Title: Fractional unobserved components models
Authors: Tobias Hartl - University of Regensburg (Germany) [presenting]
Abstract: The decomposition of time series into trend and cycle is addressed for the general state space model $y_t = x_t + c_t$, where $c_t$ represents a stationary cyclical component, the $d$-th difference of the trend $x_t$ is assumed to be a stationary martingale difference sequence, and both $x_t$ and $c_t$ are unobserved. The model allows for $d$ in the set of positive real numbers, thus generalizes unobserved components models to fractionally integrated trends, and does not require any prior knowledge about $d$. A closed-form solution for the estimation of trend and cycle is provided and is identical to the Kalman filter and smoother but computationally superior. In addition, a conditional sum-of-squares estimator allowing for the joint estimation of $d$ together with all other model parameters is introduced and is shown to be consistent. Monte Carlo studies reveal good estimation properties of the proposed estimators for parameters and unobserved components in finite samples, both in comparison to nonparametric estimators and integer-integrated unobserved components models. The practical benefits of the new methods are demonstrated in several applications, among others, to global temperature curves.