Association between COVID-19 cases and international equity indices

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.

The changing economic relationship between some of the major COVID-19 impacted countries with prominent wealth: a comparative study from the view point of stock markets

In the present work, a study has been made over the prime stock indices of some fiscally prominent countries impacted by COVID-19. The countries are separated in two ways: (1) considering gross total number of infected cases-here seven mostly impacted countries with certain global economic influence are selected; (2) considering the concentration of the infected cases-here six major impacted countries with considerable influence are selected. This sort of categorization is itself a novel strategy which is capable of including some less populated, but severely impacted countries of economic importance. The objective of the present analysis is to comprehend the impact of COVID-19 on these markets and to recognize the effect of COVID-19 on mutual association and dependence between these markets. To add more flavour of reliability, we have taken a new and fresh strategy of fixing the time frames under consideration before and during COVID-19 pandemic as uniform. We have used both linear and nonlinear Granger causality analysis and employed generalized forecast error variance decomposition analysis to review the exogeneity and endogeneity of the individual markets. The present study shows that this pandemic has changed the underlying relationship: some exogenous stock markets have become endogenous and vice versa in the pandemic. Linear relationship has been reduced radically, whereas nonlinear relationship has been improved during the COVID-affected period. TASE, the highest returned and significantly uncorrelated index, emerged as the most exogenous market in the pre-COVID period, though it is nonlinearly endogenous in the long term, in the COVD-affected period. CAC 40 is the most endogenous market for the short term in both pre-COVID and COVID-affected period. B3 and NYSE, exogenous in the pre-COVID period, turned out to be linearly endogenous in the COVID-affected duration, whereas BIST 100 and BSE SENSEX are found to be exogenous markets in the COVID-affected period according to both linear and nonlinear causal analysis. They were also exogenous in the pre-COVID era for the short-term period, with BSE SENSEX exhibiting exogeneity anti-persistently for the COVID-affected period too. Association among the markets is more in long term rather than short term. A possible conclusion is also that the markets may regain long-term association once the effect of COVID would fade away.

Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil

This paper compares and contrasts the spread and impact of COVID-19 in the three countries most heavily impacted by the pandemic: the United States (US), India and Brazil. All three of these countries have a federal structure, in which the individual states have largely determined the response to the pandemic. Thus, we perform an extensive analysis of the individual states of these three countries to determine patterns of similarity within each. First, we analyse structural similarity and anomalies in the trajectories of cases and deaths as multivariate time series. Next, we study the lengths of the different waves of the virus outbreaks across the three countries and their states. Finally, we investigate suitable time offsets between cases and deaths as a function of the distinct outbreak waves. In all these analyses, we consistently reveal more characteristically distinct behaviour between US and Indian states, while Brazilian states exhibit less structure in their wave behaviour and changing progression between cases and deaths.

In search of peak human athletic potential: A mathematical investigation

This paper applies existing and new approaches to study trends in the performance of elite athletes over time. We study both track and field scores of men and women athletes on a yearly basis from 2001 to 2019, revealing several trends and findings. First, we perform a detailed regression study to reveal the existence of an "Olympic effect," where average performance improves during Olympic years. Next, we study the rate of change in athlete performance and fail to reject the notion that athlete scores are leveling off, at least among the top 100 annual scores. Third, we examine the relationship in performance trends among men and women's categories of the same event, revealing striking similarity, together with some anomalous events. Finally, we analyze the geographic composition of the world's top athletes, attempting to understand how the diversity by country and continent varies over time across events. We challenge a widely held conception of athletics that certain events are more geographically dominated than others. Our methods and findings could be applied more generally to identify evolutionary dynamics in group performance and highlight spatiotemporal trends in group composition.

Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States

This paper introduces new methods to track the offset between two multivariate time series on a continuous basis. We then apply this framework to COVID-19 counts on a state-by-state basis in the United States to determine the progression from cases to deaths as a function of time. Across multiple approaches, we reveal an "up-down-up" pattern in the estimated offset between reported cases and deaths as the pandemic progresses. This analysis could be used to predict imminent increased load on a healthcare system and aid the allocation of additional resources in advance.

Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time

This paper introduces new methods to study behaviours among the 52 largest cryptocurrencies between 01-01-2019 and 30-06-2021. First, we explore evolutionary correlation behaviours and apply a recently proposed turning point algorithm to identify regimes in market correlation. Next, we inspect the relationship between collective dynamics and the cryptocurrency market size-revealing an inverse relationship between the size of the market and the strength of collective dynamics. We then explore the time-varying consistency of the relationships between cryptocurrencies' size and their returns and volatility. There, we demonstrate that there is greater consistency between size and volatility than size and returns. Finally, we study the spread of volatility behaviours across the market changing with time by examining the structure of Wasserstein distances between probability density functions of rolling volatility. We demonstrate a new phenomenon of increased uniformity in volatility during market crashes, which we term volatility dispersion.

