Connectedness of high-frequency data

• Thesis title in Czech: Propojenost vysokofrekvenčních dat
• Thesis title in English: Connectedness of high-frequency data
• Key words: Vektorová autoregrese, Hawkesovy procesy, Vysokofrekvenční analýza, Propojenost
• English key words: Vector Autoregression, Hawkes process, High-frequency analysis, Connectedness
• Academic year of topic announcement: 2014/2015
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Institute of Economic Studies (23-IES)
• Supervisor: Mgr. Tomáš Křehlík, Ph.D.
• Author: hidden - assigned by the advisor
• Date of registration: 05.06.2015
• Date of assignment: 05.06.2015
• Date and time of defence: 15.09.2016 00:00
• Venue of defence: IES
• Date of electronic submission: 27.07.2016
• Date of proceeded defence: 15.09.2016
• Opponents: Ing. Aleš Maršál, Ph.D.

References

- Al-Deehani, Talla, and Imad A. Moosa. ;Volatility spillover in regional emerging stock markets: a structural time- series approach.; Emerging Markets Finance and Trade 42, no. 4 (2006): 78-89.
- Bauwens, Luc, and Nikolaus Hautsch. Modelling financial high frequency data using point processes. Springer Berlin Heidelberg, 2009.
- Bacry, Emmanuel, Iacopo Mastromatteo, and Jean-François Muzy. ;Hawkes processes in finance.; arXiv preprint arXiv:1502.04592 (2015).
- Booth, G. Geoffrey, Teppo Martikainen, and Yiuman Tse.;Price and volatility spillovers in Scandinavian stock markets." Journal of Banking; Finance 21, no. 6 (1997): 811-823.
- Diebold, Francis X., and Kamil Yilmaz. ;Measuring financial asset return and volatility spillovers, with application to global equity markets*.; The Economic Journal 119, no. 534 (2009): 158-171.
- Liniger, Thomas Josef. Multivariate hawkes processes; PhD diss., Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 18403, 2009, 2009.

Preliminary scope of work in English

Motivation:
At the beginning modelling of market behaviour was done by the simplest methods possible, by linear modelling. Every prediction was based only on some weighted previous values. After that economists started using more complex, non-linear modelling as it provided better prediction values. They started to measure connectedness of time series, which can explain how observed series are connected and how shock transfers through them. We will continue with this evolution and we will try to provide even better measure using methods designed for high- frequency data and trading.
In recent studies [Al-Deehani and Moosa 2007; Booth at el. 1997] researchers started to estimating spill-over effects, which describes how are multinomial series influenced by their factors. However, when using lower- frequency data, estimated values can be influenced by feedback between series. This can occur, as multiple signals can travel between series within one sampling window. This can possibly happen even when 1-day data are used and when this happens, results can suggest that series are connected together and influence each other, when in fact only one series cause changes in the second one. We are therefore using high-frequency data, in which we should be able to precisely detect direction in which the influence goes. Intra-day data feedback, if exist, should occur later then initial change, and we should be able to capture that and estimate the effects appropriately. If we find that our estimates are different from those obtained from daily or slower data, we can claim, that there exist some intra-day influences and we are able to detect them and for example our prediction for future values should account for them. This need for models that capture within day price changes are driven by real world development of the markets. As operations on the markets are faster than ever before, it is not enough to base our model on daily values, we have to capture all changes made by high-frequency trading to model them, since they can contain important informations about market dynamics.
Since we are using intra-day data we can also, as an addition to standard time-series methods, use mathematical method based on continuous time and point processes. The Hawkes process. This process is suitable for changes that occur rather randomly in time and can be observed in exact time, when they occur and not only in specific sampling periods. [Liniger 2009] For purpose of continuous modelling it is no longer possible to use standard time- series methods. And vice versa, for normal time-series data it is not possible to use Hawkes methodology. So we are interested what are the results of continuous modelling and if they differ from discrete models. And if we can find difference in estimated coefficients there is probably also some information hidden in time which are lost, when data-frame with fixed observation periods is created.
Our main concern will be influence between cash indices. If we can find some cross-correlation, spillover effect between them and if this spillovers are similar with branching coefficients which are obtained from continuous modelling.
Methodology:
The first step will be synchronizing data into data frame with fixed sampling. Then we will use Vector auto- regression (VAR) and Generalized autoregressive conditional heteroskedasticity (GARCH) multi-variable models to obtain correlation between indices. Output from this part should be cross-correlation matrix in which we can see, how each of the series influence itself and also others. This between influence will be of our main interest.
In the second part we will be fitting Hawkes process on the same dataset. Hawkes process have as parameter of our interest the branching coefficient. This, similarly as in the first part, determines how much of the influence is reflected in subsequent observation.
Expected contribution:
The published studies already covered the spillover effect of time series, however sampling of this series are daily or less frequent. Our contribution therefore is providing evaluation of this effect on high-frequency sample. We can also compare how this effects differ. If we can find statistical difference between spillover estimates, we can then state, that low-frequency analysis is omitting some crucial part of the information.
Secondly we would like to use Hawkes process, which is build for continuous time, to address possible differences or problems in standard spillover computation. Branching coefficient in Hawkes process is direct analogy to cross- correlation, and therefore we can compare them.
Hypotheses:
1. Hypothesis #1: The existence of spillovers in high-frequency data between cash indices.
2. Hypothesis #2: The branching coefficients are non-zero.
3. Hypothesis #3: The indifference between spillovers and branching coefficients