Coherent forecasting for count time series using Box–Jenkins's AR(p) model

During the last three decades, integer‐valued autoregressive process of order p [or INAR(p)] based on different operators have been proposed as a natural, intuitive and maybe efficient model for integer‐valued time‐series data. However, this literature is surprisingly mute on the usefulness of the standard AR(p) process, which is otherwise meant for continuous‐valued time‐series data. In this paper, we attempt to explore the usefulness of the standard AR(p) model for obtaining coherent forecasting from integer‐valued time series. First, some advantages of this standard Box–Jenkins's type AR(p) process are discussed. We then carry out our some simulation experiments, which show the adequacy of the proposed method over the available alternatives. Our simulation results indicate that even when samples are generated from INAR(p) process, Box–Jenkins's model performs as good as the INAR(p) processes especially with respect to mean forecast. Two real data sets have been employed to study the expediency of the standard AR(p) model for integer‐valued time‐series data.     

Poisson–geometric INAR(1) process for modeling count time series with overdispersion

In this paper, we propose a new first‐order non‐negative integer‐valued autoregressive [INAR(1)] process with Poisson–geometric marginals based on binomial thinning for modeling integer‐valued time series with overdispersion. Also, the new process has, as a particular case, the Poisson INAR(1) and geometric INAR(1) processes. The main properties of the model are derived, such as probability generating function, moments, conditional distribution, higher‐order moments, and jumps. Estimators for the parameters of process are proposed, and their asymptotic properties are established. Some numerical results of the estimators are presented with a discussion of the obtained results. Applications to two real data sets are given to show the potentiality of the new process.     

Impacts of COVID-19 on global stock sectors: Evidence from time-varying connectedness and asymmetric nexus analysis

In this paper, we analyze the impact of the COVID-19 crisis on global stock sectors from two perspectives. First, to measure the effect of the COVID-19 on the volatility connectedness among global stock sectors in the time–frequency domain, we combine the time-varying connectedness and frequency connectedness method and focus on the total, directional, and net connectedness. The empirical results indicate a dramatic rise in the total connectedness among the global stock sectors following the outbreak of COVID-19. However, the high level of the total connectedness lasted only about two months, representing that the impact of COVID-19 is significant but not durable. Furthermore, we observe that the directional and net connectedness changes of different stock sectors during the COVID-19 pandemic are heterogeneous, and the diverse possible driving factors. In addition, the transmission of spillovers among sectors is driven mainly by the high-frequency component (short-term spillovers) during the full sample time. However, the effects of the COVID-19 outbreak also persisted in the long term. Second, we explore how the changing COVID-19 pandemic intensity (represented by the daily new COVID-19 confirmed cases and the daily new COVID-19 death cases worldwide) affect the daily returns of the global stock sectors by using the Quantile-on-Quantile Regression (QQR) methodology of Sim and Zhou (2015). The results indicate the different characteristics in responses of the stock sectors to the pandemic intensity. Specifically, most sectors are severely impacted by the COVID-19. In contrast, some sectors (Necessary Consume and Medical & Health) that are least affected by the COVID-19 pandemic (especially in the milder stage of the COVID-19 pandemic) are those that are related to the provision of goods and services which can be considered as necessities and substitutes. These results also hold after several robustness checks. Our findings may help understand the sectoral dynamics in the global stock market and provide significant implications for portfolio managers, investors, and government agencies in times of highly stressful events like the COVID-19 crisis.     

Forecasting economic time series with unconditional time-varying variance

The classical forecasting theory of stationary time series exploits the second-order structure (variance, autocovariance, and spectral density) of an observed process in order to construct some prediction intervals. However, some economic time series show a time-varying unconditional second-order structure. This article focuses on a simple and meaningful model allowing this nonstationary behaviour. We show that this model satisfactorily explains the nonstationary behaviour of several economic data sets, among which are the U.S. stock returns and exchange rates. The question of how to forecast these processes is addressed and evaluated on the data sets.     

