Multifractal analysis of petrol and diesel prices in the Czech Republic

• Název práce v češtině: Multifraktální analýza cen benzínu a motorové nafty v České republice
• Název v anglickém jazyce: Multifractal analysis of petrol and diesel prices in the Czech Republic
• Klíčová slova: benzín, diesel, fraktální analýza, multifraktální analýza, autokorelace, dlouhá paměť
• Klíčová slova anglicky: petrol, diesel, fractal analysis, multifractal analysis, auto-corellation, long memory
• Akademický rok vypsání: 2011/2012
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: prof. PhDr. Ladislav Krištoufek, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 07.06.2012
• Datum zadání: 07.06.2012
• Datum a čas obhajoby: 11.09.2013 00:00
• Místo konání obhajoby: IES
• Datum odevzdání elektronické podoby: 24.07.2013
• Datum proběhlé obhajoby: 11.09.2013
• Oponenti: doc. PhDr. Martin Gregor, Ph.D.

Seznam odborné literatury

Di Matteo, T., T. Aste & M. Dacarogna (2005): "Long-term memories of devel-
oped and emerging markets: Using the scaling analysis to characterize their stage of
development." Journal of Banking & Finance 29(4): pp. 827-851.

Di Matteo, T. (2007): "Multi-scaling in �nance." Quantitative Finance 7(1): pp.
21-36.

Kantelhardt, J. W. (2008): "Fractal and Multifractal Time Series" Institute of
Physics, Martin-Luther-University.

Předběžná náplň práce

Topic characteristics
The thesis will focus on multifractal analysis of changes
in price of petrol and diesel in the Czech Republic. Starting from raw time
series of prices, which would need to be adjusted for taxes to be usable for our
analysis, since both petrol and diesel are heavily taxed. The auto-correlation
function would suggest strong signi�cance with long lags. Using common sense
only, one would expect them to show the same behavior as crude oil, the core
element of both fuels. However, crude oil market is much more e�cient and
does not show the same long memory as fuels. This suggests that both fuels
are fractal processes. We will try to �nd a proper model for the time series
using both fractal and multifractal analytics. To the author's best knowledge,
this kind of analysis has not been performed with the fuel prices yet.

Hypotheses
At this early stage of the research, we expect the changes in
petrol and diesel prices to be strongly auto-correlated. To have long memory
and thick tailed distributions. Additionally, the time series are expected to be
multifractal.

Methodology
The time series cover long time data of petrol and diesel retail
prices for the Czech Republic. To analyze them thoroughly adjustments for
taxes will be required, because both excise tax and value added tax have been
changed during the time window. Further, the time series will be examined
via variance scaling, AutoRegressive Fractionally Integrated Moving Average
(ARFIMA) and Maximum Likelihood Estimator (MLE).

Outline
1. Introduction
2. Theoretical Background
3. Related Work
4. The Model
5. Empirical Veri�cation
6. Conclusion

Předběžná náplň práce v anglickém jazyce

Topic characteristics
The thesis will focus on multifractal analysis of changes
in price of petrol and diesel in the Czech Republic. Starting from raw time
series of prices, which would need to be adjusted for taxes to be usable for our
analysis, since both petrol and diesel are heavily taxed. The auto-correlation
function would suggest strong signi�cance with long lags. Using common sense
only, one would expect them to show the same behavior as crude oil, the core
element of both fuels. However, crude oil market is much more e�cient and
does not show the same long memory as fuels. This suggests that both fuels
are fractal processes. We will try to �nd a proper model for the time series
using both fractal and multifractal analytics. To the author's best knowledge,
this kind of analysis has not been performed with the fuel prices yet.

Hypotheses
At this early stage of the research, we expect the changes in
petrol and diesel prices to be strongly auto-correlated. To have long memory
and thick tailed distributions. Additionally, the time series are expected to be
multifractal.

Methodology
The time series cover long time data of petrol and diesel retail
prices for the Czech Republic. To analyze them thoroughly adjustments for
taxes will be required, because both excise tax and value added tax have been
changed during the time window. Further, the time series will be examined
via variance scaling, AutoRegressive Fractionally Integrated Moving Average
(ARFIMA) and Maximum Likelihood Estimator (MLE).

Outline
1. Introduction
2. Theoretical Background
3. Related Work
4. The Model
5. Empirical Veri�cation
6. Conclusion