Transition Periods and Long Memory Property

• Název práce v češtině: Období přeměn a dlouhá paměť dat
• Název v anglickém jazyce: Transition Periods and Long Memory Property
• Klíčová slova: frakční integrace, dlouhá paměť dat, strukturální změny
• Klíčová slova anglicky: fractional integration, long memory, structural break, clustering
• Akademický rok vypsání: 2012/2013
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: Mgr. Lukáš Vácha, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 19.06.2013
• Datum zadání: 19.06.2013
• Datum a čas obhajoby: 22.06.2015 00:00
• Místo konání obhajoby: IES
• Datum odevzdání elektronické podoby: 14.05.2015
• Datum proběhlé obhajoby: 22.06.2015
• Oponenti: Mgr. Petr Polák, M.Sc., Ph.D.

Předběžná náplň práce v anglickém jazyce

In my diploma thesis I intend to examine and discuss the topic of long memory property, which can be generated either by an I(d) process present in the data or by structural breaks. Granger & Hyung (2004) show in their paper that these two phenomenons are easy to be mistakenly interchanged when trying to identify the data generating process and the cause of the long memory, which fact leads to decreased forecasting performance. To demonstrate the complication, authors employ a simple occasional break model and test the simulated data for an I(d) process. In the theis, I intend to introduce a group of more sophisticated models for structural breaks, examining outcomes of tests for long memory processes and their dependence on parameters of the models.

A question of highest interest to me is the consequence of structural breaks’ clustering, i.e. of occurrence of certain transition periods, and its impact on the long memory properties estimated in the simulated data. The two possibilities as seen prior to doing the research are:
1) When the breaks happen in ‘groups’ (clustered together), their effect corresponds to one of a proportionally magnified break (or diminished, based on the direction of particular changes), as on bigger scale they can be perceived as one turbulence. However as we are speaking of clustering of breaks, i.e. grouping them together in time, the aggregate change remains unaffected and so do the overall properties of data including the long memory. Such scenario would be in line with the research of Granger & Hyung (2004), and the simple occasional break model with shifts in mean would be an efficient generalization.
2) From the point of view of spectral analysis, different degree of clustering introduces differently low ‘frequency’ to the data (meant as a consequence for the long memory estimation). In that case I would attempt to identify some basic pattern and find the rationale behind it.

There are more parameters to be adjusted, such as the degree of ‘volatility clustering’ (or in general probability of occurrence dependent on size of previous break), the lag of probability dependence or shifts in volatility. In all cases there will be danger of introducing a non-linearity to the model or breaking some other assumption which will have to be considered.

Dependent on the extent and difficulty of the above described research I will consider employing the STAR (Smooth Transition Autoregressive) model to define the progress of the transition period, getting closer to real world situations when not all changes happen in form of sudden breaks.
Furthermore, having the simulated data from the various data generating processes there is an option of extending the research to test performance of the method introduced by Wang, Bauwens & Hsiao (2012) on the data with clustered breaks. Their AR-based approach is suited for forecasting an ARFIMA process with unknown dates of shifts to mean and to long memory parameter. I will possibly test the performance of this approach on the processes with changes distributed based on rules specified in the above described part of my thesis.
My thesis will contribute to the current state of research by elaborating on very up-to-date and frequently cited working papers and by extending and detailing their conclusions.