As a benchmark mortality model in forecasting future mortality rates and hedging longevity risk, the widely employed Lee–Carter model (Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.) suffers from a restrictive constraint on the unobserved mortality index for ensuring model’s identification and a possible inconsistent inference. Recently, a modified Lee–Carter model (Liu, Q., Ling, C. and Peng, L. (2018) Statistical inference for Lee–Carter mortality model and corresponding forecasts. North American Actuarial Journal, to appear.) removes this constraint and a simple least squares estimation is consistent with a normal limit when the mortality index follows from a unit root or near unit root AR(1) model with a nonzero intercept. This paper proposes a bias-corrected estimator for this modified Lee–Carter model, which is consistent and has a normal limit regardless of the mortality index being a stationary or near unit root or unit root AR(1) process with a nonzero intercept. Applications to the US mortality rates and a simulation study are provided as well.

Motivated by a recent discovery that the two-step inference for the Lee–Carter mortality model may be inconsistent when the mortality index does not follow from a nearly integrated AR(1) process, we propose a test for a unit root in a Lee–Carter model with an AR(p) process for the mortality index. Although testing for a unit root has been studied extensively in econometrics, the method and asymptotic results developed in this paper are unconventional. Unlike a blind application of existing R packages for implementing the two-step inference procedure in Lee and Carter (1992) to the U.S. mortality rate data, the proposed test rejects the null hypothesis that the mortality index follows from a unit root AR(1) process, which calls for serious attention on using the future mortality projections based on the Lee–Carter model in policy making, pricing annuities and hedging longevity risk. A simulation study is conducted to examine the finite sample behavior of the proposed test too.

This study tests the causal direction between captive supply and cash market price in the U.S. cattle procurement market. Finding the correct causality should provide useful information to the decades-long debate on packers’ anti-competitive behavior in the U.S. cattle procurement market. It should also help researchers find better econometric specifications for the cash price-captive supply relationship. Two causality tests—the Granger test and the Modified Wald test—were conducted. Overall test results indicate that captive supply causes cash market price, and it favors the price-dependent model.

The standard model of the small open economy is burdened with a unit root that greatly complicates numerical computation of the global saddle path. In this paper we solve the unit root problem by developing a set of innovative forward-shooting algorithms. Exploiting the fact that the algorithms are mechanical and model-free, we have placed canned, fully automated programs in the public domain. The programs do not require any substantive human input. The user's only responsibility is to type in the equations of the model correctly.

It is common to interpret rejections of the unit-root null hypothesis in favor of a trend stationary process with possible trend breaks as evidence that the data are better characterized as stationary about a broken trend. This interpretation is valid only if the model postulated under the alternative hypothesis is the only plausible alternative to the model postulated under the null. We argue that there are economically plausible models that are not well captured under either the null hypothesis or the alternative hypothesis of these tests. We show that applied researchers who ignore this possibility are likely to reject the unit-root null with high probability in favor of a trend stationary process with possible breaks. Our evidence shows that this potential pitfall is both economically relevant and quantitatively important. We explore the extent to which applied users may mitigate inferential errors by using finite-sample and bootstrap critical values.

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.