We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, measured on a ratio scale, which aims at enforcing two essential features: additivity and orthogonality of the components. The posterior mean and variance of the seasonally adjusted series...

The paper derives an algorithm for computing leave-k-out diagnostics for the detection of patches of outliers for stationary and nonstationary state-space models with regression effects. The algorithm is based on a reverse run of the Kalman filter on the smoothing errors and is both efficient...

A univariate first-order stochastic cycle can be represented as an element of a bivariate first-order vector autoregressive process, or VAR(1), where the transition matrix is associated with a rotation along a circle in the plane, and the reduced form is ARMA(2,1). This paper generalizes this...