key: cord-0813318-7jamy6j8
authors: Daglis, Theodoros; Melissaropoulos, Ioannis G.; Konstantakis, Konstantinos N.; Michaelides, Panayotis G.
title: The impact of COVID-19 on global stock markets: early linear and non-linear evidence for Italy
date: 2021-11-15
journal: Evolut Inst Econ Rev
DOI: 10.1007/s40844-021-00230-4
sha: d313cb061fd79adcd74875793b0c159bc17204ed
doc_id: 813318
cord_uid: 7jamy6j8

The scientific community still struggles to understand the magnitude of the worldwide infections and deaths induced by COVID-19, partly ignoring the financial consequences. In this paper, using the autoregressive fractionally integrated moving average (ARFIMA)—general autoregressive conditional heteroskedasticity (GARCH) model, we quantify and show the impact of the COVID-19 spread in Italy, utilizing data for the stock market. Using information criteria and forecasting accuracy measures, we show that the COVID-19 confirmed cases contribute with statistically significant information to the modeling of volatility, and also increase the forecasting ability of the volatility of the Italian stock market index, leading to a decrease in the mean stock index.

The pandemic of the so-called coronavirus disease has gained a global character as it has spread from one country to another, having its origin in Wuhan-Hubei, China (Liu et al. 2020) . The fact that the total confirmed COVID-19 cases amount to several millions globally, underlines the importance of this pandemic (WHO 2020) . In fact, the case of COVID-19 is unique, differing in many ways from previous disease spread, for instance the severe acute respiratory syndrome (SARS) spread in 2003 (Wilder-Smith et al. 2020) , or the H1N1 virus of 2009. However, thus far, the financial consequences of such a pandemic remain less widely discussed.

Studies on the macroeconomic effects of other epidemics, for instance the one caused by the SARS virus in 2003, have shown significant effects on the total economy, through large reductions in consumption of various goods and services, increases in business operating costs, and re-evaluation of country risks reflected in increased risk premia (McKibbin and Fernando 2020) . In addition, due to the global trade and financial integration, these shocks were also transmitted to other economies as well, whereas the degree of contagion between the different economies varied according to the strength of financial and trade relationships among them. In general, in the case of previous epidemics, global costs were significant (Lee and McKibbin 2004) .

To cast a glimpse on the economic consequences of such a situation, in terms of monetary units, previous studies showed that the economic effect of influenza on the US economy is estimated to be around $73.1-$166.5 billion (Meltzer et al. 1999 ). In fact, many economies in their attempt to put a halt to the spread of COVID-19, imposed the closing of many businesses, markets, etc. Other measures that were enforced included the suspension of all entry of immigrants and non-immigrants that had travelled to high-risk zones (The White House 2020). Furthermore, many countries suspended several public transport services across the border (Sohrabia et al. 2020) . Even the Olympic games, an event of high importance (Gallego et al. 2020) , were postponed.

Of course, the financial system, which is a crucial part of the economic system, also faces the adverse consequences of a pandemic. In fact, the financial markets are the first that capitalized the risk induced by the pandemic. A prominent study by Donadelli et al. (2017) , showed that the declaration of pandemics, induced by the SARS-COV-2 and the H1N1 virus, had a positive impact on the stock market index of pharmaceuticals that were likely to develop a vaccine and a negative effect on associated stock prices of other firms in different sectors.

Regarding the COVID-19 pandemic, several studies show that stock market indices of various economies experienced a negative longstanding effect. See among others, Ashraf (2020), Albuquerque et al. (2020) , Cheng (2020) , Gormsen and Koijen (2020) , Ramelli and Wagner (2020) . Nonetheless, most of these studies, examine the impact of the pandemic just by comparing stock exchange data during the COVID-19 period and the pre-pandemic period. Therefore, a mechanism on how the exogenous effect of the pandemic impacts the stock market is still vague in the literature.

