Improving Rozanov (1967, Stationary Random Processes. San Francisco: Holden-day.)'s algebraic-analytic solution to the canonical factorization problem of the rational spectral density matrix, this article presents a feasible computational procedure for the spectral factorization. We provide...

In the case of state space models with an unknown initial condition, the diffuse Kalman smoother can be used to obtain smoothed state estimates. When the full initial state is not estimable because the available data are insufficient, some linear combinations of the states can still be...

In this article, we look again at the derivation of Black-Scholes option value equation. The risk function involved, as we discussed, if looked at more closely, is more complicated than the standard deviation function that people are used to. This observed risk function implies interesting...

This article examines the behaviour of some recently proposed 'robust' (to the order of integration of the data) tests for the presence of a deterministic linear trend in a univariate times series in situations where the magnitude of the initial condition of the series is non-negligible. We...

Quantiles provide a comprehensive description of the properties of a variable, and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how departures from strict stationarity can be detected using stationarity tests based on weighted...

For purposes such as rate setting and long-term capacity planning, electrical utility companies are interested in dividing their customers into homogeneous groups or clusters in terms of the customers' electricity demand profiles. Such demand profiles are typically represented by load series,...

In this article we consider a CHARME model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. To provide sets of conditions under which such processes are geometrically ergodic and, therefore, satisfy some mixing conditions, we apply the theory of Markov chains to...

We study the problem of intervention effects generating various types of outliers in a linear count time-series model. This model belongs to the class of observation-driven models and extends the class of Gaussian linear time-series models within the exponential family framework. Studies about...