Evidence of Inflation Using Harmonized Consumer Price Indices in Some Euro Countries: France, Germany, Italy, and Spain, along with the Euro Zone

This paper deals with the analysis of the persistence in the Harmonized Indices of Consumer Prices in France, Germany, Italy, and Spain. The degree of persistence is measured through fractional integration or I (d) techniques, using monthly data from January 2010 to February 2023. We first conducted the analysis with data ending in December 2019, that is, with data prior to the COVID-19 pandemic. Then, we extended the sample, first up to December 2021 and finally to February 2023. Our results show that the findings of our series are highly persistent, with values of the differencing parameter about one or higher than one in the majority of cases. In fact, mean reversion is only observed in the case of Germany with pre-pandemic data. Generally, we observed an increase in the degree of persistence of the series as a consequence of both the COVID-19 pandemic and the Russia–Ukraine war, with the only exception being Spain, where we observe a reduction in the order of integration when including 2022–2023 data. © 2023 by the authors.

Dying together: A convergence analysis of fatalities during COVID-19.

Governments implemented countermeasures to mitigate the spread of the COVID-19 virus. This had a severe effect on the economy. We examine convergence patterns in the evolution of COVID-19 deaths across countries. We aim to investigate whether countries that implemented different measures managed to limit the number of COVID-19 deaths. We extend the most recent macro-growth convergence methodology to examine convergence of COVID-19 deaths. We combine a long memory stationarity framework with the maximal clique algorithm. This provides a rich and flexible club formation strategy that goes beyond the stationary/non stationary approach adopted in the previous literature. Our results suggest that strict measures (even belated) or an aggressive vaccination scheme can confine the spread of the disease while maintaining the strictness of the measures steady can lead to a burst of the virus. Finally, we observe that fiscal measures did not have an effect on the containment of the virus.

Generalized Weierstrass-Mandelbrot with Disturbance for Big Data Applications in Economic and Financial Systems

Disturbance such as COVID-19, pollution or policy variation to the economic and financial system has significant effect in the big data applications. Hence to study the effect of the disturbance on the related time series plays important role in further applying the big data in economic and financial system. Generalized Weierstrass-Mandelbrot Function is presented to study the complexity of the related time series theoretically and simultaneously. The results show that the disturbance indicated as the exponential form can generate multifractal features for the related time series. And the irregularity and long memory are also simulated by this model and described by the R/S method and multifractal analysis. © 2023 IEEE.

Bond Portfolio Optimization with Long-Range Dependent Credits

Consider the optimal allocation between money market account and corporate bond fund. While the money market account is free of credit risk, corporate bonds are defaultable and exhibit long-range dependence (LRD) in credit risk. We propose a Volterra default intensity model to capture the LRD in credit risk. Using utility maximization, we derive the novel optimal investment strategy for a corporate bond fund. As empirical study shows that the COVID-19 pandemic has lowered the level of LRD in credit risk, we conduct sensitivity analysis and empirically investigate the changes in demand for corporate bonds before and during the pandemic period.

US biofuel market persistence and mean reversion properties

This paper investigates the market persistence and mean reversion properties for corn, bioethanol and gasoline prices in the US biofuel industry, evaluating long memory effects with fractional integration techniques from January 1982 to May 2022 with USDA data. Empirical results show evidence of no mean reversion properties for the prices in the three series though some support of it is found when the differences of bioethanol and gasoline are taken with respect to corn. Thus, external shocks in the original series are expected to remain persistent and would require additional policy measures to recover the original trend. Furthermore, the impact of Covid on the time series has been analyzed by comparing the scenarios pre and post pandemic, finding evidence of no major changes in the integration orders in all the series under analysis. © 2023 Economic Society of Australia, Queensland

Stock market responses to COVID-19: The behaviors of mean reversion, dependence and persistence.