Spillover and connectedness among G7 real estate investment trusts: The effects of investor sentiment and global factors

This paper examines the dynamic spillover interconnectedness of G7 Real Estate Investment Trusts (REITs) markets. We use the spillover index of Diebold and Yilmaz (2012), the time-varying parameters vector-autoregression (TVP-VAR) model, and the quantile regression approach. The result show that REITs network connectedness is dynamic and experiences an abrupt increase in the first wave of COVID-19 outbreak (2020Q1). We also observe a substantial abrupt decrease in connectedness during the success of vaccination programs (end 2021). The connectedness among assets is much stronger during COVID-19 than before. The REITs of Japan and Italy are net receivers of spillover and those of US and UK are net transmitters of spillovers before and during COVID-19. Conversely, the REIT of Canada and Germany (France) switches from net receivers (contributors) of spillovers before the pandemic to net contributors (receivers) during the COVID-19. Finally, we show that News Sentiment index, Geopolitical Risk index, Economic Policy Uncertainty index, US Treasury yield, and Stock Volatility index influence the spillover magnitude across quantiles.     

Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates

Hawkes processes are used in statistical modeling for event clustering and causal inference, while they also can be viewed as stochastic versions of popular compartmental models used in epidemiology. Here we show how to develop accurate models of COVID-19 transmission using Hawkes processes with spatial-temporal covariates. We model the conditional intensity of new COVID-19 cases and deaths in the U.S. at the county level, estimating the dynamic reproduction number of the virus within an EM algorithm through a regression on Google mobility indices and demographic covariates in the maximization step. We validate the approach on both short-term and long-term forecasting tasks, showing that the Hawkes process outperforms several models currently used to track the pandemic, including an ensemble approach and an SEIR-variant. We also investigate which covariates and mobility indices are most important for building forecasts of COVID-19 in the U.S.     

Impact of the COVID-19 outbreak and its related announcements on the Chinese conventional and Islamic stocks’ connectedness

In this paper, we assess the impacts of the COVID-19 counts (infected cases, deaths and recovered) and related announcements on the Islamic and conventional stocks interplays in the Chinese market. We test whether Islamic stocks are perceived as assets providing diversification benefits in time of COVID-19 pandemic. Doing so, we implement a multivariate GJR-GARCH model under dynamic conditional correlation (DCC) as well as multiple and partial wavelet coherence methods to recent Chinese daily data ranging from 2 December 2019 to 8 May 2020 and COVID-19 related announcement for the period. Our results from multivariate GJR-GARCH models reveal that COVID-19 infected cases and deaths do impact mean DCCs between Islamic and conventional stocks, number of recovered do not have such impact, while none of the above have any significant impact on the DCCs fluctuations. However, when we analyze the impact of COVID-19 related announcement on the variation of conditional correlation between two stocks (i.e. DCC volatility) our findings show that 7 out of 10 such announcements (mainly those with serious health treats or economic implications) do effect those volatilities in Chinese equity market. The empirical findings from partial and multiple wavelet coherences provide robust evidence of instability in the co-movement between Islamic and conventional indexes for different scales and over dissimilar sub-periods. Indeed, the weakening of co-movements is especially notable in the very short and short-run where operating the short-term investors. Our empirical findings offer several key propositions for policy makers and portfolio managers in China with broad implications applicable to other markets.     

The impact of COVID-19 on the G7 stock markets: A time-frequency analysis

We examine the co-movement of the G7 stock returns with the numbers of confirmed COVID-19 cases and causalities based on daily data from December 31, 2019 to November 13, 2020. We employ the wavelet coherence approach to measure the impact of the numbers of confirmed cases and deaths on the G7 stock markets. Our findings reveal that both the number of confirmed COVID-19 cases and the number of deaths exhibit strong coherence with the G7 equity markets, although we find heterogeneous results for the Canadian and Japanese equity markets, in which the numbers of COVID-19 cases and the deaths exhibit only a weak relationship. This evidence is more pronounced in the long-term horizon rather than the short-term horizon. Moreover, the lead-lag relationship entails a mix of lead-lag relations across different countries. We present the implications of these findings for both policymakers and the international investment community.     

