Measuring high-frequency phase shifts between stock markets

• Název práce v češtině: Měřění vysokofrekvenčních posunů na finančních trzích
• Název v anglickém jazyce: Measuring high-frequency phase shifts between stock markets
• Klíčová slova: Spektrální analýza, vlnková analýza, akciové trhy, fázový posun, kauzalita
• Klíčová slova anglicky: spectral analysis, wavelets, stock markets, phase difference, causality
• Akademický rok vypsání: 2015/2016
• 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: 17.06.2016
• Datum zadání: 17.06.2016
• Datum a čas obhajoby: 16.01.2019 09:00
• Místo konání obhajoby: Opletalova - Opletalova 26, O105, Opletalova - místn. č. 105
• Datum odevzdání elektronické podoby: 03.01.2019
• Datum proběhlé obhajoby: 16.01.2019
• Oponenti: doc. Bc. Jiří Novák, M.Sc., Ph.D.

Seznam odborné literatury

BARUNÍK, Jozef, and Lukáš VÁCHA. "Contagion among Central and Eastern European Stock Markets during the Financial Crisis." Czech Journal of Economics and Finance (Finance a uver) 63.5 (2013): 443-453.
CANDELON, Bertrand; HECQ, Alain; VERSCHOOR, Willem FC. Measuring common cyclical features during financial turmoil: Evidence of interdependence not contagion. Journal of International Money and Finance, 2005, 24.8: 1317-1334.
CAZELLES, Bernard, et al. Wavelet analysis of ecological time series. Oecologia, 2008, 156.2: 287-304.
FISCHER, Klaus P.; PALASVIRTA, A. P. High road to a global marketplace: the international transmission of stock market fluctuations. Financial Review, 1990, 25.3: 371-394.
GRAHAM, Michael; KIVIAHO, Jarno; NIKKINEN, Jussi. Integration of 22 emerging stock markets: A three-dimensional analysis. Global Finance Journal, 2012, 23.1: 34-47.
LOH, Lixia. Co-movement of Asia-Pacific with European and US stock market returns: A cross-time-frequency analysis. Research in International Business and Finance, 2013, 29: 1-13.
REBOREDO, Juan C.; RIVERA-CASTRO, Miguel A.; UGOLINI, Andrea. Wavelet-based test of co-movement and causality between oil and renewable energy stock prices. Energy Economics, 2017, 61: 241-252.
TORRENCE, Christopher; WEBSTER, Peter J. Interdecadal changes in the ENSO–monsoon system. Journal of Climate, 1999, 12.8: 2679-2690.
WU, Ming-Chya, et al. Phase distribution and phase correlation of financial time series. Physical Review E, 2006, 73.1: 016118.

Předběžná náplň práce v anglickém jazyce

Motivation:
Information about relationships between stock markets around the world is vital for portfolio management and diversification. Important part of literature has tried to unveil it. Probably the first work finding statistically significant relationship was paper by Fisher and Palasvirta (1990), who found interdependence between several stock markets with U.S. Stock market being the global leader – for example a lag of 48 days of Canadian stock market after U.S. Market. Many others (e.g. Candelon et al. (2005), Loh (2013)) have investigated correlations between stock markets. Interesting findings were presented by Graham et al. (2012), who examined relations ships between emerging markets and U.S. Market, finding evidence of co-movements only for part of the selected countries and consistent over time only for frequencies larger than a year. Above mentioned works have one thing in common – they all explore these relationships on lower frequencies of at most 1 day.

Wu et al. (2006) examined phase difference between NASDAQ and DJIA on inter-day data using Hilbert-Huang method. They find that some big events (9/11 attacks) had in phase reaction, at other periods the two indexes were out-of-phase, with changing relationship over time. For example during 2001 and 2002 DJIA was ahead in phase to NASDAQ, implying that DJIA had greater effect on NASDAQ than vice versa.

Baruník and Vácha (2013) used wavelet methods to explore correlations and contagion of the 2008 crisis across CEE markets. Using high-frequency data they find correlations mainly on lower frequencies. They also report a little evidence of correlations on high frequencies and find it only on longer horizons. Yet the data-set used ends in 2009 and the causality on different scales is not explored in this work.

This work aims to build on existing literature (abovementioned stock index related papers and other papers using useful wavelet methods) and investigate existence and nature of the shift (lead-lag relationship) between stock indexes with focus on czech stock market.

Hypotheses:
• Market indexes are correlated and in phase on higher frequency level among developed countries
• Less developed market indexes (such as Czech or Hungarian) exhibit phase-shift after classical indexes
• There is Granger causality from developed to developing stock exchanges at some frequency which is increasing over time (lag is diminishing)
Methodology:
Data I will use for this thesis will be PX, BUX, DAX, FTSE and maybe other indexes and will be obtained from Charles university database. Then high-frequency price data will be converted to 5-minutes data – such high frequency should open the possibility to explore all shifts in the data.

To test the hypotheses, I will use spectral methods, mainly wavelets. For the start, we will follow methodology used by Cazelles et al. (2008) and Torrence et al. (1999), which give us good information about dependence structure of examined markets in time-frequency domain. Later, we may extend our methods to general frequency domain with moving vindows. Wavelets, unlike Fourier analysis, offer possibility to analyse time series both in time and frequency domains. This will allow observation of time-evolution of the frequency relationships. Anchor method is going to be wavelet phase coherency that measures how out-of-phase is one signal (time-series) compared to anoher on different scales.

Following Reboredo (2017), I will use Granger (1969) causality test (linear and non-linear) to further explore the dependencies in the time series. After trasforming the series using discrete wavelet transform (which will decompose the series into different time-scales with shortest being in 10-minutes frequency (capturing 5-minute moves)), it will be possible to learn more about the causality between the indexes. That should also help to investigate if the difference is diminishing – the causality is expected to shift across scales and parts of the data sample.

Other methods will be added during the work to increase robustness of the results. There is a possibility to use abovementioned Hilbert-Huang method and many others. Possible extension added throughout the work might be observing influence of the volatility (and other features of the indexes, such as assymetricity of responses dependent on the sign of the returns) on the results.
Expected Contribution:
This work will asses the question of possible phase difference between stock markets with different level of development. Wavelet analysis brings slightly different approach than classical econometrics since it works in time-frequency domain and thus will allow me to explore causality and shifts not only on the entire series, but also on its diferent scales (frequencies). That will allow us to understand the relationship more deeply and might serve as tool to exploit the interdependencies between the markets.
Since the thesis is expected to bring new information about stock indexes it might be useful for both portfolio analysts and policy makers.
Outline:
Introduction
Literature review – here I will asses existing literature related to the topic with focus both on the global stock markets convergence and correlations and previous use of the methodology use in following part
Data and Methodology – In this part I will provide summary statistics of the data, deal with possible shortcomings and thoroughly introduce the methods that will be used in this work (such as continuous and discrete wavelet transform, wavelet power spectrum, wavelet phase coherency, granger linear and non-linear causality etc.)
Empirical Results – this chapter will be divided into several parts explaining what has been found in all the methods that will be used and provide evidence for (or against) the hypotheses stated.
Conclusion