Essays in finance: time-frequency decompositions and the impact of surprise

Abstract

In the first part of this thesis, we study the informative value of time-frequency decompositions based on wavelets. In chapter 2 we address the challenge of forecasting major stock indices. For the binary classification task, we identify three wavelet filters out of fifteen, namely $D4$, $D6$ and $CF6$, which outperform the naive approach. We exemplify the performance of the forecasting algorithm by simulating a trading application in which the wavelet-based approach outperforms the naive strategy by a factor of about two in terms of Sharpe ratio. In chapter 3 we study the transmission processes between the European stock markets and the nominal European exchange rate. To effectively distinguish between contagion and interdependence we estimate the spectral characteristics of the time series as a function of time and frequency using a continuous wavelet transform. This approach allows to reveal linkages and co-movement patterns, including lead-lag relationships, between periodic components. The empirical results support both cyclical and anti-cyclical relationships between the time-series while existing casual and reverse casual relation vary across scale and time. We strongly emphasize the limitations of a bivariate approach and encourage the conduction of a multivariate analysis to revisit our findings. In the second part of the thesis, namely chapter 4, we aim to quantify the level of surprise in events published on Twitter. The proposed methodology maps the informational content of every Twitter account belonging to at least one S\&P500 constituent into a network. This approach allows to observe the formation of events and to quantify its propagation on an aggregate level. In a regression analysis, we investigate whether the proposed surprise metric has any explanatory power for the SP500 logarithmic returns and volatility. We find that an increase in the surprise index has an inverse effect on daily returns and a positive impact on the daily volatility. Moreover, the results support the hypothesis of a pre-report effect for both the return and volatility models. Future work might also explore the limits of a multivariate approach to analyze directional interdependence and contagion patterns at different time scales. Considering deep neural network embeddings to reduce the dimensionality of frequency decompositions is one of the next steps in this research.