We examine stock market responses during the COVID-19 pandemic period using fractional integration techniques. The evidence suggests that stock markets generally follow a synchronized movement before and the stages of the pandemic shocks. We find while mean reversion significantly declines, the degree of persistence and dependence has been increased in the majority of the stock market indices in whole sample analysis covering the period of August 02, 2019 and July 09, 2020. This outcome implies increasing integration and possibly declining benefits of diversification for the global stock portfolio management.

Addendum: Predictive form of the FPM model

The article Oustaloup et al. (2021) has shown that the Fractional Power Model (FPM), A+Btm, enables well representing the cumulated data of COVID infections, thanks to a nonlinear identification technique. Beyond this identification interval, the article has also shown that the model enables predicting the future values on an unusual prediction horizon as for its range. The objective of this addendum is to explain, via an autoregressive form, why this model intrinsically benefits from such a predictivity property, the idea being to show the interest of the FPM model by highlighting its predictive specificity, inherent to non-integer integration that conditions the model. More precisely, this addendum establishes a predictive form with long memory of the FPM model. This form corresponds to an autoregressive (AR) filter of infinite order. Taking into account the whole past through an indefinite linear combination of past values, a first predictive form, said to be with long memory, results from an approach using one of the formulations of non-integer differentiation. Actually, as this first predictive form is the one of the power-law, tm, its adaptation to the FPM model, A+Btm, which generalizes the linear regression, A+Bt, is then straightforward: it leads to the predictive form of the FPM model that specifies the model in prediction. This predictive form with long memory shows that the predictivity of the FPM model is such that any predicted value takes into account the whole past, according to a weighted sum of all the past values. These values are taken into account through weighting coefficients, that, for m>−1 and a fortiori for m>0, correspond to an attenuation of the past, that the non-integer power, m, determines by itself. To confirm the specificity of the FPM model in considering the past, this model is compared with a model of another nature, also having three parameters, namely an exponential model (Liu et al. (2020);Sallahi et al. (2021)): whereas, for the FPM model, the past is taken into account globally through all past instants, for the exponential model, the past is taken into account only locally through one single past instant, the predictive form of the model having a short memory and corresponding to an AR filter of order 1. Comparative results, obtained in prediction for these two models, show the predictive interest of the FPM model.

Efficiency dynamics across segmented Bitcoin Markets: Evidence from a decomposition strategy

Heterogeneity in informational inefficiency in a cross-market virtual currency, such as Bitcoin, allows for the extraction of differential gains from a portfolio of investments over time. In this paper, we measure inefficiency in five country/region segmented Bitcoin markets based on dynamic estimation of the fractional integration order of their price series. Results reveal a time-varying and country-specific pattern of inefficiency in the five Bitcoin markets, although the degree of inefficiency in each market has declined over time. Further, we introduce a new decomposition method to disentangle components of the inefficiency degree. Results suggest that the total variation around the convergence benchmark has fallen, whilst the proportion due to the difference between convergence and efficiency has risen from approximately 77% in 2013 to almost 100% in 2020. Besides, evidence of convergence emerges until the outbreak of COVID-19, beyond which the inefficiency degree diverges measurably. We show that Bitcoin markets have become more efficient after the first-wave COVID era and then the nature of market segmentation has played a less important role, levelling the cross-market difference and thus reducing the potential for arbitrage. © 2023 Elsevier B.V.

Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19

In this paper, we study the long memory behavior of the hourly cryptocurrency returns during the COVID-19 pandemic period. Initially, we apply different tests against the spurious long memory, with the results indicating the presence of true long memory for most cryptocurrencies. Yet, using the multivariate test, the series are found to be contaminated by level shifts or smooth trends. Then, we adopt the wavelet-based multivariate long memory approach suggested by Achard and Gannaz (2016) to model their long memory connectivity. The findings indicate a change in persistence for all series during the sample period. The fractal connectivity clustering indicates a similarity among Ethereum (ETH) and Litecoin (LTC), Monero (XMR), Bitcoin (BTC), and EOC token (EOS), while Stellar (XLM) is clustered away from the remaining series, indicating the absence of any interdependence with other crypto returns. Overall, shocks arising from COVID-19 crisis have led to changes in long-run correlation structure. © 2022 Elsevier B.V.

