A Multivariate Regression with Time Series Error in Forecasting Jakarta Composite Index and Stock Prices of Banking Industry in Indonesia by Considering COVID-19 Effect

The stability of the financial system in Indonesia and the world has been severely disrupted by COVID-19. With the unstable financial system conditions, there were drastic fluctuations in the composite stock price index and other stocks. This study focuses on stocks of the banking industry in Indonesia, especially banks that are State-Owned Enterprises. The main objectives of this study are to evaluate the significant effect of COVID-19 on the price of the Jakarta Composite Index (JCI) and some stocks in the banking industry, determine the dependence between the prices of these shares, and forecast the price of JCI and other stock prices in the banking industry.  The method used in this study is Multivariate Regression with Time Series Errors, a multivariate technique for analyzing time series data. One of the interesting independent variables included in the model is a variable representing three phases of the COVID-19 pandemic, based on newly confirmed cases. The results indicate a significant impact of the pandemic on the Jakarta Composite Index (JCI) and stock prices of state-owned banks. Furthermore, the study reveals a dependency between the JCI and the stock prices of these banks.

Banking industry; COVID-19; Financial system stability; Jakarta Composite Index; Multivariate regression with time series error

        Coronavirus Disease 2019 (COVID-19) has been designated as a pandemic by WHO due to its rapid spread in almost all parts of the world (Cucinotta and Vanelli, 2020). The increasing number of countries affected by the COVID-19 virus over the world has made the global economic situation worse (Mofijur et al., 2020). The International Monetary Fund (IMF) predicts the global economy to have a minus 3% growth (Puspasari, 2020). This is one of the focuses of the Sustainable Development Goals (SDGs) because every economic impact that occurs is the key to realizing sustainable economic growth. In Southeast Asia, the COVID-19 pandemic has been found in all states and has had a serious influence on all aspects, especially on the economy (Amul et al., 2021). The country in Southeast Asia that has had a sharp increase in COVID-19 cases in Indonesia. The number of confirmed COVID-19 cases in Indonesia has even exceeded the number of cases in China, where the virus originated (Worldometers, 2021).

Indonesia recorded a GDP growth of only 2.97% in the first quarter of 2020, which represents a significant slowdown compared to the previous achievement of a 4.97% growth rate (Setianto and Kurniawan, 2020). The contraction occurred due to activity restrictions and lockdowns to control the spread of the COVID-19 pandemic (Ministry PPN RI, 2020). This condition disrupts financial system stability. The unstable and inefficient financial system will affect the allocation of funds. The fund allocation will not work properly, so it can obstruct economic growth. Based on the experience, an unstable financial system, especially if a crisis happens, will require high costs for recovery (OJK, 2021; Galbraith, 2015). The financial system also includes transactions in the stock market that are predicted to be affected by this pandemic (Chu et al., 2022; Zhang, Hu and Ji, 2020).

Therefore, some efforts are needed to model stock prices in Indonesia to produce very useful predictions for investors and the government as a reference for making policies. This study focuses on stocks of the banking industry in Indonesia, especially banks that are State-Owned Enterprises (BUMN). The goal of this study is to examine the significant effect of COVID-19 on the price of the Jakarta Composite Index (JCI) and some stocks in the banking industry. In addition, this study also wants to determine the dependence between the prices of these shares so that later several recommendations will be formulated for Bank Indonesia as one of the controlling financial stabilities in Indonesia. The final objective is to forecast the JCI price and other stock prices in the banking industry based on the modeling results obtained.

A stock price index is a number that is used to express changes in stock prices within a certain time interval and becomes a measuring instrument for the situation in the capital market (Damajanti, Yulianti, and Rosyati, 2018).The Composite Stock Price Index (abbreviated as JCI, or also known as the Jakarta Composite Index (JKSE)) is a stock price index to measure the combination of all common and preferred shares listed at the Indonesia Stock Exchange (IDX) (Robiyanto et al., 2019; Andreas, Rahmayanti, and Ulyah, 2021). Stocks are capital market instruments that provide attractive benefits so that they are in demand by investors (Parameswaran, 2007; Zhao, et.al., 2023).

