We explore a periodic analysis in the context of unobserved components time series models that decompose time series into components of interest such as trend and seasonal. Periodic time series models allow dynamic characteristics to depend on the period of the year, month, week or day. In the...

We model 1981-2002 annual US default frequencies for a panel of firms in different rating and age classes. The data is decomposed into a systematic and firm-specific risk component, where the systematic component reflects the general economic conditions and default climate. We have to cope with...

To gain insights in the current status of the economy, macroeconomic time series are often decomposed into trend, cycle and irregular components. This can be done by nonparametric band-pass filtering methods in the frequency domain or by model-based decompositions based on autoregressive moving...

Risk is at the center of many policy decisions in companies, governments and other institutions. The risk of road fatalities concerns local governments in planning counter- measures, the risk and severity of counterparty default concerns bank risk managers on a daily basis and the risk of...

The failure to describe the time series behaviour of most realexchange rates as temporary deviations from fixedlong-term means may be due to time variation of the equilibriathemselves, see Engel (2000). We implement thisidea using an unobserved components model and decompose theobservations on...

The linear Gaussian state space model for which the common variance istreated as a stochastic time-varying variable is considered for themodelling of economic time series. The focus of this paper is on thesimultaneous estimation of parameters related to the stochasticprocesses of the mean part...

D-order processes is a sort of important stochastic processes, it is a class of useful stochastic processes in practices, its study is very value. In this paper, we study 1-order processes using haar wavelet and wavelet transform on R. We study its some properties and wavelet expansion.