Two-step estimators of high-dimensional correlation matrices.

We investigate block diagonal and hierarchical nested stochastic multivariate Gaussian models by studying their sample cross-correlation matrix on high dimensions. By performing numerical simulations, we compare a filtered sample cross-correlation with the population cross-correlation matrices by using several rotationally invariant estimators (RIEs) and hierarchical clustering estimators (HCEs) under several loss functions. We show that at large but finite sample size, sample cross-correlations filtered by RIE estimators are often outperformed by HCE estimators for several of the loss functions. We also show that for block models and for hierarchically nested block models, the best determination of the filtered sample cross-correlation is achieved by introducing two-step estimators combining state-of-the-art nonlinear shrinkage models with hierarchical clustering estimators.

LSTM-GARCH Hybrid Model for the Prediction of Volatility in Cryptocurrency Portfolios.

In the present work, the volatility of the leading cryptocurrencies is predicted through generalised autoregressive conditional heteroskedasticity (GARCH) models, multilayer perceptron (MLP), long short-term memory (LSTM), and hybrid models of the type LSTM and GARCH, where parameters of the GARCH family are included as features of LSTM models. The study period covered the scenario of the World Health Organization pandemic declaration around March 2020 at hourly frequency. We have found that the different variants of deep neural network models outperform those of the GARCH family in the sense of the hetorerocedastic error, and absolute and squared error (HSE). Under the sharpe ratio, the volatility forecasting of a uniform portfolio at long horizons systematically outperforms the stablecoin Tether, which is considered here as the risk-free asset. Also, including transaction volume helps reduce the value at risk or loss probability for the uniform portfolio. Moreover, in a minimum variance portfolio, it is observed that before the pandemic declaration, a large proportion of the capital was allocated to bitcoin (BTC). In contrast, after March 2020, the portfolio is more diversified with short positions for BTC. Moreover, the MLP models give the best predictive results, although not statistically different in accuracy compared to the LSTM and LSTM-GARCH versions under the Diebold-Mariano test. In sum, MLP models outperform most stylised financial models and are less computationally expensive than more complex neural networks. Therefore, simple learning models are suggested in highly non-linear time series volatility forecasts as it is the cryptocurrency market.

What Drives Bitcoin? An Approach from Continuous Local Transfer Entropy and Deep Learning Classification Models.

Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins' price direction under the continuous transfer entropy approach as a feature selection criterion. Accordingly, the statistically significant assets in the sense of permutation test on the nearest neighbour estimation of local transfer entropy are used as features or explanatory variables in a deep learning classification model to predict the price direction of bitcoin. The proposed variable selection do not find significative the explanatory power of NASDAQ and Tesla. Under different scenarios and metrics, the best results are obtained using the significant drivers during the pandemic as validation. In the test, the accuracy increased in the post-pandemic scenario of July 2020 to January 2021 without drivers. In other words, our results indicate that in times of high volatility, Bitcoin seems to self-regulate and does not need additional drivers to improve the accuracy of the price direction.

Measuring information flux between social media and stock prices with Transfer Entropy.

Transfer Entropy was applied to analyze the correlations and flow of information between 200,500 tweets and 23 of the largest capitalized companies during 6 years along the period 2013-2018. The set of tweets were obtained applying a text mining algorithm and classified according to daily date and company mentioned. We proposed the construction of a Sentiment Index applying a Natural Processing Language algorithm and structuring the sentiment polarity for each data set. Bootstrapped Simulations of Transfer Entropy were performed between stock prices and Sentiment Indexes. The results of the Transfer Entropy simulations show a clear information flux between general public opinion and companies' stock prices. There is a considerable amount of information flowing from general opinion to stock prices, even between different Sentiment Indexes. Our results suggest a deep relationship between general public opinion and stock prices. This is important for trading strategies and the information release policies for each company.

Multistage allocation problem for Mexican pension funds.

The problem of multistage allocation is solved using the Target Date Fund (TDF) strategy subject to a set of restrictions which model the latest regulatory framework of the Mexican pension system. The investment trajectory or glide-path for a representative set of 14 assets of heterogeneous characteristics is studied during a 161 quarters long horizon. The expected returns are estimated by the GARCH(1,1), EGARCH(1,1), GJR-GARCH(1,1) models, and a stationary block bootstrap model is used as a benchmark for comparison. A fixed historical covariance matrix and a multi-period estimation of DCC-GARCH(1,1) are also considered as inputs of the objective function. Forecasts are evaluated through their asymmetric dependencies as quantified by the transfer entropy measure. In general, we find very similar glide-paths so that the overall structure of the investment is maintained and does not rely on the particular forecasting model. However, the GARCH(1,1) under a fixed historical covariance matrix exhibits the highest Sharpe ratio and in this sense represents the best trade-off between wealth and risk. As expected, the initial stages of the obtained glide-paths are initially dominated by risky assets and gradually transition into bonds towards the end oof the trajectory. Overall, the methodology proposed here is computationally efficient and displays the desired properties of a TDF strategy in realistic settings.

Network Analysis of Multivariate Transfer Entropy of Cryptocurrencies in Times of Turbulence.

We investigate the effects of the recent financial turbulence of 2020 on the market of cryptocurrencies taking into account the hourly price and volume of transactions from December 2019 to April 2020. The data were subdivided into time frames and analyzed the directed network generated by the estimation of the multivariate transfer entropy. The approach followed here is based on a greedy algorithm and multiple hypothesis testing. Then, we explored the clustering coefficient and the degree distributions of nodes for each subperiod. It is found the clustering coefficient increases dramatically in March and coincides with the most severe fall of the recent worldwide stock markets crash. Further, the log-likelihood in all cases bent over a power law distribution, with a higher estimated power during the period of major financial contraction. Our results suggest the financial turbulence induce a higher flow of information on the cryptocurrency market in the sense of a higher clustering coefficient and complexity of the network. Hence, the complex properties of the multivariate transfer entropy network may provide early warning signals of increasing systematic risk in turbulence times of the cryptocurrency markets.

Transfer entropy as a variable selection methodology of cryptocurrencies in the framework of a high dimensional predictive model.

We determine the number of statistically significant factors in a high dimensional predictive model of cryptocurrencies using a random matrix test. The applied predictive model is of the reduced rank regression (RRR) type; in particular, we choose a flavor that can be regarded as canonical correlation analysis (CCA). A variable selection of hourly cryptocurrencies is performed using the Symbolic estimation of Transfer Entropy (STE) measure from information theory. In simulated studies, STE shows better performance compared to the Granger causality approach when considering a nonlinear system and a linear system with many drivers. In the application to cryptocurrencies, the directed graph associated to the variable selection shows a robust pattern of predictor and response clusters, where the community detection was contrasted with the modularity approach. Also, the centralities of the network discriminate between the two main types of cryptocurrencies, i.e., coins and tokens. On the factor determination of the predictive model, the result supports retaining more factors contrary to the usual visual inspection, with the additional advantage that the subjective element is avoided. In particular, it is observed that the dynamic behavior of the number of factors is moderately anticorrelated with the dynamics of the constructed composite index of predictor and response cryptocurrencies. This finding opens up new insights for anticipating possible declines in cryptocurrency prices on exchanges. Furthermore, our study suggests the existence of specific-predictor and specific-response factors, where only a small number of currencies are predominant.