Cryptocurrency Market Consolidation in 2020-2021

Time series of price returns for 80 of the most liquid cryptocurrencies listed on Binance are investigated for the presence of detrended cross-correlations. A spectral analysis of the detrended correlation matrix and a topological analysis of the minimal spanning trees calculated based on this matrix are applied for different positions of a moving window. The cryptocurrencies become more strongly cross-correlated among themselves than they used to be before. The average cross-correlations increase with time on a specific time scale in a way that resembles the Epps effect amplification when going from past to present. The minimal spanning trees also change their topology and, for the short time scales, they become more centralized with increasing maximum node degrees, while for the long time scales they become more distributed, but also more correlated at the same time. Apart from the inter-market dependencies, the detrended cross-correlations between the cryptocurrency market and some traditional markets, like the stock markets, commodity markets, and Forex, are also analyzed. The cryptocurrency market shows higher levels of cross-correlations with the other markets during the same turbulent periods, in which it is strongly cross-correlated itself.

Nonlinear science against the COVID-19 pandemic

This special issue showcases recent uses of mathematical and nonlinear science methods in the study of different problems arising in the context of the COVID-19 pandemic. The sixteen original research papers included in this collection span a wide spectrum of studies including classical epidemiological models, new models accounting for COVID-19 specificities, non-pharmaceutical control measures, network models and other problems related to the pandemic.

Modeling and forecasting the COVID-19 pandemic with heterogeneous autoregression approaches: South Korea

This paper deals with time series analysis for COVID-19 in South Korea. We adopt heterogeneous autoregressive (HAR) time series models and discuss the statistical inference for various COVID-19 data. Seven data sets such as cumulative confirmed (CC) case, cumulative recovered (CR) case and cumulative death (CD) case as well as recovery rate, fatality rate and infection rates for 14 and 21 days are handled for the statistical analysis. In the HAR models, model selections of orders are conducted by evaluating root mean square error (RMSE) and mean absolute error (MAE) as well asR 2 , AIC, and BIC. As a result of estimation, we provide coefficients estimates, standard errors and 95% confidence intervals in the HAR models. Our results report that fitted values via the HAR models are not only well-matched with the real cumulative cases but also differenced values from the fitted HAR models are well-matched with real daily cases. Additionally, because the CC and the CD cases are strongly correlated, we use a bivariate HAR model for the two data sets. Out-of-sample forecastings are carried out with the COVID-19 data sets to obtain multi-step ahead predicted values and 95% prediction intervals. As for the forecasting performances, four accuracy measures such as RMSE, MAE, mean absolute percentage error (MAPE) and root relative square error (RRSE) are evaluated. Contributions of this work are three folds: First, it is shown that the HAR models fit well to cumulative numbers of the COVID-19 data along with good criterion results. Second, a variety of analysis are studied for the COVID-19 series: confirmed, recovered, death cases, as well as the related rates. Third, forecast accuracy measures are evaluated as small values of errors, and thus it is concluded that the HAR model provides a good prediction model for the COVID-19.

Efficiency of communities and financial markets during the 2020 pandemic

This paper investigates the relationship between the spread of the COVID-19 pandemic, the state of community activity, and the financial index performance across 20 countries. First, we analyze which countries behaved similarly in 2020 with respect to one of three multivariate time series: daily COVID-19 cases, Apple mobility data, and national equity index price. Next, we study the trajectories of all three of these attributes in conjunction to determine which exhibited greater similarity. Finally, we investigate whether country financial indices or mobility data responded more quickly to surges in COVID-19 cases. Our results indicate that mobility data and national financial indices exhibited the most similarity in their trajectories, with financial indices responding quicker. This suggests that financial market participants may have interpreted and responded to COVID-19 data more efficiently than governments. Furthermore, results imply that efforts to study community mobility data as a leading indicator for financial market performance during the pandemic were misguided.