Market volatility and illiquidity during the COVID-19 outbreak: Evidence from the Saudi stock exchange through the wavelet coherence approaches

The aim of this paper is to examine the explanatory power of realized volatility on the illiquidity in Saudi stock market during the COVID-19 outbreak. To achieve this objective, we consider the Wavelet Coherence approaches as empirical tools to investigate the combined effect of realized volatility and COVID-19 counts on the market illiquidity across frequencies and over time space by taking in account the number of infected cases in Saudi Arabia and over the World, and the number of death cases in Saudi Arabia as well as over the World. Our study reaches two main findings. First, the preliminary results reported by the ARDL bound test as a benchmark model showed significant long-run and short-run effects of the market volatility on illiquidity in contemporaneous and lagged manner. Second, the wavelet coherence analysis tools exhibited important results: (i) the wavelet coherency between illiquidity ratio and realized volatility in Saudi Arabia appear highly pronounced over all time horizons. (ii) PWC plots showed a significant mutual effect between liquidity risk and realized volatility when eliminating the effect of local COVID-19 cases. (iii) MWC plots highlighted that the response of the market illiquidity index to both the amplification in confirmed local cases (resp. international confirmed cases) and the stock market volatility appear significant in the short and middle horizons.     

Risk spillovers between cryptocurrencies and traditional currencies and gold under different global economic conditions

This paper applies a Diagonal BEKK model to investigate the risk spillovers of three major cryptocurrencies to ten leading traditional currencies and two gold prices (Spot Gold and Gold Futures). The daily data used are from 7 August 2015 to 15 June 2020. The dataset is analyzed in its entirety and is also subdivided into four distinct subsets in order to study and compare the patterns of spillover effects during economic turmoil, such as the 2018 cryptocurrency crash and the COVID-19 pandemic. The results reveal significant co-volatility spillover effects between cryptocurrency and traditional currency or gold markets, especially during the whole sample period and amid the uncertainty raised by COVID-19. The capabilities of cryptocurrency are time-varying and related to economic uncertainty or shocks. There are significant differences between normal and extreme markets with regard to the capabilities of cryptocurrency as a diversifier, a hedge or a safe haven. We find the significant co-volatility spillover effects are asymmetric in most cases especially during the COVID-19 pandemic period, which means the negative return shocks have larger impacts on co-volatility than positive return shocks of the same magnitude. Evidently, cryptocurrencies and traditional currencies or gold can be incorporated into financial portfolios for financial market participants who seek effective risk management and also for optimal dynamic hedging purposes against economic turmoil and downward movements.     

Latent social distancing: Identification,causes and consequences

It is not directly observable how effectively a society practices social distancing during the COVID-19 pandemic. This paper proposes a novel and robust methodology to identify latent social distancing at the country level. We extend the Susceptible-Exposed-Infectious-Recovered-Deceased (SEIRD) model with a time-varying, country-specific distancing term, and derive the Model-Inferred DIStancing index (MIDIS) for 120 countries using readily available epidemiological data. The index is not sensitive to measurement errors in epidemiological data and to the values assigned to model parameters. The evolution of MIDIS shows that countries exhibit diverse patterns of distancing during the first wave of the COVID-19 pandemic—a persistent increase, a trendless fluctuation, and an inverted U are among these patterns. We then implement regression analyses using MIDIS and obtain the following results: First, MIDIS is strongly correlated with available mobility statistics, at least for high income countries. Second, MIDIS is also strongly associated with (i) the stringency of lockdown measures (governmental response), (ii) the cumulative number of deceased persons (behavioral response), and (iii) the time that passed since the first confirmed case (temporal response). Third, there is statistically significant regional variation in MIDIS, and more developed societies achieve higher distancing levels. Finally, MIDIS is used to explain output losses experienced during the pandemic, and it is shown that there is a robust positive relationship between the two, with sizable economic effects.     

First-Order Integer-Valued Autoregressive (INAR (1)) Process: Distributional and Regression Properties

Some properties of a first-order integer-valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self-decomposability and unimodality of the 1-dimensional marginals of the process {X_n} generated according to the scheme X_n=α° X _n-i +e_n, where α° X _n-1 denotes a sum of X_{n - 1}, independent 0 - 1 random variables Y^(n-1), independent of X _n-1 with Pr -( y ^{(n - 1)}= 1) = 1 - Pr ( y ^(n-i)= 0) =α. The distribution of the innovation process ( e _n) is obtained when the marginal distribution of the process ( X _n) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.     

