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Identification and Estimation of . . .

By Pierre Collin-Dufresne, Robert S. Goldstein and Christopher S. Jones


We propose a canonical representation for affine term structure models where the state vector is comprised of the first few Taylor-series components of the yield curve and their quadratic (co-)variations. With this representation: (i) the state variables have simple physical interpretations such as level, slope and curvature, (ii) their dynamics remain affine and tractable, (iii) the model is by construction ‘maximal ’ (i.e., it is the most general model that is econometrically identifiable), and (iv) model-insensitive estimates of the state vector process implied from the term structure are readily available. We find that the ‘unrestricted ’ A 1(3) model of Dai and Singleton (2000) estimated by ‘inverting ’ the yield curve for the state variables generates volatility estimates that are negatively correlated with the time series of volatility estimated using a standard GARCH approach. This occurs because the ‘unrestricted’ A 1 (3) model imposes the restriction that the volatility state variable is simultaneously a linear combination of yields (i.e., it impacts the cross-section of yields), and the quadratic variation o

Year: 2003
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