This study used stock price data from state-owned banks, including Bank Rakyat Indonesia (BRI), Bank Negara Indonesia (BNI), Bank Tabungan Negara (BTN), and Mandiri Bank. These banks were selected because they are the state-owned banks with the largest assets in Indonesia. According to the bank's financial report as of the first quarter of 2020, BRI is ranked first with assets of Rp 1287.09 trillion, followed by Mandiri Bank with assets of Rp 1130.7 trillion, and BNI with assets of Rp 953.7 trillion. The positive stock return and a high number of assets make them attractive to investors. Moreover, these four banks have a long-standing history and have made significant contributions to the banking industry and the Indonesian economy (Herlin, 2018).

Previous studies in forecasting were done using classical regression (Smolak et al., 2020; Zubakin et al., 2015), exponential smoothing (Ostertagova and Ostertag, 2012; Hyndman et al., 2002), and ARIMA (Berawi et al., 2018; Dhini et al., 2015). Furthermore, a work involving exogenous variables was conducted by (Ulyah, Susilaningrum, and Suhartono, 2014), in which the exogenous variable used is the Eid al-Fitr dummy variable to predict the total number of motorcycle sales. Ulyah (2019) predicts the JCI and SRTG stock prices with the influence of the presidential election in Indonesia using the univariate Autoregressive Integrated Moving Average (ARIMAX) and multivariate Vector Autoregressive with Exogenous Input (VARX) models. Then, Ulyah, Andreas, and Rahmayanti (2021) constructed a forecasting model of gold and oil prices with the effect of the US-China trade war. Besides,  Pradita, Ongkunaruk, and Leingpibul (2020) utilized intervention analysis to forecast the demand of reefer containers. Unlike those previous studies, the exogenous variable in our study is a dummy variable based on the number of new confirmed COVID-19 cases. In addition, the method that will be used in this study is a multivariate method for time series data, namely Multivariate Regression with Time Series Errors. This model is a special case of the VARX model with several advantages in interpretation (Nicholson, Matteson, and Bien, 2017). 

The use of exogenous variables that consider the COVID-19 pandemic with the Multivariate Regression with Time Series Errors method in predicting the stock price is the novelty of this study. This work produces statistical models and predictions of JCI prices and banking stock prices in Indonesia over a certain period. The results of this study can be used as a reference and statistical review in formulating policies in the capital market, especially in Indonesia.

The organization of the paper is as follows. Section 1 gives the motivation and the aims of this study. Section 2 provides some useful literature. Then, section 3 explains the dataset and the method used in this work. The results and discussion section elaborate the descriptive statistics, modeling, and forecasting. Finally, the last section summarizes this work.

2.1. Size of Dataset and Research Variables

       This study used secondary data downloaded from Yahoo Finance and kawalcovid19.id website. These include the Jakarta Composite Index (JKSE or JCI), stock prices of Bank Negara Indonesia (BBNI), Bank Rakyat Indonesia (BBRI), Bank Tabungan Negara (BBTN), and Bank Mandiri (BMRI). The data used in this study are daily data from January 1^st, 2018 to July 1^st, 2021, and are expressed in Indonesian Rupiah (IDR). In addition, the data taken from the website kawalcovid19.id are daily data on the number of Indonesia's new positive COVID-19 cases. We split the data into two parts, which are training and testing data. Data from 1^st January 2018 – 22^nd June 2021 are called training data, and data from 23^rd June – 1^st July 2021 are considered testing data. Training data are used to construct the model, whereas testing data will be used for validation. The variables in this study were divided into endogenous (core) variables and exogenous variables. The endogenous variables include JCI (JKSE), BNI (BBNI), BRI (BBRI), BTN (BBTN), and Mandiri Bank (BMRI) stock prices. Then, the exogenous variables are the dummy variables representing the period of COVID-19 with a value of 1 (from 2^nd March 2020-31^st to July 2021) and zero otherwise. In general, the COVID-19 pandemic in Indonesia has formed several trends. The pandemic period was divided into three parts based on the trend and pattern in Figure 1.