Modelling Time Series of Counts in Epidemiology

We review generalized dynamic models for time series of count data. Usually temporal counts are modelled as following a Poisson distribution, and a transformation of the mean depends on parameters which evolve smoothly with time. We generalize the usual dynamic Poisson model by considering continuous mixtures of the Poisson distribution. We consider Poisson‐gamma and Poisson‐log‐normal mixture models. These models have a parameter for each time t which captures possible extra‐variation present in the data. If the time interval between observations is short, many observed zeros might result. We also propose zero inflated versions of the models mentioned above. In epidemiology, when a count is equal to zero, one does not know if the disease is present or not. Our model has a parameter which provides the probability of presence of the disease given no cases were observed. We rely on the Bayesian paradigm to obtain estimates of the parameters of interest, and discuss numerical methods to obtain samples from the resultant posterior distribution. We fit the proposed models to artificial data sets and also to a weekly time series of registered number of cases of dengue fever in a district of the city of Rio de Janeiro, Brazil, during 2001 and 2002.     

Autoregresive conditional volatility, skewness and kurtosis

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t distribution proposed by [Harvey, C. R. & Siddique, A. (1999). Autorregresive Conditional Skewness. Journal of Financial and Quantitative Analysis 34, 465–487). Moreover, this approach accounts for time-varying skewness and kurtosis while the approach by Harvey and Siddique [Harvey, C. R. & Siddique, A. (1999). Autorregresive Conditional Skewness. Journal of Financial and Quantitative Analysis 34, 465–487] only accounts for non-normal skewness. We apply this method to daily returns of a variety of stock indices and exchange rates. Our results indicate a significant presence of conditional skewness and kurtosis. It is also found that specifications allowing for time-varying skewness and kurtosis outperform specifications with constant third and fourth moments.     

Dynamic connectedness of China’s green bonds and asset classes

This paper quantifies the co-movement and time-varying integration between China's green bonds and other asset classes across different time domains using the wavelet coherence and time-frequency connectedness model based on the time-varying parameter VAR (TVP-VAR). First, we predominantly detect a strong positive co-movement of green and conventional bonds, especially in the medium and long term. Second, strong bidirectional spillovers exist between green bonds and treasury, corporate, and financial bonds regardless of the time horizon. Lastly, cross-market spillovers between the green bonds and the stock, energy, low-carbon stock market were quite limited in the short-run but strengthened towards the long-term except during the 2015 China stock market crash and the COVID-19 recession when short-term integration rose sharply. The results document some practical enlightenment for investors and policymakers with various time horizons.     

Real-time inflation forecasting using non-linear dimension reduction techniques

In this paper, we assess whether using non-linear dimension reduction techniques pays off for forecasting inflation in real-time. Several recent methods from the machine learning literature are adopted to map a large dimensional dataset into a lower-dimensional set of latent factors. We model the relationship between inflation and the latent factors using constant and time-varying parameter (TVP) regressions with shrinkage priors. Our models are then used to forecast monthly US inflation in real-time. The results suggest that sophisticated dimension reduction methods yield inflation forecasts that are highly competitive with linear approaches based on principal components. Among the techniques considered, the Autoencoder and squared principal components yield factors that have high predictive power for one-month- and one-quarter-ahead inflation. Zooming into model performance over time reveals that controlling for non-linear relations in the data is of particular importance during recessionary episodes of the business cycle or the current COVID-19 pandemic.     

