Long Memory Characteristics of the Distribution of Treasury Security Yields, Returns, and Volatility

The distributions of Treasury security yields, returns, and volatility play critical roles in finance theory, and there are many papers that characterize features of these distributions. Our aim is to extend earlier work on short-term dependence of these by documenting and measuring long-range dependence in debt markets. Our long-memory tests focus on the R/S statistic and a statistic for fractional differencing. We estimate the degree of fractional differencing using semiparametric Gaussian and averaged periodogram estimators and a log periodogram estimator. To help select the optimal spectral bandwidth, we apply various automatic bandwidth results. We apply these tests and estimators to the U.S. Treasury security markets and focus on instances where long memory is for understanding important financial economics issues. We sample weekly holding-period returns on seven Treasury bills and bonds for the 7/62Ü5/96 period and check our results with comparable maturity Treasury bills drawn from the CRSP bond file. Our findings can be grouped into three categories. First, we show that one-week and one-month gross holding-period returns on Treasury Bills display strong evidence of long memory, whereas Treasury Bond holding-period returns do not. Bill returns give results different from those reported for equity markets. Lo shows the equity market reflects significant short-term dependence that biases estimates of long memory; once short-term dependence is eliminated, long-memory evidence disappears. We use Lo's methods but find strong evidence of long memory in Treasury Bill returns. We find short-term dependence produces biased tests for long memory, but LoÍs bias correction eliminates evidence of long memory only for long-maturity Treasury bonds. We find excess returns on bills and bonds show no evidence of long memory, suggesting it to be less relevant to empirical asset pricing studies. Second, short- and long-maturity bond yields strongly appear to be long-memory processes. Comte and Renault show this implies term-structure and bond-pricing models must accommodate long memory in the short-term yield. We show the implications of long memory in the short-rate process for empirical bond pricing. We also show that the term premium clearly displays long-memory properties. What remains unclear is whether this contributes term premium's ability to predict excess returns in conditional asset-pricing models. Third, gross and excess holding-period returns, yields, and yield spreads all display long memory in volatility. This is important because our results imply that GARCH-type conditional volatility models and certain stochastic volatility models are mis-specified. This undermines hypothesis testing in asset-pricing settings where the GARCH-type models are used to calculate robust standard errors.