         Figure 1 displays the behaviour of new confirmed cases in Indonesia. COVID-19 first infected Indonesia on March 2, 2020, and the number of cases gradually increased until late October 2020. This period was referred to as the first phase of the COVID-19 wave (T₁), during which there was an upward trend in cases, and people were concerned about the spread of COVID-19. The second phase of the COVID-19 wave (T₂) represents periods in which COVID-19 cases have a significant rising trend. This increase is more drastic than that of the T₁ period. Then, the third phase of the COVID-19 wave (T₃) was the period with decreasing trend of new confirmed COVID-19 cases.

The details about the dummy variables are as follows.

Figure 1 Time Series Plot of New Confirmed COVID-19 Cases

2.2. Procedure of Analysis

          The analysis was carried out using the MINITAB 18 and RStudio software. The stages of analysis in this study are as follows:

a)       Conducting exploration and visualization on each research variable. The descriptive analysis conducted in this study is the mean, standard deviation, diagrams, and correlations.

b)       Multivariate modeling was conducted using multivariate regressions. Two regression models were developed. The first model included the COVID-19 dummy variable as a predictor to determine whether there were differences between the stock prices before and during the pandemic. The second model incorporated the T₁, T₂, and T₃ dummy variables as predictors to gain a better understanding of the price variations among the different patterns of the pandemic period.

c)       Modelling and forecasting of the prices were conducted using Multivariate Regression with Time Series Errors. The steps included identifying data patterns through the results of descriptive statistics. The effect of the COVID-19 pandemic was removed from the response variable by fitting the multivariate regression equation with T₁, T₂, and T₃ predictors to obtain the residual. Subsequently, VAR modelling of the residuals was performed to obtain the best model that met all the residual assumptions.

d)       Computing the accuracy of the forecasts using Mean Absolute Percentage Error (MAPE).

e)       Performing model interpretation and giving the recommendation.

2.3. Multivariate Regression with Time Series Error Model

In general, every condition that occurs in the financial industry will have an impact on other variables. This is called an exogenous variable. By considering the effect of exogenous variables on the response variable, the analysis and forecasting of the response variable will be closer to the actual value. This concept has been applied in the univariate forecasting of gold prices and Brent crude oil prices using the Autoregressive Integrated Moving Average with Exogenous Input (ARIMAX) model. By considering the effect of the US-China Trade War, which had a significant effect on price movements, forecasting results with a good level of accuracy were obtained (Andreas, Rahmayanti, and Ulyah, 2021; Rahmayanti Andreas, and Ulyah, 2021). In addition, multivariate modeling by considering exogenous variables can also provide forecasting results with good accuracy. This is shown by (Ulyah Andreas, and Rahmayanti, 2021), which uses the Vector Autoregressive with Exogenous Input (VARX) model to predict gold prices and Brent crude oil prices multivariate.

is a k x k coefficient matrix of autoregressive and  is a k x r coefficient matrix of moving average. The variable x in Equation 1 is an exogenous variable that can affect the endogenous variable y.

3.1. Statistical Features of The Data

Figure 2 presents the time series plots of the Jakarta Composite Index and some state-owned banks’ stock prices. Overall, considering the time series plot of COVID-19 new confirmed cases in Figure 1, all the indexes and stock prices had a significant fall during the beginning period of the COVID-19 case in Indonesia (T₁). This condition happened because all people were panicking and facing the effect of the COVID-19 pandemic. Then, in the second period (T), when the cases rocketed significantly, the prices of index and stock prices started to rise, but the value was still lower than that before the pandemic. During this period, the Government introduced the “New Normal” and people were adapting to it. Therefore, the business has already adapted and adjusted and made good upward movements in the prices (Fridayani and Iqbal, 2020; Vaithilingam et al., 2022). The third period is the period where COVID-19 cases are controllable (i.e., the decreasing number of new cases).  However, the price of the index and stock prices have decreasing trends, although not as significant as the previous fall at the beginning of the pandemic. During this period, vaccines have already achieved the final stage of development, and there was a prohibition of homecoming during the Eid Al-Fitr holiday period that had a significant impact on some business sectors such as land transportation, hotel, tourism, and amusement.

