Predicting the European stock market during COVID-19: A machine learning approach

This research attempts to explore the total of 21 potential internal and external shocks to the European market during the Covid-19 Crisis. Using the time series of 1 Jan 2020 to 26 June 2020, I employ a machine learning technique, i.e. Least Absolute Shrinkage and Selection Operator (LASSO) to examine the research question for its benefits over the traditional regression methods. This further allows me to cater to the issue of limited data during the crisis and at the same time, allows both variable selection and regularization in the analysis. Additionally, LASSO is not susceptible to and sensitive to outliers and multi-collinearity. The European market is mostly affected by indices belonging to Singapore, Switzerland, Spain, France, Germany, and the S&P500 index. There is a significant difference in the predictors before and after the pandemic announcement by WHO. Before the Pandemic period announcement by WHO, Europe was hit by the gold market, EUR/USD exchange rate, Dow Jones index, Switzerland, Spain, France, Italy, Germany, and Turkey and after the announcement by WHO, only France and Germany were selected by the lasso approach. It is found that Germany and France are the most predictors in the European market.• A LASSO approach is used to predict the European stock market index during COVID-19• European market is mostly affected by the indices belonging to Singapore, Switzerland, Spain, France, Germany, and the S&P500 index.• There is a significant difference in the predictors before and after the pandemic announcement by WHO.


Introduction
The world has seen enough of the catastrophic implication of the COVID-19. Till 27 June, confirmed COVID-19 infections have crossed 10 million and with the loss of 5,02,208 lives around the globe. This had a further devastating impact on the global economy (See: [1][2][3] ). Global Financial markets are also not spared, and the impact is destructive to the overall global financial markets.
The international market integration has been a topic of interest in recent times. The coronavirus has had a significant impact on the global economy. This increased volatility and impact on the world financial market is well documented in the literature [4][5][6] and in literature focusing on regional financial markets as well [7][8][9][10][11][12] . Fig. 1 shows the movement of the Euro STOXX-50 index throughout the sampling period. Since all the markets around the globe have been experiencing shocks, it is not clear which market, inside or outside Europe, played a role in affecting the European market.
The literature on pandemic and financial markets is evolving and currently explores rising volatility due to COVID-19 and uncertainty in the financial markets (see [13][14][15][16] ).
In this study, we analyze the potential European and global markets that shook Europe. To do this, 21 different potential predictors of the European financial market including predictors inside and outside Europe are used. The 21 indicators include indices from countries which got impacted by the COVID-19 the most along with gold, oil and bitcoins. This is done using a machine learning approach named LASSO regression, which allows both the model selection and regularization in the analysis. Germany, France, Gold, the S&P500, Singapore, Switzerland, Spain, Italy, Turkey, the Dow Jones, and the EUR/USD are found to be among the most important predictors of Europe. Germany and France are found to be the top predictors of Europe.
The remainder of the article is structured as follows: the following section provides information on data and methods which describe the data sources, the variables specification, and estimation methods. This followed by a detailed discussion on the analysis and discussion on the importance of the predictors found to be important to Europe. Finally, the conclusion section.

Data and methods
We employ daily data from 1 January 2020 till 26 June 2020 1 sourced from various sources having (153 observations). We consider the full period as well as two sub-periods separately: First, sub-period is before the WHO announcement of a global pandemic, from 1 Jan to 10th march, and second, after the WHO declared a pandemic on 11th March. This second period is from 11th March to 26 June. We use the EURO STOXX 50 index as the dependent variable for all the models.
We employ a machine learning technique, known as the Least Absolute Shrinkage and Selection Operator (LASSO) for the default sample and subsample periods. The literature on LASSO provides two main advantages of employing lasso over other methodologies like wavelet or ANN; first, LASSO offers a special feature of coefficient shrinkage, which automates the model selection in linear regression due to the nature of 1-penalty, and while doing so it further removes some variables from the model. It also factors in the the issue of multicollinearity as it is not sensitive to outliers and multicollinearity [17] .
LASSO combines the least-squares estimator with an extra constraint on the sum of the absolute values of the coefficients. The limited data availability, during the COVID-19 crisis, might be an issue for traditional times series analysis, however, learning from the data, lasso also takes care of this problem and gives the best predictors.
Where λ indicates the tuning parameter, which regulates the overall penalty level and γ i are predictor-specific penalty loadings. The lasso coefficient path, which signifies the trajectory of the estimated coefficient as a function of λ, is piecewise linear with changes in slope where the variable enters or leaves the active set. If λ = 0, it gives the OLS solution and λ approaching to ∞ gives an empty model, where all coefficients are zero. For more on LASSO see [18][19][20][21] . Table 1 presents the estimated coefficients of the selected predictors for the default sample, before the pandemic, after the pandemic announcement by WHO. It appears that not all the predictors have similar control over Europe across different periods and the predictor selection changes across different subsamples. For the full sample, the most important indices affecting the European financial market are the S&P500 and the indices of Singapore, Switzerland, Spain, France, and Germany.

Results and discussion
Before the pandemic announcement, Gold, EUSDD, DJ, Switzerland, Spain, France, Italy, Germany, and Turkey indices are found to be the most important commodities and indices that impacted Europe. For the third sample, that is after the announcement of the global pandemic by WHO, only France and Germany are found to be impacting Europe. However, no commodity market is found to be impacting Europe. The plausible reason could be that oil prices were falling due to its own dynamics [22] . Secondly, oil and gold showed inefficient behavior during the period understudy [23] To get further insights into the degree of importance of the selected predictors, the coefficient paths obtained from models are plotted in Figs. 2 -4 . The magnitude of the coefficient is shown on the    y -axis and the L1 norm is shown on the x -axis. For the default sample, it is found that all the selected predictors shown in Table 1 show a significant impact on the European market. the first covariate that shows any impact and diverges first from zero is Germany, followed by France, Switzerland, Singapore, Spain, and S&P500. This indicates that Germany and France are of the most important predictors of the European Market. For the period before the pandemic, Germany, and France, once again, show the most importance. This is followed by Spain and Gold. Turkey, Switzerland, Dow Jones. EUR/USD and Italy are among the last covariates to diverge. For the period of the Pandemic, only Germany and France are found to be the predictors of the European market. This further strengthens the earlier finding that Germany and France are potential predictors of the European market and these two markets are shaping the overall European market. The plausible reasons could be, first, they are two of the strongest stock markets in Europe [24] . Secondly, these two were also the most affected countries from COVID-19.
Addressing the nature of the impact of these predictors, these figures suggest that overall, the impact on Europe is (1) negative from Gold, the S&P500, and Singapore. And (2) positive from, along with the indices from, Switzerland, Spain, Italy, Turkey, the Dow Jones, and the EUR/USD. While Germany and France are found to be the top positive predictors of Europe. Though the LASSO selects different variables across different subsamples, the impact of selected variables remains unchanged.

Conclusion
We attempted to explore the potential predictors of the European financial market by examining the impact of protentional internal and external determinants. Germany, France, Gold prices, S&P500, Singapore, Switzerland, Spain, Italy, Turkey, Dow Jones, and the EUR/USD are found to be the predictors of the Europe market. Germany and France are found to be the most important determinants of the European market. Though the LASSO selects different variables across different subsamples, the impact of selected variables remains unchanged.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.