Efficiency Dynamics across Segmented Bitcoin Markets: Evidence from a Decomposition Strategy

Heterogeneity in informational inefficiency in a cross-market virtual currency, such as Bitcoin, allows for the extraction of differential gains from a portfolio of investments over time. In this paper, we measure inefficiency in five country/region segmented Bitcoin markets based on dynamic estimation of the fractional integration order of their price series. Results reveal a time-varying and country-specific pattern of inefficiency in the five Bitcoin markets, although the degree of inefficiency in each market has declined over time. Further, we introduce a new decomposition method to disentangle components of the inefficiency degree. Results suggest that the total variation around the convergence benchmark has fallen, whilst the proportion due to the difference between convergence and efficiency has risen from approximately 77% in 2013 to almost 100% in 2020. Besides, evidence of convergence emerges until the outbreak of COVID-19, beyond which the inefficiency degree diverges measurably. We show that Bitcoin markets have become more efficient after the first-wave COVID era and then the nature of market segmentation has played a less important role, levelling the cross-market difference and thus reducing the potential for arbitrage.

Long Memory in the High Frequency Cryptocurrency Markets using Fractal Connectivity Analysis: The Impact of COVID-19

In this paper, we study the long memory behavior of the hourly cryptocurrency returns during the COVID-19 pandemic period. Initially, we apply different tests against the spurious long memory, with the results indicating the presence of true long memory for most cryptocurrencies. Yet, using the multivariate test, the series are found to be contaminated by level shifts or smooth trends. Then, we adopt the wavelet-based multivariate long memory approach suggested by Achard and Gannaz (2016) to model their long memory connectivity. The findings indicate a change in persistence for all series during the sample period. The fractal connectivity clustering indicates a similarity among Ethereum (ETH) and Litecoin (LTC), Monero (XMR), Bitcoin (BTC), and EOC token (EOS), while Stellar (XLM) is clustered away from the remaining series, indicating the absence of any interdependence with other crypto returns. Overall, shocks arising from COVID-19 crisis have led to changes in long-run correlation structure.

Oil tail-risk forecasts: from financial crisis to COVID-19

The coronavirus outbreak has caused unprecedented volatility in oil prices. This paper extends previous studies on oil Value-at-Risk (VaR) by providing extra insights into Expected Shortfall (ES) forecasting over the last decade, including several oil crises. We introduce a conditional volatility model combined with the Cornish-Fisher expansion for ES forecasting. In comparison to the widely used volatility models and innovation distributions, this approach is superior for predicting the ES of long positions but overestimates VaR for short positions. Overall, the volatility model addressing leverage effects with skewed t innovation produces the most accurate joint VaR and ES forecasting. Moreover, the magnitude of ES relative to VaR varies across models and time, implying that ES should be used in conjunction with VaR to inform timely risk management decisions. The results would be of interest to the regulatory authorities, energy companies, and financial institutions for oil tail-risk forecasting.

Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19 br

In this paper, we study the long memory behavior of Bitcoin, Litecoin, Ethereum, Ripple, Monero, and Dash with a focus on the COVID-19 period. Initially, we apply a time-varying Lifting method to estimate the Hurst exponent for each cryptocurrency. Then we test for a change in persistence over time. To model the multivariate con-nectivity, the wavelet-based multivariate long memory approach proposed by Achard and Gannaz (2016) is implemented. Our results indicate a change in the long-range dependence for the majority of cryptocurrencies, with a noticeable downward trend in persistence after the 2017 bubble and then a dramatic drop after the outbreak of COVID-19. The drop in persistence after COVID-19 is further illustrated by the Fractal connectivity matrix obtained from the Wavelet long-memory model. Our findings provide important implications regarding the evolution of market efficiency in the cryptocurrency market and the associated fractal structure and dy-namics of the crypto prices over time

