Skewed non-Gaussian GARCH models for cryptocurrencies volatility modelling

Collective Dynamics, Diversification and Optimal Portfolio Construction for Cryptocurrencies

Since its conception, the cryptocurrency market has been frequently described as an immature market, characterized by significant swings in volatility and occasionally described as lacking rhyme or reason. There has been great speculation as to what role it plays in a diversified portfolio. For instance, is cryptocurrency exposure an inflationary hedge or a speculative investment that follows broad market sentiment with amplified beta? We have recently explored similar questions with a clear focus on the equity market. There, our research revealed several noteworthy dynamics such as an increase in the market's collective strength and uniformity during crises, greater diversification benefits across equity sectors (rather than within them), and the existence of a "best value" portfolio of equities. In essence, we can now contrast any potential signatures of maturity we identify in the cryptocurrency market and contrast these with the substantially larger, older and better-established equity market. This paper aims to investigate whether the cryptocurrency market has recently exhibited similar mathematical properties as the equity market. Instead of relying on traditional portfolio theory, which is grounded in the financial dynamics of equity securities, we adjust our experimental focus to capture the presumed behavioral purchasing patterns of retail cryptocurrency investors. Our focus is on collective dynamics and portfolio diversification in the cryptocurrency market, and examining whether previously established results in the equity market hold in the cryptocurrency market and to what extent. The results reveal nuanced signatures of maturity related to the equity market, including the fact that correlations collectively spike around exchange collapses, and identify an ideal portfolio size and spread across different groups of cryptocurrencies.

Time-varying higher moments in Bitcoin

Cryptocurrencies represent a new and important class of investments but are associated with asymmetric distributions and extreme price changes. We use a modeling structure where higher-order moments (scale, skewness and kurtosis) are time-varying, and additionally we used nontraditional innovations distributions to study the return series of the most important cryptocurrency, Bitcoin. Based on the estimation of a series of Generalized Autoregressive Score (GAS) models, we compare predictive performance using a loss function based on Value at Risk performance.

COVID Asymmetric Impact on the Risk Premium of Developed and Emerging Countries’ Stock Markets

We estimated the stock market risk premium during the COVID-19 pandemic with a GARCH-in-Mean (GARCH-M)(1,1) model. The analysis then explored the presence of regime changes using a two-regime Markov-Switching GARCH (MS GARCH)(1,1) model. The sample we used included the stock market indexes of nine countries from three geographical regions, including: North America (Canada, USA, and Mexico), South America (Brazil and Argentina), and Asia (Japan, South Korea, Hong Kong, and Singapore), over two periods: (a) pre-COVID (from 1 January 2015 to 31 December 2019); and (b) COVID (from 1 January 2020 to 31 December 2021). Our GARCH-M(1,1) estimation results indicate that the more developed countries’ stock markets experienced an important increase in their risk premium during the COVID period, likely explained by the massive government anticyclical policies. By contrast, developing countries’ stock markets, particularly in Latin America, experienced a reduction, and in some cases, even a total loss of the risk premium effect. From the perspective of investors and portfolio risk managers, the identification of high and low volatility periods and their estimated probability of occurrence is useful for the characterization of stress scenarios and the design of emerging strategies. For governments and central bankers, the implementation of different policies should respond to the more likely scenarios but should also be prepared to respond to other less likely scenarios. Institutional preparedness to respond to as many different scenarios as may be identified with the use of MS GARCH models can make their interventions more successful. This work presents an objective example of how the use of MS GARCH models may be of use to practitioners in both the financial industry and government. We confirmed that the results of a two-regime MS GARCH model are superior to those obtained from a single-regime model.

Connectedness among major cryptocurrencies in standard times and during the COVID-19 outbreak

The cryptocurrency markets are perceived as being dominated by Bitcoin leading the overall system dynamics. Although the previous empirical evidence points towards strong connections among selected cryptocurrencies or, from the other side, weak dependence between Bitcoin and traditional financial assets, a focused study on the dynamics of return and volatility connectedness among a wider range of cryptocurrencies is lacking, and more so, one directed towards the very first actual critical period of the global economy coinciding with relevant crypto-markets. Using data for the 10 most capitalized cryptocurrencies between 1st October 2017 and 5th January 2021, we examine how cryptocurrencies interact and whether they have a clear leader, with a special focus on differences with respect to investment horizons and how the relationship structure evolves in time. We uncover a structural change in the connectedness evolving in 2020 as the market restructures in reaction to the unprecedented monetary injections as a counter to the COVID-19-induced economic standstill. The structural change is shown not only for cryptocurrencies considered separately but also when we jointly examine them with traditional assets.