The facts on the early pandemic stage show that the stock markets of various economies started to experience sudden drops in their overall price index before the 11th of March 2020, when the recent situation was declared to be a pandemic. These market drops are associated with negative news regarding the evolution of COVID-19 and the sudden increase in COVID-19 incidents globally (Akhtaruzzaman et al. 2020; Baket et al. 2020) . In other words, the stock markets capitalized the increased exogenous risk from the pandemic, due to the fact that investors anticipated that the spread of the virus will force policy actors to take lockdown measures to secure public health (Haroon and Rizvi 2020; Hoshikawa and Yoshimi 2021) . As a result, the lockdown measures will decrease consumption and production diminishing at the same time the margin profits of firms and thus the overall expected return of investors' portfolio. This mechanism describes compactly how the evolution of the pandemic directly affected the stock market index of various economies.

In this paper, for the first time in the literature, using relevant econometric and forecasting techniques, to test the direct effect of the pandemic on the stock market index, we model the impact of COVID-19 confirmed cases on the stock market index. To do so, we will focus on a European stock market that was severely hit in the early stages of the pandemic, namely the Italian stock market. Based on official data that come from the Central Bank of Italy, the Italian stock market faced the eighth most extreme drop in its history in February 2020, when the pandemic in Italy was expanding rapidly (Just and Echaust 2020) . Despite the efforts made by policy makers to suspend short-selling actions in the Italian stock market, on the 12th of March 2020, the Italian Stock market faced a tremendous drop of almost 17% (Statista Research Department, 23-11-2020) . The aforementioned facts highlight our choice for selecting the Italian stock market as our primary field of research.

Next, to study the characteristics of the Italian stock market and their potential dependence from the pandemic, we make use of an autoregressive fractionally integrated model with a generalized autoregressive conditional heteroskedasticity error (ARFIMA-GARCH), we model the volatility of the stock market indices of the aforementioned economy.

Our modelling choice regarding the use of an ARFIMA GARCH model lies in previous attempts made in the literature of volatility modeling of stock markets. See, among others, Bekaert and Harvey (1997) , Scheicher (2001 ) Syriopoulos (2007 , Abdalla 2012 , Daglis et al. (2020 . Based on our findings, we witness a negative impact of COVID-19 on the Italian stock index, and an increase in its volatility, whereas both effects are statistically significant.

The paper is structured as follows: Sect. 2 sets out the methodology; Sect. 3 presents the results; finally, Sect. 4 concludes the paper.

In this paper, we need to explicitly test whether the COVID-19 cases, reported daily, have an impact on the mean and variance of the Italian stock market index. In this context, based on relevant financial econometrics techniques, as a first step we define the naïve optimal model for the evolution of the Italian stock market index in the class of ARFIMA models. Then, by augmenting the model with a GARCH process that alleviates heteroskedasticity and fat-tails in the distribution of the stock market index, we assess whether COVID-19 cases have a statistically significant effect on the mean and volatility of the Index. In addition, for the sake of robustness, we check whether the alternative model, which consists of the naïve model, augmented with the exogenous variable of COVID-19 cases, has a better forecasting ability than the naïve model.

Following the econometric literature, we make use of a baseline autoregressive fractionally integrated moving average model (ARFIMA) for the Italian stock market index. The general form of an ARFIMA is the following:

where: y t is the respective time series, p(L) is the lag polynomial of the time series, (L) is the moving average polynomial, L denotes the lag operator, d is the fractional parameter, and t is the error term. Note that in our analysis, the time series under scrutiny is the Italian stock market index.

The fractional-integration parameter d ∈ (−0.5, 0.5) captures the long-run effects, while the ARMA parameters capture the short-run effects. Of course, in case d = 1 , then the time series is integrated of degree one, i.e. I(1) and the ARFIMA model becomes an ARIMA model. See Beran (1994) , Baillie (1996) and Palma (2007) .

