In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982–2008

Abstract

We review and construct consistent in-sample specification and out-of-sample model selection tests on conditional distributions and predictive densities associated with continuous multifactor (possibly with jumps) and (non)linear discrete models of the short term interest rate. The results of our empirical analysis are used to carry out a "horserace" comparing discrete and continuous models across multiple sample periods, forecast horizons, and evaluation intervals. Our evaluation involves comparing models during two distinct historical periods, as well as across our entire weekly sample of Eurodollar deposit rates from 1982-2008. Interestingly, when our entire sample of data is used to estimate competing models, the "best" performer in terms of distributional "fit" as well as predictive density accuracy, both in-sample and out-of-sample, is the three factor Chen (CHEN: 1996) model examined by Andersen, Benzoni and Lund (2004). Just as interestingly, a logistic type discrete smooth transition autoregression (STAR) model is preferred to the "best" continuous model (i.e. the one factor Cox, Ingersoll, and Ross (CIR: 1985) model) when comparing predictive accuracy for the "Stable 1990s" period that we examine. Moreover, an analogous result holds for the "Post 1990s" period that we examine, where the STAR model is preferred to a two factor stochastic mean model. Thus, when the STAR model is parameterized using only data corresponding to a particular sub-sample, it outperforms the "best" continuous alternative during that period. However, when models are estimated using the entire dataset, the continuous CHEN model is preferred, regardless of the variety of model specification (selection) test that is carried out. Given that it is very difficult to ascertain the particular future regime that will ensue when constructing ex ante predictions, thus, the CHEN model is our overall "winning" model, regardless of sample period.

Out‐of‐sample performance of bias‐corrected estimators for diffusion processes

“…The empirical results demonstrated that the modified bias‐corrected estimators improved the out‐of‐sample forecasting performance of the LS estimator for almost all the selected interest rate series. There are numerous studies on interest rate and yield curve forecasting in the finance literature, including Byers and Nowman (1998); Duffee (2002); Nowman and Saltoglu (2003); Hong, Li, and Zhao (2004); Inci and Lu (2004); Diebold and Li (2006); Treepongkaruna (2006); Guidolin and Timmermann (2009); Cai and Swanson (2011); and de Rezende and Ferreira (2013). Our results contribute to the literature on interest rate forecasting.…”

On the characteristic function for asymmetric Student t distributions

“…The mentioned models and the mentioned tests are popular in economics and finance". Some other recent applications of CHFs not stated in Nadarajah and Teimouri (2012) are: average rate claims with emphasis on catastrophe loss options (Bakshi and Madan, 2002); international cooperation, coalitions stability and free riding in a game of pollution control (Breton et al, 2006); oil price dynamics (Askari and Krichene, 2008); in-and out-ofsample specification analysis of spot rate models (Cai and Swanson, 2011); and, evaluation of European compound option prices (Griebsch, 2013).…”