A hybrid ARFIMA-fuzzy time series (FTS) model for forecasting daily cases of Covid-19 in Iraq

Most time series are characterized in practice that they consist of two components, linear and nonlinear, and when making predictions, the single models are not sufficient to model these series. Recently several linear, non-linear and hybrid models have been proposed for prediction, In this research, a new hybrid model was proposed based on the combination of the linear model Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) with the non-linear model fuzzy time series model (FTS). The proposed hybrid model analyzes the linear component of the specified time series using the ARFIMA model, calculates the estimated values, and then calculates the residuals for this model by subtracting the estimated values from the original time series. The nonlinear component is analyzed using the (FTS) model for the computed residuals, which inherently contain the nonlinear patterns of the time series. The final values for the prediction by applying the hybrid model (ARFIMA-FTS) are obtained by combining the predictions of the (ARFIMA) model of the original series with the predictions of the model (FTS) for the residual series. The new hybrid model was used to predict those infected with Covid-19 virus in Iraq for the period from 24/2/2020 to 11/8/2021. The proposed model was more efficient in the prediction process than the single (ARFIMA) model using a number of comparison criteria, including (RMSE), (MAPE) and (MAE). The final results showed that the proposed model has the ability to predict time series that contain linear and nonlinear components.

Multivariate long memory structure in the cryptocurrency markets: The impact of COVID-19

In this paper, we study the long memory behavior of Bitcoin, Litecoin, Ethereum, Ripple, Monero, and Dash with a focus on the COVID-19 period. Initially, we apply a time-varying Lifting method to estimate the Hurst exponent for each cryptocurrency. Then we test for a change in persistence over time. To model the multivariate connectivity, the wavelet-based multivariate long memory approach proposed by Achard and Gannaz (2016) is implemented. Our results indicate a change in the long-range dependence for the majority of cryptocurrencies, with a noticeable downward trend in persistence after the 2017 bubble and then a dramatic drop after the outbreak of COVID-19. The drop in persistence after COVID-19 is further illustrated by the Fractal connectivity matrix obtained from the Wavelet long-memory model. Our findings provide important implications regarding the evolution of market efficiency in the cryptocurrency market and the associated fractal structure and dynamics of the crypto prices over time.

Multifractality during upside/downside trends in the MENA stock markets: the effects of the global financial crisis, oil crash and COVID-19 pandemic

Purpose This paper examines asymmetric multifractality (A-MF) in the leading Middle East and North Africa (MENA) stock markets under different turbulent periods (global financial crisis [GFC] and European sovereign debt crisis [ESDC], oil price crash and COVID-19 pandemic). Design/methodology/approach This study applies the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method of Cao et al. (2013) to identify A-MF and MENA stock market efficiency during the COVID-19 pandemic. Findings The results show strong evidence of different patterns of MF during upward and downward trends. Inefficiency is higher during upward trends than during downward trends in most of the stock markets in the whole sample period, and the opposite is true during financial crises. The Turkish stock market is the least inefficient during upward and downward trends. A-MF intensifies with an increase in scales. The evolution of excessive A-MF for MENA stock returns is heterogeneous. Most of the stock markets are more inefficient during a pandemic crisis than during an oil crash and other financial crises. However, the inefficiency of the Saudi Arabia and Qatar stock markets is highly sensitive to oil price crashes. Overall, the level of inefficiency varies across market trends, scales and stock markets and over time. The findings of this study provide investors and policymakers with valuable insights into efficient investment strategies, risk management and financial stability. Originality/value This paper first explores A-MF in the MENA emerging stock markets. The A-MF analysis provides useful information to investors regarding asset allocation, portfolio risk management and investment strategies during bullish and bearish market states. In addition, this paper examines A-MF under different turbulent periods, such as the GFC, the ESDC, the 2014-2016 oil crash and the COVID-19 pandemic.