A Nonparametric Approach for Testing Long Memory in Stock Returns’ Higher Moments

In this paper, by considering a model-based approach for conditional moment estimation, a nonparametric test was performed to study the long-memory property of higher moments. We considered the daily returns of the stocks included in the S&P500 index in the last ten years (for the period running from the 1st of January 2011 to the 1st of January 2021). We found that mean and skewness were characterized by short memory, while variance and shape had long memory. These results have deep implications in terms of asset allocation, option pricing and market efficiency evaluation.

Optimal forecasting accuracy using Lp-norm combination

A well-known result in statistics is that a linear combination of two-point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves (Bates and Granger in J Oper Res Soc 20(4):451-468, 1969). The only case in which no improvements are possible is when one of the single forecasts is already the optimal one in terms of MSE. The kinds of combination methods are various, ranging from the simple average (SA) to more robust methods such as the one based on median or Trimmed Average (TA) or Least Absolute Deviations or optimization techniques (Stock and Watson in J Forecast 23(6):405-430, 2004). Standard regression-based combination approaches may fail to get a realistic result if the forecasts show high collinearity in several situations or the data distribution is not Gaussian. Therefore, we propose a forecast combination method based on Lp-norm estimators. These estimators are based on the Generalized Error Distribution, which is a generalization of the Gaussian distribution, and they can be used to solve the cases of multicollinearity and non-Gaussianity. In order to demonstrate the potential of Lp-norms, we conducted a simulated and an empirical study, comparing its performance with other standard-regression combination approaches. We carried out the simulation study with different values of the autoregressive parameter, by alternating heteroskedasticity and homoskedasticity. On the other hand, the real data application is based on the daily Bitfinex historical series of bitcoins (2014-2020) and the 25 historical series relating to companies included in the Dow Jonson, were subsequently considered. We showed that, by combining different GARCH and the ARIMA models, assuming both Gaussian and non-Gaussian distributions, the Lp-norm scheme improves the forecasting accuracy with respect to other regression-based combination procedures.

Distribution-Based Entropy Weighting Clustering of Skewed and Heavy Tailed Time Series

The goal of clustering is to identify common structures in a data set by forming groups of homogeneous objects. The observed characteristics of many economic time series motivated the development of classes of distributions that can accommodate properties, such as heavy tails and skewness. Thanks to its flexibility, the skewed exponential power distribution (also called skewed generalized error distribution) ensures a unified and general framework for clustering possibly skewed and heavy tailed time series. This paper develops a clustering procedure of model-based type, assuming that the time series are generated by the same underlying probability distribution but with different parameters. Moreover, we propose to optimally combine the estimated parameters to form the clusters with an entropy weighing k-means approach. The usefulness of the proposal is shown by means of application to financial time series, demonstrating also how the obtained clusters can be used to form portfolio of stocks.

Exchange Market Liquidity Prediction with the K-Nearest Neighbor Approach: Crypto vs. Fiat Currencies

In this paper, we compare the predictions on the market liquidity in crypto and fiat currencies between two traditional time series methods, the autoregressive moving average (ARMA) and the generalized autoregressive conditional heteroskedasticity (GARCH), and the machine learning algorithm called the k-nearest neighbor (KNN) approach. We measure market liquidity as the log rates of bid-ask spreads in a sample of three cryptocurrencies (Bitcoin, Ethereum, and Ripple) and 16 major fiat currencies from 9 February 2018 to 8 February 2019. We find that the KNN approach is better suited for capturing the market liquidity in a cryptocurrency in the short-term than the ARMA and GARCH models maybe due to the complexity of the microstructure of the market. Considering traditional time series models, we find that ARMA models perform well when estimating the liquidity of fiat currencies in developed markets, whereas GARCH models do the same for fiat currencies in emerging markets. Nevertheless, our results show that the KNN approach can better predict the log rates of the bid-ask spreads of crypto and fiat currencies than ARMA and GARCH models.