英文文献：Deterministic and stochastic trends in the Lee-Carter mortality model-李-卡特死亡率模型中的确定性和随机趋势
英文文献作者：Laurent Callot,Niels Haldrup,Malene Kallestrup Lamb
英文文献摘要：
The Lee and Carter (1992) model assumes that the deterministic and stochastic time series dynamics loads with identical weights when describing the development of age specific mortality rates. Effectively this means that the main characteristics of the model simplifies to a random walk model with age specific drift components. But restricting the adjustment mechanism of the stochastic and linear trend components to be identical may be a too strong simplification. In fact, the presence of a stochastic trend component may itself result from a bias induced by properly fitting the linear trend that characterizes mortality data. We find empirical evidence that this feature of the Lee-Carter model overly restricts the system dynamics and we suggest to separate the deterministic and stochastic time series components at the benefit of improved fit and forecasting performance. In fact, we find that the classical Lee-Carter model will otherwise over estimate the reduction of mortality for the younger age groups and will under estimate the reduction of mortality for the older age groups. In practice, our recommendation means that the Lee-Carter model instead of a one-factor model should be formulated as a two (or several)-factor model where one factor is deterministic and the other factors are stochastic. This feature generalizes to the range of models that extend the Lee-Carter model in various directions.

Lee和Carter(1992)模型在描述特定年龄死亡率的发展时，假设具有相同权重的确定性和随机时间序列动力学载荷。这有效地意味着模型的主要特征简化为一个带有年龄漂移成分的随机游走模型。但是限制随机趋势分量和线性趋势分量的调整机制相同可能是一种过于简化的方法。事实上，随机趋势成分的存在本身可能是由适当地拟合死亡率数据的线性趋势所引起的偏差造成的。我们发现经验证据表明，这一特征的李-卡特模型过度限制了系统动力学，我们建议分离确定性和随机时间序列成分，以提高拟合和预测性能。事实上，我们发现经典的Lee-Carter模型会高估较年轻年龄组的死亡率降低，而低估较年长年龄组的死亡率降低。在实践中，我们的建议是，李-卡特模型应该表述为两个(或多个)因素模型，其中一个因素是确定性的，其他因素是随机的，而不是单因素模型。这个特性可以概括为从各个方向扩展Lee-Carter模型的模型范围。