(2) Objectives

This paper investigates the presence of long memory in yield spreads.  Specifically, the focus is on the yield spread between Moody’s Baa and Aaa bonds, and between each series and the long-term Treasury bond rate.

(3) Data/Methods

Monthly data on Moody’s Baa and Aaa bond yields and Treasury bond yields from January 1, 1919 to August 1, 2008, are made available by the Board of Governors of the Federal Reserve System.  Using the wavelet OLS estimator method, these data are used to test the hypothesis that yield spreads follow a fractionally integrated process.  The presence of a long memory process in yield spreads requires a slow decay of the autocorrelation coefficients, and therefore, the existence of long memory or long-range dependence.  The proposed method allows the use of information generated by a wavelet multiresolution analysis to examine a process in each localized time-scale space.

It is known that the persistence of autocorrelation coefficients or the presence of long memory is inconsistent with either stationary ARMA or non-stationary unit root models. For a FARIMA process, the often used maximum likelihood method lacks computational efficiency. The reason is that the presence of long memory is often accompanied by a dense autocovariance matrix with few zeros. The derivation of an exact likelihood function requires the inversion of this covariance matrix.  To process a lengthy time series, this inversion poses a technical challenge. 

With its ability to localize a process in a time-scale space, wavelet analysis results in computational efficiency.  This gives the wavelet OLS estimator method an advantage in estimating the long memory parameter when a lengthy time series results in a dense autocovariance matrix with few zeros.  Furthermore, wavelet analysis, a member of the family of sieve methods, has an additional advantage because it has asymptotic efficiency.

(4) Results/Expected Results
Yield spreads can serve as a leading indicator of economic conditions.  As the economy gains strength, the yield spreads typically become smaller; a growing number of investors are willing to acquire riskier Baa bonds.  On the other hand, as the economy weakens, more investors are interested in AAA bonds or, even less risky Treasury bonds, to lower their portfolio risk.  The wavelet OLS estimator method allows the testing for autocorrelation in spreads, the existence of which has implications for forecasting future yield spreads.

Our preliminary results suggest the presence of long memory in these yield spreads over the sample period.  This long-range dependence is characterized by a hyperbolic decay of its autocovariance function. The corresponding fractional differencing parameter falls within the range between 0 and 1/2.