The IntCal04 and Marine04 radiocarbon calibration curves have been updated from 12 cal kBP (cal kBP is here defined as thousands of calibrated years before AD 1950), and extended to 50 cal kBP, utilizing newly available data sets that meet the IntCal Working Group criteria for pristine corals and other carbonates and for quantification of uncertainty in both the 14C and calendar timescales as established in 2002. No change was made to the curves from 0–12 cal kBP. The curves were constructed using a Markov chain Monte Carlo (MCMC) implementation of the random walk model used for IntCal04 and Marine04. The new curves were ratified at the 20th International Radiocarbon Conference in June 2009 and are available in the Supplemental Material at www.radiocarbon.org.

This paper proposes some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long memory moving average process, independent of the covariate. The tests are based on a partial sum process of the residuals from the fitted regression. The asymptotic null distribution of this process is discussed in some detail under each set of these assumptions. The proposed tests are shown to have known asymptotic null distributions in the case of martingale difference errors and also in the case of fitting a polynomial of a known degree through the origin when the errors have long memory. The theory is then illustrated with some examples based on the forward premium anomaly where a squared interest rate differential proxies a time dependent risk premium. The paper also shows that the proposed test statistic converges weakly to nonstandard distributions in some cases.The authors gratefully acknowledge the helpful comments of the co-editor Don Andrews and two anonymous referees. The research of the first two authors was partly supported by NSF grant DMS 00-71619.

The radiocarbon calibration curve IntCal04 extends back to 26 cal kyr B P. While several high-resolution records exist beyond this limit, these data sets exhibit discrepancies of up to several millennia. As a result, no calibration curve for the time range 26–50 cal kyr BP can be recommended as yet, but in this paper the IntCal04 working group compares the available data sets and offers a discussion of the information that they hold.

Most asset pricing models postulate a positive relationship between a stock portfolio's expected returns and risk, which is often modeled by the variance of the asset price. This paper uses GARCH in mean models to examine the relationship between mean returns on a stock portfolio and its conditional variance or standard deviation. After estimating a variety of models from daily and monthly portfolio return data, we conclude that any relationship between mean returns and own variance or standard deviation is weak. The results suggest that investors consider some other risk measure to be more important than the variance of portfolio returns.