We develop a systematic framework for the joint modelling of returns and multiple daily realised measures. We assume a linear state space representation for the log realised measures, which are noisy and biased estimates of the log daily integrated variance, at least due to Jensen's inequality....

Many seasonal macroeconomic time series are subject to changes in their means and variances over a long time horizon. In this paper we propose a general treatment for the modelling of time-varying features in economic time series. We show that time series models with mean and variance functions...

State space models with nonstationary processes and fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for the estimation of parameters in time series models with diffuse initial conditions. In this paper we consider...

We present a model for hourly electricity load forecasting based on stochastically time-varying processes that are designed to account for changes in customer behaviour and in utility production efficiencies. The model is periodic: it consists of different equations and different parameters for...

We investigate changes in the time series characteristics of postwar U.S. inflation. In a model-based analysis the conditional mean of inflation is specified by a long memory autoregressive fractionally integrated moving average process and the conditional variance is modelled by a stochastic...

The linear Gaussian state space model for which the common variance is treated as a stochastic time-varying variable is considered for the modelling of economic time series. The focus of this paper is on the simultaneous estimation of parameters related to the stochastic processes of the mean...