To study the possible existence of fractionally integrated time series, we make use of the popular Geweke and Porter-Hudak (GPH) test (1983). Next, using relevant information criteria, we select the number of autoregressive (AR) and moving average (MA) terms for each baseline model. Finally, to account for the potential heteroskedasticity in the residuals, we augment the ARFIMA model described in (1) with a generalized autoregressive conditional heteroskedasticity (GARCH) model (Bollerslev 1986) . The GARCH (p, q) specification is of the form:

where: t is the standard deviation of the residuals, b j , j = 1, … p are the lagged coefficients, t denotes the residuals obtained by the estimation of the ARFIMA model, a i , i = 1, … p are the lagged coefficients, and is the fixed term which represents the mean variance of the residuals, where in Eq. (2) there are q lags of the squared error terms and p lags of the variance. Note that in our analysis, t is the standard deviation of the residuals of the ARFIMA model that captures the evolution of the Italian stock market index, whereas t denotes the residuals obtained by the estimation of the ARFIMA.

Therefore, to establish the lag length p and q of the GARCH (p, q), we make use of relevant information criteria, such as AIC, BIC, Shibata and Hannah-Quinn. Next, to model the effect of COVID-19 cases on the various market indices, we introduce exogenous variables in the GARCH model (exogenous covariate). Therefore, we consider the volatility model:

and let Ω t be the filtration representing the information set at time t. Then, We assume t ~ (0, 1) and is adapted to the information set available at time t(Ω t ) and t+1 is given by:

Var y t+1 |Ω t = 2 t+1 , For parameters w, α, β ϵ J ⊂ ℝ + and it is assumed that

) is assumed to be strictly positive and ∈ ℝ d . In the context of the model, the covariate z t is a nearly integrated process. To ensure a positive effect of z t , a logistic distribution function is employed: and the density by:

In this work, we follow Park and Han (2012), who propose asymptotic theory of the maximum likelihood estimator for ARCH/GARCH model with persistent covariate, to establish consistency and obtain limit distribution. Note that the covariate in our analysis consists of the time series variable of COVID-19.

In this work, we compare the estimates of the baseline ARFIMA model with an alternative specification, which comprises an ARFIMA-GARCH model with exogenous variables, namely:

where: y t is the respective time series, p 1 (L) is the lag polynomial of the time series, (L) is the moving average polynomial, L denotes the lag operator, d is the fractional parameter, p 2 (L) is the lag polynomial for the exogenous time series variable x t and t is the error term.

Analytically, Eq. (8) can be written as follows:

or since t , is: and and t , the variance part of the model, is:

Ιn the case, for instance, of a GARCH (1, 1):

where and F t is the information set available at time t, or

Finally, to assess the out-of-sample forecasting superiority of the ARFIMA-GARCH model with exogenous variables, we use the popular mean average percentage error (MAPE) and root mean squared forecasting error (RMSFE) criteria for an horizon of twelve (12) days, i.e. h = 1,…,12. The out-of-sample forecasting has been conducted using both an expanding rolling windows as well as a fixed rolling windows approach.

All the data related to the COVID-19 pandemic were downloaded in daily format from the Johns Hopkins University database. In our analysis, we chose one important epicenter for Europe, namely the country of Italy. The respective stock market index was downloaded in daily format from the Yahoo finance webpage. As the confirmed cases of the COVID-19 victims are represented by a cumulative summation time series, the effect of the weekends-during which no data for stocks are available-is represented by Monday's stock behavior. Based on this fact, we use only the common dates for both time series. Table 1 shows the descriptive statistics of the time series. 

We begin by testing for the long memory properties in our time series, using the Geweke/Porter-Hudak test, for establishing the baseline model for the stock market index. The test for long memory is an important aspect in the econometric framework of time series since, in financial econometrics, there are time series that exhibit long memory, in the sense that two points of the time series are dependent. The econometric question here is how this dependence varies depending on the time distance of these two points. In other words, if a time series is fractionally integrated then the statistical dependence between any two point of the time series decreases using power decay in their distance and not exponential that is the case when a time series exhibits a unit root behavior (Hassler 2018 ). According to Table 2 , all the time series exhibit long-term memory, which means that we have to use an ARFIMA model, instead of ARIMA.

Next, we proceed to the implementation of the ARFIMA-GARCH model with and without exogenous variables. The use of a GARCH specification in our analysis is done to coherently model the error term structure of our model by correcting for heteroskedasticity. For the MIB stock market index the baseline specification is the ARFIMA (1, 1, 0)-GARCH (1, 1). In this way, based on common practice in financial econometrics, we set the baseline model structure that could be used to coherently describe the evolution of the Italian stock market index.