COVID-19 and credit risk: A long memory perspective.

The COVID-19 pandemic shows significant impacts on credit risk, which is the key concern of corporate bond holders such as insurance companies. Credit risk, quantified by agency credit ratings and credit default swaps (CDS), usually exhibits long-range dependence (LRD) due to potential credit rating persistence. With rescaled range analysis and a novel affine forward intensity model embracing a flexible range of Hurst parameters, our studies on Moody's rating data and CDS prices reveal that default intensities have shifted from the long-range to the short-range dependence regime during the COVID-19 period, implying that the historical credit performance becomes much less relevant for credit prediction during the pandemic. This phenomenon contrasts sharply with previous financial-related crises. Specifically, both the 2008 subprime mortgage and the Eurozone crises did not experience such a great decline in the level of LRD in sovereign CDS. Our work also sheds light on the use of historical series in credit risk prediction for insurers' investment.

Unemployment persistence in Europe: evidence from the 27 EU countries.

This paper investigates unemployment persistence in the 27 EU member states by applying fractional integration methods to quarterly data (both seasonally adjusted and unadjusted) from 2000q1 to 2020q4. The obtained evidence points to high levels of persistence in all cases. With seasonally adjusted data, a small degree of mean reversion is found in the case of Belgium, Luxembourg and Malta, but this evidence disappears under the assumption of weakly correlated disturbances. More cases of mean reversion are found instead when analysing the unadjusted series. In particular, countries such as Belgium, France, Croatia, Italy, Luxembourg and Malta display orders of integration significantly lower than 1. In addition, significant negative time trends are found in the case of Bulgaria, Croatia, Malta and Romania, and a positive one for Luxembourg. Finally, the Covid-19 pandemic had mixed effects, with (seasonal) persistence increasing in some countries whilst decreasing in others and not changing in a minority of cases. On the whole, our results support the hysteresis hypothesis for the European economies.

The effect of COVID-19 on long memory in returns and volatility of cryptocurrency and stock markets.

We examine long memory (self-similarity) in digital currencies and international stock exchanges prior and during COVID-19 pandemic. Specifically, ARFIMA and FIGARCH models are respectively employed to evaluate long memory parameter in returns and volatility. The dataset contains 45 cryptocurrency markets and 16 international equity markets. The t-test and F-test are performed to estimated long memory parameters. The empirical findings follow. First, the level of persistence in return series of both markets has increased during the COVID-19 pandemic. Second, during COVID-19 pandemic, variability level in persistence in return series has increased in both digital currencies and stock markets. Third, return series in both markets exhibited comparable level of persistence prior and during the COVID-19 pandemic. Fourth, return series in volatility series of cryptocurrency exhibited high degree of persistence compared to international stock markets during the COVID-19 pandemic. Therefore, it is concluded that COVID-19 pandemic significantly affected long memory in return and volatility of cryptocurrency and international stock markets. In addition, our results suggest that the hybrid long memory model represented by the integration of ARFIMA-FIGARCH is significantly suitable to describe returns and volatility of cryptocurrencies and stocks and to reveal differences before and during COVID-19 pandemic periods.

Modelling stock market data in China: Crisis and Coronavirus.

Global financial markets experienced distinct collapses during the global financial crisis in 2008 and the COVID-19 pandemic in 2020, and similarity in the underlying nature is still a hot topic to be investigated. This paper investigates their degree of persistence in order to detect whether the shocks affecting them have temporary or permanent effects by examining the closing prices of the Shanghai and Shenzhen Composite Indices from 1991 to 2020. The results before the coronavirus indicate large degrees of persistence with shocks having permanent effects, while during the coronavirus the results indicate a mean reversion with shocks having temporary effects.