Abstract The damped trend model is a strong benchmark for time series forecasting. This model is usually estimated by adopting the innovations approach rather than the structural one, since the latter is more complex, requiring the use of the Kalman filter. In this paper, we introduce a simple method for estimating the damped trend using the structural approach. The proposed method relies on the analytical solution to the algebraic Riccati equation for the covariance matrix of the state vector’s estimation error. The solution fully simplifies both the Kalman filter recursions and the likelihood evaluation. The likelihood evaluation using the proposed method actually becomes very similar to that of the innovations approach. Moreover, the solution facilitates the smoothing of the state vector, which is crucial for signal extraction. A Monte Carlo simulation shows that both innovations and structural approaches have a similar out-of-sample forecasting performance. This is also confirmed empirically by working with the annual time series from the M3-competition database and with quarterly time series on total credit to the non-financial sector relative to GDP published by the Bank for International Settlements.

中文翻译：

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使用结构方法使用阻尼趋势模型进行预测

摘要 阻尼趋势模型是时间序列预测的有力基准。该模型通常通过采用创新方法而不是结构方法来估计，因为后者更复杂，需要使用卡尔曼滤波器。在本文中，我们介绍了一种使用结构方法估计阻尼趋势的简单方法。所提出的方法依赖于状态向量估计误差的协方差矩阵的代数Riccati方程的解析解。该解决方案完全简化了卡尔曼滤波器递归和似然评估。使用所提出的方法的可能性评估实际上变得非常类似于创新方法的可能性评估。此外，该解决方案有助于状态向量的平滑，这对于信号提取至关重要。蒙特卡罗模拟表明，创新方法和结构方法都具有相似的样本外预测性能。通过使用 M3 竞争数据库中的年度时间序列和国际清算银行公布的非金融部门总信贷相对于 GDP 的季度时间序列，这也得到了实证证实。