Country transition index based on hierarchical clustering to predict next COVID-19 waves

COVID-19 has widely spread around the world, impacting the health systems of several countries in addition to the collateral damage that societies will face in the next years. Although the comparison between countries is essential for controlling this disease, the main challenge is the fact of countries are not simultaneously affected by the virus. Therefore, from the COVID-19 dataset by the Johns Hopkins University Center for Systems Science and Engineering, we present a temporal analysis on the number of new cases and deaths among countries using artificial intelligence. Our approach incrementally models the cases using a hierarchical clustering that emphasizes country transitions between infection groups over time. Then, one can compare the current situation of a country against others that have already faced previous waves. By using our approach, we designed a transition index to estimate the most probable countries' movements between infectious groups to predict next wave trends. We draw two important conclusions: (1) we show the historical infection path taken by specific countries and emphasize changing points that occur when countries move between clusters with small, medium, or large number of cases; (2) we estimate new waves for specific countries using the transition index.

Extracted features of national and continental daily biweekly growth rates of confirmed COVID-19 cases and deaths via Fourier analysis

AIMS

By associating features with orthonormal bases, we analyse the values of the extracted features for the daily biweekly growth rates of COVID-19 confirmed cases and deaths on national and continental levels.

METHODS

By adopting the concept of Fourier coefficients, we analyse the inner products with respect to temporal and spatial frequencies on national and continental levels. The input data are the global time series data with 117 countries over 109 days on a national level; and 6 continents over 447 days on a continental level. Next, we calculate the Euclidean distance matrices and their average variabilities, which measure the average discrepancy between one feature vector and all others. Then we analyse the temporal and spatial variabilities on a national level. By calculating the temporal inner products on a continental level, we derive and analyse the similarities between the continents.

RESULTS

On the national level, the daily biweekly growth rates bear higher similarities in the time dimension than the ones in the space dimension. Furthermore, there exists a strong concurrency between the features for biweekly growth rates of cases and deaths. As far as the trends of the features are concerned, the features are stabler on the continental level, and less predictive on the national level. In addition, there are very high similarities between all the continents, except Asia.

CONCLUSIONS

The features for daily biweekly growth rates of cases and deaths are extracted via orthonormal frequencies. By tracking the inner products for the input data and the orthonormal features, we could decompose the evolutionary results of COVID-19 into some fundamental frequencies. Though the frequency-based techniques are applied, the interpretation of the features should resort to other methods. By analysing the spectrum of the frequencies, we reveal hidden patterns of the COVID-19 pandemic. This would provide some preliminary research merits for further insightful investigations. It could also be used to predict future trends of daily biweekly growth rates of COVID-19 cases and deaths.

COVID-19 pandemic and stability of stock market-A sectoral approach

The COVID-19 pandemic seems to be the most important phenomenon observed from March 2020 in virtually all countries of the world. The necessity to prevent the spread of COVID-19 and keep health care systems efficient resulted in the forced, drastic limitation of economic activity. Many service sectors were hit particularly hard with this but industry and agriculture were also affected. In particular, the pandemic substantially influenced financial markets and we can observe that some markets or instruments vary in stability since they have been affected in the different degree. In the paper, we present the problem of stability of stock markets during the COVID-19 pandemic. Due to the low number of works related to CEE countries during the pandemic, we analyze the Warsaw Stock Exchange, which is one of the most important markets in the CEE. Our main goal was to find how various industries represented by stock market indices have reacted to the COVID-19 shock and consequently which sectors turned out to keep stability and remained resistant to the pandemic. In our investigation, we use two clustering methods: the K-means and the Ward techniques with the criterion of maximizing the silhouette coefficient and six indicators describing stability in terms of profitability, volume, overbought/oversold conditions and volatility. The results of the research present that during the pandemic it was possible to identify 5 clusters of sector indices in the short term and 4 in the medium term. We found that the composition of the clusters is quite stable over time and that none of the obtained clusters can be univocally considered the most or the least stable taking into account all the analyzed indicators. However, we showed that the obtained clusters have different stability origins, i.e. they vary from each other in terms of the investigated indicators of stability.

Dynamics, behaviours, and anomaly persistence in cryptocurrencies and equities surrounding COVID-19

This paper uses new and recently introduced methodologies to study the similarity in the dynamics and behaviours of cryptocurrencies and equities surrounding the COVID-19 pandemic. We study two collections; 45 cryptocurrencies and 72 equities, both independently and in conjunction. First, we examine the evolution of cryptocurrency and equity market dynamics, with a particular focus on their change during the COVID-19 pandemic. We demonstrate markedly more similar dynamics during times of crisis. Next, we apply recently introduced methods to contrast trajectories, erratic behaviours, and extreme values among the two multivariate time series. Finally, we introduce a new framework for determining the persistence of market anomalies over time. Surprisingly, we find that although cryptocurrencies exhibit stronger collective dynamics and correlation in all market conditions, equities behave more similarly in their trajectories and extremes, and show greater persistence in anomalies over time.