Long Memory Nelson-Siegel Model and No-Arbitrage Restrictions

Adam Golinski

Long Memory Nelson-Siegel Model and No-Arbitrage Restrictions

Economics

Research output: Working paper

Abstract

We propose a discrete-time, arbitrage-free, dynamic term structure model with 3 latent factors with Nelson-Siegel loadings. The factors are of a flexible, ARFIMA specification, thus they are allowed to exhibit long range persistence. Therefore, we achieve an ease of estimation and incorporate factors which are able to produce long range persistence of different degree for level, slope and curvature factors. Moreover, in our model we impose No-Arbitrage restrictions in the spirit of Christensen, Diebold and Rudebusch (2009a), which have beneficial effects for the model properties, such as in-sample fit or out-of-sample forecastability. We show that the long memory model with ARFIMA factors can also be adjusted to be consistent with No-Arbitrage conditions. For the arbitrage-free Nelson-Siegel model with ARFIMA factors we derive the specific form of the price of risk. Moreover, we show that incorporating long memory factors improves the out-of-sample forecast, but imposing no-arbitrage conditions with long memory factors provides a significantly better fit and out-of-sample forecast even more.

Original language	English
Number of pages	52
Publication status	In preparation - 2010

Cite this

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abstract = "We propose a discrete-time, arbitrage-free, dynamic term structure model with 3 latent factors with Nelson-Siegel loadings. The factors are of a flexible, ARFIMA specification, thus they are allowed to exhibit long range persistence. Therefore, we achieve an ease of estimation and incorporate factors which are able to produce long range persistence of different degree for level, slope and curvature factors. Moreover, in our model we impose No-Arbitrage restrictions in the spirit of Christensen, Diebold and Rudebusch (2009a), which have beneficial effects for the model properties, such as in-sample fit or out-of-sample forecastability. We show that the long memory model with ARFIMA factors can also be adjusted to be consistent with No-Arbitrage conditions. For the arbitrage-free Nelson-Siegel model with ARFIMA factors we derive the specific form of the price of risk. Moreover, we show that incorporating long memory factors improves the out-of-sample forecast, but imposing no-arbitrage conditions with long memory factors provides a significantly better fit and out-of-sample forecast even more.",

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AB - We propose a discrete-time, arbitrage-free, dynamic term structure model with 3 latent factors with Nelson-Siegel loadings. The factors are of a flexible, ARFIMA specification, thus they are allowed to exhibit long range persistence. Therefore, we achieve an ease of estimation and incorporate factors which are able to produce long range persistence of different degree for level, slope and curvature factors. Moreover, in our model we impose No-Arbitrage restrictions in the spirit of Christensen, Diebold and Rudebusch (2009a), which have beneficial effects for the model properties, such as in-sample fit or out-of-sample forecastability. We show that the long memory model with ARFIMA factors can also be adjusted to be consistent with No-Arbitrage conditions. For the arbitrage-free Nelson-Siegel model with ARFIMA factors we derive the specific form of the price of risk. Moreover, we show that incorporating long memory factors improves the out-of-sample forecast, but imposing no-arbitrage conditions with long memory factors provides a significantly better fit and out-of-sample forecast even more.

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