The superiority of the alternative model that includes the COVID-19 cases as exogenous, over the baseline model without exogenous, is confirmed by the various information criteria employed in Table 3 . The information criteria are used to evaluate the performance of each competing model.

Next, Table 4 shows the alternative optimal model for the Italian stock price index, based on relevant information criteria. According to these results, we can infer that the COVID-19 coefficient (κ) in mean of the GARCH model is negative and statistically significant. This means that COVID-19 has a negative impact on the stock market, which implies that the coronavirus spread affects statistically significantly the stock market price index in a negative way. Moreover, the coefficient of the volatility of COVID-19 ( 1 ) is positive and statistically significant, indicating that the volatility of the recent pandemic increased the volatility of the stock price index. Next, we assess whether a non-linear GARCH specification should be considered for capturing the volatility of the stock market index under scrutiny. The use of a linear GARCH model is justified due to the fact that in the alternative non-linear case (Table 5) , the coefficient of the volatility of COVID-19, is not statistically significant, as indicated by the t-stat. Table 6 presents the MAPE and RMSFE results for the baseline and alternative model, respectively. The results indicate that the alternative model is better in terms of its forecasting ability than the baseline, which means that the presence of the information captured through the COVID-19 time series, is important for the forecasting of the stock price index time series. 

In this paper, we investigated the impact of the recent COVID-19 pandemic on the Italian stock market volatility. More precisely, early evidence regarding the impact of COVID-19 on the Italian stock market index is found to be statistically significant. In fact, based on our findings, we witness a decreasing impact of COVID-19 on the Italian stock market index, and an increasing impact on its volatility, where both effects are statistically significant. Also, based on its forecasting ability, the alternative model, which incorporates the information induced by the COVID-19 cases, is better in every forecasting horizon, except for the case of the first horizon. This means that the COVID-19 time series contributes with statistically significant information in the modeling of the stock market index as well as its volatility, and also increases the forecasting ability of the model. Based on our findings, the pandemic of COVID-19 played a negative role for the Italian stock market index. On one hand, Italy's stock market index witnessed an abrupt shock due to the pandemic, despite the fact that the COVID-19 pandemic per se is exogenous to the operations of the financial market. Nonetheless, the financial market of Italy, had a negative reaction to the pandemic and the COVID-19 cases, due to the pandemic. This, in turn, gives credence to the view that negative news play a major role in investor sentiment, in the sense that investors, in the Italian stock market, identified the external shock as a primary factor that could lead daily operations of firms and industries to a halt, diminishing at the same time their expected annual profitability. As a result, investors tried to protect their portfolios' profitability by turning to other commodities and assets vis-a-vis the stock market. This led the Italian stock market to experience high volatility that is captured in the analysis by the GARCH specification and the statistically significant effect of COVID-19 cases on the volatility of the market. Our research has certain policy implications. To begin with, policy actors should try to eliminate the negative impact of news like COVID-19 daily cases by boosting and backing up the overall activity with stimulus packages, in a more timely manner. In other words, the EU announced the stimulus package of the entire EMU on the 23rd of April, more than a month after the declaration of COVID-19 virus as a pandemic. This delay, forced a number of EMU stock exchange markets to face drops that accounted for almost 20% of their overall stock exchange price index. In addition, policy actors should make publicly available the "whole picture" about the pandemic, by reporting not only new cases and deaths but also the number of tests conducted, the positivity rate, the number of hospitalized cases, etc. In this way, a high reported number of new cases would not have the same effect, since this high number could be the result of more tests conducted, with the same or even diminishing positivity rate.

Clearly, as a future research, a multivariate GARCH model with many countries' stock market indices with exogenous variables would be of great interest, to capture the various spillover effects of the various stock prices, and also the multivariate effect of the COVID-19 pandemic on global stock markets.

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The authors would like to thank the anonymous referees and the Guest Editor of this Journal, Professor Dr. Theodore Mariolis, for their helpful comments and suggestions.Funding No funds, Grants, or other support was received.

The authors have no competing interests to declare that are relevant to the content of this article.