Figure 2 Time Series Plots of Index and Stock Prices

Table 1 displays the statistical descriptive analysis, indicating that the average share price of BBNI is higher than those of JKSE, BBRI, BBTN, and BMRI. However, the standard deviation of BBNI's stock price is very large, reaching 23.8% of the average value. This suggests that the fluctuations that occurred during the last two years were very high. The same condition also occurs in BBTN's stock price, with a deviation of 33.6% from the average. In general, the skewness value of variables (except BBTN) is negative, which indicates that the data tends to skew to the left. In addition, the distribution of JKSE and BMRI data tends to be more pointed. The stock price of BBNI and BBRI tend to be flatter than the normal distribution (indicated by their respective kurtosis values), while the BBTN data is close to a normal distribution.

Moreover, based on the results of the correlation plot in Figure 3, it is concluded that the prices between stocks, both JKSE, BBNI, BBRI, BBTN, and BMRI, behave in the same direction, proven by the positive correlation among each other. All the stock prices of state-owned banks are highly correlated with JKSE, which means that the association between them is very strong. The least correlated stock price is between BBTN and BBRI, followed by the correlation between BBNI and BBRI. In contrast, BBNI has a strong correlation with BMRI and BBTN.

Table 1 Statistics Descriptive of The Data

Variable	Count	Mean	StDev	Minimum	Maximum	Skewness	Kurtosis
JKSE	841	5910.8	550.1	3937.6	6689.3	-1.19	3.60
BBNI	841	7108.8	1695.1	3160.0	10175.0	-0.35	2.08
BBRI	841	3765.7	583.5	2170.0	4890.0	-0.23	2.02
BBTN	841	2158.3	725.4	745.0	3840.0	0.38	2.87
BMRI	841	6775.2	999.2	3720.0	9050.0	-0.78	3.24

The COVID-19 pandemic has had a significant influence on the movement of the JCI and stock prices in the Indonesian banking industry. BBRI has a different trend among others, where it has good performance in the second and third phases of COVID-19. The prediction results show that the JCI value will tend to decrease slightly, while the stock price of the Indonesian banking industry has an increasing trend with the assumption that there will still be an increase in the number of positive cases of COVID-19 in Indonesia. The recommendations for the governments are (1) to take more serious action in dealing with COVID-19 cases as it affects JCI and the stock prices, (2) to encourage people to invest, and (3) to minimize the gap between the local interest rate and the Federal Reserve fund rate. The limitation of the study is that the data for the analysis is limited to the range specified in Section 2. More updated data may have different results. Therefore, the future study can consider more updated data to be carried out using another time series or machine learning approach to improve the accuracy of the forecasts.

        The authors thank Universitas Airlangga for the support of this work.

Amul, G.G., Ang, M., Kraybill, D., Ong, S.E., Yoong, J., 2021. Responses to COVID?19 in Southeast Asia: Diverse Paths and Ongoing Challenges. Asian Economic Policy Review, Volume 17 (1), pp. 90–110. DOI: https://doi.org/10.1111/aepr.12362

Andreas, C., Rahmayanti, I.A., Ulyah, S.M., 2021. The Impact of US-China Trade War in Forecasting the Gold Price using ARIMAX Model. In: AIP Conference Proceedings, Volume 23299(1), p. 060011. DOI: https://doi.org/10.1063/5.0042361

Berawi, M.A., Suwartha, N., