In this study, we model realized volatility constructed from intra-day high-frequency data. We explore the possibility of confusing long memory andstructural breaks in the realized volatility of the following spot exchange rates: EUR/USD, EUR/JPY, EUR/CHF, EUR/GBP, and EUR/AUD. The resultsshow evidence for the presence of long memory in the exchange rates’ realizedvolatility. From the Bai–Perron test, we found structural breakpoints that matchsignificant events in financial markets. Furthermore, the findings provide strongevidence in favour of the presence of long memory.
The aim of this contribution is to derive a general matrix formula for the net period premium paid in more than one state. In order to avoid “overpayment” which implies higher premiums we give a formula for replacement of lump sum benefit into annuity benefits paid in more than one state. The obtained result is useful for example to more advanced models of dread disease insurances allowing period premiums paid by both healthy and ill person (e.g. not terminally yet). As an application, we supply analysis of dread disease insurances against the risk of lung cancer based on the actual data for the Lower Silesian Voivodship in Poland.
In economics we often face a system which intrinsically imposes a structure of hierarchy of its components, i.e., in modeling trade accounts related to foreign exchange or in optimization of regional air protection policy. A problem of reconciliation of forecasts obtained on different levels of hierarchy has been addressed in the statistical and econometric literature many times and concerns bringing together forecasts obtained independently at different levels of hierarchy. This paper deals with this issue with regard to a hierarchical functional time series. We present and critically discuss a state of art and indicate opportunities of an application of these methods to a certain environment protection problem. We critically compare the best predictor known from the literature with our own original proposal. Within the paper we study a macromodel describing the day and night air pollution in Silesia region divided into five subregions.
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