In their seminal work, Lettau, M., and S. Ludvigson, 2001, “Consumption, Aggregate Wealth, and Expected Stock Returns.” The Journal of Finance 56 (3): 815–49. https://doi.org/10.1111/0022-1082.00347, demonstrated that there exists a long-run relationship between consumption, asset holdings, and labor income. They denoted this relationship as cay and showed it to be quite successful in predicting the behavior of real stock returns. Their estimation procedure assumes that consumption, asset wealth, and labor income are first-order integrated ( I (1), nonstationary) and that their linear combination forms a zero-order integrated ( I (0), stationary) series. This paper proposes a more general framework in the estimation of the cay model by allowing both the series and the long-run equilibrium to be fractionally integrated. We use the recently developed Fractionally Cointegrated VAR (FCVAR) approach to estimate the cay model. Results show that: (i) the series are nonstationary but mean-reverting processes, (ii) there exists a long-run equilibrium between consumption, asset wealth, and labor income, (iii) this long-run relationship is a stationary fractionally integrated process, and (iv) the estimated cay using the FCVAR approach shows the same desirable forecasting properties as its predecessor.

中文翻译：

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消费，总财富和预期股票收益：FCVAR方法

在其开创性的工作中，M。Lettau和S. Ludvigson，2001年，“消费，总财富和预期的股票收益”。金融学杂志56（3）：815–49。https://doi.org/10.1111/0022-1082.00347证明，消费，资产持有量和劳动收入之间存在长期的关系。他们称这种关系为“ cay”，并表明它在预测实际股票收益的行为方面非常成功。他们的估计程序假设消费，资产财富和劳动收入是一阶积分（I（1），非平稳），并且它们的线性组合形成零阶积分（I（0），平稳）系列。通过允许对序列和长期均衡进行部分积分，本文为cay模型的估计提出了一个更通用的框架。我们使用最近开发的分数协整VAR（FCVAR）方法来估计cay模型。结果表明：（i）系列不是平稳的但均值回复过程；（ii）消费，资产财富和劳动收入之间存在长期均衡；（iii）这种长期关系是平稳的，部分积分的流程，以及（iv）使用FCVAR方法估算的原因显示出与其前身相同的理想预测属性。