Analysis of the impact of COVID-19 pandemic on G20 stock markets

We examine the impact of the COVID-19 pandemic on G20 stock markets from multiple perspectives. To measure the impact of COVID-19 on cross-market linkages and deeply explore the dynamic evolution of risk transmission relations and paths among G20 stock markets, we statically and dynamically measure total, net, and pairwise volatility connectedness among G20 stock markets based on the DY approach by Diebold and Yilmaz (2012, 2014). The results indicate that the total volatility connectedness among G20 stock markets increases significantly during the COVID-19 crisis, moreover, the volatility connectedness display dynamic evolution characteristics during different periods of the COVID-19 pandemic. Besides, we also find that the developed markets are the main spillover transmitters while the emerging markets are the main spillover receivers. Furthermore, to capture the impact of COVID-19 on the volatility spillovers of G20 stock markets, we individually apply the spatial econometrics methods to analyze both the direct and indirect effects of COVID-19 on the stock markets’ volatility spillovers based on the “volatility spillover network matrix” innovatively constructed in this paper. The empirical results suggest that stock markets react more strongly to the COVID-19 confirmed cases and cured cases than the death cases. In general, our study offers some reference for both the investors and policymakers to understand the impact of COVID-19 on global stock markets.     

Upside/Downside spillovers between oil and Chinese stock sectors: From the global financial crisis to global pandemic

This paper examines the effects of the COVID-19 outbreak, recent oil price fall, and both global and European financial crises on dependence structure and asymmetric risk spillovers between crude oil and Chinese stock sectors. Using time-varying symmetric and asymmetric copula functions and the conditional Value at Risk measure, we provide evidence of positive tail dependence in most sectors using copula and conditional Value-at-Risk techniques. We can see the average dependence between oil and industries during the oil crisis. Moreover, we find strong evidence of bidirectional risk spillovers for all oil-sector pairs. The intensity of risk spillovers from oil to all stock sectors varies across sectors. The risk spillovers from sectors to oil are substantially larger than those from oil to sectors during COVID-19. Furthermore, the return spillover is time varying and sensitive to external shocks. The spillover strengths are higher during COVID-19 than financial and oil crises. Finally, oil do not exhibit neither hedge nor safe-haven characteristics irrespective of crisis periods.     

Risk spillover from crude oil prices to GCC stock market returns: New evidence during the COVID-19 outbreak

In this study, we examine oil price extreme tail risk spillover to individual Gulf Cooperation Council (GCC) stock markets and quantify this spillover’s shift before and during the COVID-19 pandemic. A dynamic conditional correlation generalized autoregressive heteroscedastic (DCC- GARCH) model is employed to estimate three important measures of tail dependence risk: conditional value at risk (CoVaR), delta CoVaR (ΔCoVaR), and marginal expected shortfall (MES). Using daily data from January 2017 until May 2020, results point to significant systemic oil risk spillover in all GCC stock markets. In particular, the effect of oil price systemic risk on GCC stock market returns was significantly larger during COVID-19 than before the pandemic. Upon splitting COVID-19 into two phases based on severity, we identify Saudi Arabia as the only GCC market to have experienced significantly higher exposure to oil risk in Phase 1. Although all GCC stock markets received greater oil systemic risk spillover in Phase 2 of COVID-19, Saudi Arabia and the United Arab Emirates appeared more vulnerable to oil extreme risk than other countries. Our empirical findings reveal that investors should carefully consider the extreme oil risk effects on GCC stock markets when designing optimal portfolio strategies, minimizing portfolio risk, and adopting dynamic diversification process. Policymakers and regulators should also enact awareness, oversight, and action plans to minimize adverse oil risk effects.     

Detecting overdispersion in INARCH(1) processes

A statistical test for the degree of overdispersion of count data time series based on the empirical version of the (Poisson) index of dispersion is considered. The test design relies on asymptotic properties of this index of dispersion, which in turn have been analyzed for time series stemming from a compound Poisson (Poisson‐stopped sum) INAR(1) model. This approach is extended to the popular Poisson INARCH(1) model, which exhibits unconditional overdispersion but has an (equidispersed) conditional Poisson distribution. The asymptotic distribution of the index of dispersion if applied to time series stemming from such a model is derived. These results allow us to investigate the ability of the dispersion test to discriminate between Poisson INAR(1) and INARCH(1) models. Furthermore, the question is considered if the index of dispersion could be used to test the null of a Poisson INARCH(1) model against the alternative of an INARCH(1) model with additional conditional overdispersion.