This article presents a robust augmented Kalman filter that extends the data-cleaning filter (Masreliez and Martin, 1977) to the general state space model featuring nonstationary and regression effects. The robust filter shrinks the observations towards their one-step-ahead prediction based on...

Representation of continuous-time ARMA, CARMA, models is reviewed. Computational aspects of simulating and calculating the likelihood-function of CARMA are summarized. Some numerical properties are illustrated by simulations. Some real data applications are shown. -- CARMA ; maximum-likelihood ;...

There is growing literature in macroeconomics, especially on business cycle synchronization, employing different methods of time series clustering. However, even as an unsupervised learning method, this technique requires making choices that are nontrivially influenced by the nature of the data...

Many complex systems display fluctuations between alternative states in correspondence to tipping points. These critical shifts are usually associated with generic empirical phenomena such as strengthening correlations between entities composing the system. In finance, for instance, market...

The data mining technique of time series clustering is well established in many fields. However, as an unsupervised learning method, it requires making choices that are nontrivially influenced by the nature of the data involved. The aim of this paper is to verify usefulness of the time series...

We propose a new approach to deal with structural breaks in time series models. The key contribution is an alternative dynamic stochastic specification for the model parameters which describes potential breaks. After a break new parameter values are generated from a so-called baseline prior...

Trend extraction from time series is often performed by using the filter proposed by Leser (1961), also known as the Hodrick-Prescott filter. Practical problems arise, however, if the time series contains structural breaks (as produced by German unification for German time series, for instance),...

We consider an extension of the variance-gamma process implying that the linear drift rate of the process can switch suddenly by a jump. The value of jump is modeled by the multidimensional distribution, the jump time is simulated by the exponential distribution. Together with the simplest...