Exponentials, Polynomials, and Fourier Series: More Yield Curve Modelling at the Bank of Canada

Models of the yield curve and the curvature of the implied forward rate function

“…Siegel and Nelson (1988) noted the suitability of t À1 as an explanatory variable of the yield curve if the yield curve tends asymptotically to a fixed value. It is also possible to model the discount function as a polynomial function, as in Bolder and Gusba (2002).…”

Examining Simple Joint Macroeconomic and Term-Structure Models: A Practitioner's Perspective

“…There appears, for example, to be a high inflation regime associated with high short-term interest rates while there also appears to be a low-inflation regime associated with low short-term interest rates. Finally, one could characterize a third 23 For more detail about this model, see Bolder and Gusba (2002). regime describing the transition between the high-and low inflation regimes. Indeed, Demers (2003) to July 2005 including the output gap, the annual inflation rate, and the monetary-policy rate respectively.…”

“…The second variation comes from Bolder and Gusba (2002) who suggest a Fourier-series basis of the following form,…”

“…18 In actuality, we use an orthogonalized version of these basis functions computed using the Gram-Schmidt orthogonalization procedure; see Bolder and Gusba (2002) for more details.…”

“…19 Bolder and Gusba (2002) found that a choice of n ≈ 9 was optimal in terms of describing the term structure at a given instant in time.…”