Cryptocurrencies have recently experienced a new wave of price volatility and interest; activity within social media communities relating to cryptocurrencies has increased significantly. There is currently limited documented knowledge of factors which could indicate future price movements. This paper aims to decipher relationships between cryptocurrency price changes and topic discussion on social media to provide, among other things, an understanding of which topics are indicative of future price movements. To achieve this a well-known dynamic topic modelling approach is applied to social media communication to retrieve information about the temporal occurrence of various topics. A Hawkes model is then applied to find interactions between topics and cryptocurrency prices. The results show particular topics tend to precede certain types of price movements, for example the discussion of 'risk and investment vs trading' being indicative of price falls, the discussion of 'substantial price movements' being indicative of volatility, and the discussion of 'fundamental cryptocurrency value' by technical communities being indicative of price rises. The knowledge of topic relationships gained here could be built into a real-time system, providing trading or alerting signals.
In recent years, there has been a surge in demand for statistical tools for analyzing dynamic networks involving point processes. This has been driven largely by the availability of high-dimensional data in a number of application areas such as systems neuroscience and stochastic finance. Given some network data, an extremely challenging problem is to infer the causal dependencies between nodes to reconstruct the network. The high volume and decentralized storage of such data poses new challenges for analysis. Here we develop for the first time a distributed optimization algorithm based on the point process likelihood for dynamic networks of interacting Hawkes processes. We demonstrate the algorithm using genomic data to construct a transcriptional regulatory network in embryonic stem cells and tick-level financial data to construct an influence map of major currencies.
This thesis discusses symmetric random walk, its definition and basic properties. The outset is focused on the probabilistic model and subsequently on basic properties, such as the final position at time n, its mean value and variance. Furthermore, we will see what the scaling must be for the walk to converge to zero, precisely what is the consequence of the strong law of large numbers. In the second chapter we will examine the distribution of the maximum of the symmetric random walk. In chapter 3 we will define stopping time and Markov property of random walks. Then we proof many auxiliary lemmas using basic knowledge of combinatorics. The final part is devoted to the proof of the arcsine distribution, which shows great persistence of the symmetric random walk. Powered by TCPDF (www.tcpdf.org)