Seasonality with Trend and Cycle Interactions in Unobserved Components Models
提出一种非线性非观测成分时间序列模型，允许趋势-周期成分与季节性成分交互作用，用扩展卡尔曼滤波估计，应用于英国旅行数据和美国失业率与生产序列，能捕捉递增的季节变异和周期依赖的季节波动。
Summary Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, which is often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear–additive framework may be too restrictive. We formulate a non-linear unobserved components time series model which allows interactions between the trend–cycle component and the seasonal component. The resulting model is cast into a non-linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle-dependent seasonal fluctuations.