregressions of order 1, and analyze their innovations. For slope, but not for level and curvature, dividing these innovations by the Volatility Index VIX made for Standard \& Poor 500 makes them closer to independent identically distributed normal. We state and prove stability results for bond returns based on this observation. We chose zero-coupon as opposed to classic coupon Treasury bonds because it is much easier to compute returns for these.