宏观经济时间序列中的分数趋势和周期
Fractional trends and cycles in macroeconomic time series
摘要：
我们开发了一个概括的相关趋势周期分解，避免事先假设的长期动态特性的永久性组件建模为一个分数集成的过程，并将分数滞后算子的自回归多项式的周期性组件。该模型允许与其他模型参数联合的整合顺序的内源性估计，因此，不需要关于持久性的事先规格测试。我们将该模型的贝弗里奇-纳尔逊分解，并推导出一个修正的卡尔曼滤波估计的分数分量。最大似然估计的识别，一致性和渐近正态性。对于美国宏观经济数据，我们证明，与$I(1)$相关的未观察到的组件模型，新模型估计一个平稳的趋势，以及一个周期打击所有NBER的衰退。当数据生成机制的积分阶数大于1时，$I(1)$未观测分量模型产生向上偏置的信噪比，而分数积分模型由于分数趋势规范而将较小的变化归因于长期冲击，并且由于分数滞后算子而将较高的变化归因于周期冲击，导致更持久的周期和平稳的趋势估计，反映宏观经济常识。
英文摘要：
We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a fractional lag operator into the autoregressive polynomial of the cyclical component. The model allows for an endogenous estimation of the integration order jointly with the other model parameters and, therefore, no prior specification tests with respect to persistence are required. We relate the model to the Beveridge-Nelson decomposition and derive a modified Kalman filter estimator for the fractional components. Identification, consistency, and asymptotic normality of the maximum likelihood estimator are shown. For US macroeconomic data we demonstrate that, unlike $I(1)$ correlated unobserved components models, the new model estimates a smooth trend together with a cycle hitting all NBER recessions. While $I(1)$ unobserved components models yield an upward-biased signal-to-noise ratio whenever the integration order of the data-generating mechanism is greater than one, the fractionally integrated model attributes less variation to the long-run shocks due to the fractional trend specification and a higher variation to the cycle shocks due to the fractional lag operator, leading to more persistent cycles and smooth trend estimates that reflect macroeconomic common sense.
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