This paper investigates models for the euro exchange rate against the currencies of Denmark, Poland, theUnited States, and the United Kingdom. The objective of this paper is to compare different methods of modeling andout-of-sample forecasting. One of the techniques is cointegration relation, which is implemented through a vector errorcorrection model. The existence of cointegration supports the long-run relationship between the nominal exchange rateand a number of fundamental variables. The evidence presented in this paper shows that a simple multivariate randomwalk model tends to have superior predictive performance, compared to other exchange rate models, for a period of lessthan one year.

We propose a new test statistic MR ,n for detecting a changed segment in the mean, at unknown dates, in a regularly varying sample. Our model supports several alternatives of shifts in the mean, including one change point, constant, epidemic and linear form of a change. Our aim is to detect a short length changed segment * , assuming * ∕n to be small as the sample size n is large. MR ,n is built by taking maximal ratios of weighted moving sums statistics of four sub-samples. An important feature of MR ,n is to be scale free. We obtain the limiting distribution of ratio statistics under the null hypothesis as well as their consistency under the alternative. These results are extended from i.i.d. samples under H 0 to some dependent samples. To supplement theoretical results, empirical illustrations are provided by generating samples from symmetrized Pareto and Log-Gamma distributions. KeywordsChange-point detection • Changed segment in the mean • Epidemic change • Hölder norm statistics • Regularly varying random variables • Scan statistics Mathematics Subject Classification (2000) 62G10 • 60F17

We present a functional data analysis approach to modeling and analyzing daily tax revenues. The main features of daily tax revenue we need to extract are some patterns within calendar months which can be used for prediction. As standard seasonal time series techniques cannot be used due to varying number of banking days per calendar month and presence of seasonality between and within months we interpret monthly tax revenues as curves obtained from daily data. Standard smoothing techniques and registration taking into account time variability are used for data preparation.