پیش بینی منحنی بازده در یک محیط سرشار از داده ها: یک رویکرد VAR عامل تقویت شده بدون آربیتراژ

This paper suggests a term structure model which parsimoniously exploits a broad macroeconomic information set. The model uses the short rate and the common components of a large number of macroeconomic variables as factors. Precisely, the dynamics of the short rate are modeled with a Factor-Augmented Vector Autoregression and the term structure is derived using parameter restrictions implied by no-arbitrage. The model has economic appeal and provides better out-of-sample yield forecasts at intermediate and long horizons than a number of previously suggested approaches. The forecast improvement is highly significant and particularly pronounced for short and medium-term maturities.

Traditional models of the term structure decompose yields into a set of latent factors. These models commonly provide a good in-sample fit to the data (e.g. Nelson and Siegel (1987), Knez et al. (1994) and Dai and Singleton (2000)) and can also be used to predict interest rates out-of-sample (e.g. Duffee (2002) and Diebold and Li (2006)). While providing a good statistical fit, however, the economic meaning of such models is limited since they disregard the relationships between macroeconomic variables and interest rates. In this paper, I suggest a model which has both economic appeal and superior predictive ability for yields as compared to traditional approaches. In a widely recognized paper, Ang and Piazzesi (2003) augment a standard three-factor affine term structure model with two macroeconomic factors that enter the model through a Taylor-rule type of short rate equation. They find that the macro factors account for a large share of the variation in interest rates and also improve yield forecasts. Inspired by this finding, a vivid literature has emerged lately that explores different approaches to jointly model the term structure and the macroeconomy. Examples for such models are Hördahl et al. (2006), Diebold et al. (2006) and Dewachter and Lyrio (2006). While these latter studies consistently find that macroeconomic variables are useful for explaining and/or forecasting government bond yields, they only exploit very small macroeconomic information sets. Yet, by limiting the analysis to only a few variables, other potentially useful macroeconomic information is being neglected.1 This is particularly important for term structure modeling as a recent literature argues that the central bank acts in a “data-rich environment” (Bernanke and Boivin, 2003). This means that the monetary policy authority bases its decisions upon a broad set of conditioning information rather than only a few key aggregates. Consistent with this argument, a number of studies have found that factors which by construction summarize the comovement in a large number of macroeconomic time series help to explain and forecast the evolution of short-term interest rates (e.g. Bernanke and Boivin (2003), Giannone et al. (2004) and Favero et al. (2005)). In related work, Bernanke et al. (2005) suggest to combine the advantages of factor modeling and structural VAR analysis by estimating a joint vector-autoregression of the short-term interest rate and factors extracted from a large cross-section of macro time series. They label this approach a “Factor-Augmented VAR” (FAVAR) and use it to analyze the dynamics of the short rate and the effects of monetary policy on a wide range of macroeconomic variables. In this paper, I take the approach of Bernanke et al. (2005) a step further and employ the FAVAR model to study the dynamics of the entire yield curve within an arbitrage-free model. Precisely, I suggest a model that has the following structure. A Factor-Augmented VAR is used to describe the dynamics of the short-term interest rate conditional on a large macroeconomic information set. Given the dynamics of the short rate, the term structure of interest rates is then derived using parameter-restrictions implied by no-arbitrage. In sum, my model is an affine term structure model that has a Factor-Augmented VAR as the state equation, i.e. the short rate and the common components of a large number of macro time series represent the factors which drive the variation of yields. I label this approach a No-Arbitrage Factor-Augmented VAR. Estimation of the model is in two steps. First, I extract common factors from a large macroeconomic dataset using the method suggested by Stock and Watson, 2002a and Stock and Watson, 2002b and estimate the parameters governing their joint dynamics with the monetary policy instrument in a VAR. Second, I estimate a no-arbitrage vector autoregression of yields on the exogenous pricing factors. Specifically, I obtain the price of risk parameters by minimizing the sum of squared fitting errors of the model following the nonlinear least squares approach of Ang et al. (2006). Altogether, estimation of the model is fast and it is thus particularly useful for recursive out-of-sample forecasts. The results of the paper can be summarized as follows. The No-Arbitrage FAVAR model based on four macro factors and the short rate fits the US yield curve well in-sample. More importantly, the model shows a strikingly good ability to predict yields out-of-sample. In a recursive out-of-sample forecast exercise, the No-Arbitrage FAVAR model is found to provide superior forecasts with respect to a number of benchmark models which have previously been suggested in the literature. Except for extremely short forecast horizons and very long maturities, the model significantly outperforms the random walk, a standard three-factor affine model, the model suggested by Bernanke et al. (2004) which employs individual macroeconomic variables as factors, and the model recently put forth by Diebold and Li (2006) which has been documented to be particularly useful for interest rate predictions. A subsample analysis reveals that the No-Arbitrage Factor-Augmented VAR model performs particularly well in periods when interest rates vary a lot. The paper is structured as follows. In Section 2, the No-Arbitrage Factor-Augmented VAR model is presented and its parametrization discussed. Section 3 describes the estimation of the model. In Section 4, I document the in-sample fit of the model and then discuss the results of the out-of-sample forecasts in Section 5. Section 6 concludes.

This paper presents a model of the term structure based on the idea that the central bank uses a large set of conditioning information when setting the short term interest rate and that this information can be summarized by a few factors extracted from a large panel of macroeconomic time series. Precisely, the Factor-Augmented VAR (FAVAR) approach suggested by Bernanke et al. (2005) is used to model the dynamics of the short-term interest rate. Given this dynamic characterization of the short rate, the term structure is then built up using restrictions implied by no-arbitrage. This setup is labeled a “No-Arbitrage Factor-Augmented VAR” approach. In contrast to most previously proposed macro-finance models of the term structure, the model suggested in this paper does not contain latent yield factors, but is entirely built upon macroeconomic information. Fitting the model to US data, I document that it explains the dynamics of yields quite well. This underlines that most of the variation of interest rates is captured by macroeconomic variables. Most importantly, I find that the No-Arbitrage FAVAR model exhibits a strikingly good ability to predict the yield curve out-of-sample. In particular at intermediate and long forecast horizons, the model outperforms various benchmarks including the essentially affine three factor model of Duffee (2002) and the dynamic variant of the Nelson–Siegel model that Diebold and Li (2006) have recently suggested as a prediction model. A subsample analysis of the forecast results documents that the No-Arbitrage FAVAR model performs particularly well in periods when interest rates exhibit pronounced dynamics. Based on the findings of the paper, there are a number of interesting directions for future research. First, while this paper has focused on the predictive ability of the No-Arbitrage FAVAR approach, the model can also be used for structural economic analysis. For example, it would be interesting to identify monetary policy shocks as in Bernanke et al. (2005) and study their impact on the yield curve. Second, based on estimates of term premia, one could use the model to analyze the risk-adjusted expectations of future monetary policy conditional on all macro information available. Finally, estimating the model using a one-step likelihood based Bayesian approach, one could easily add latent yield factors and assess to what extent these enhance the explanatory and predictive power of the model.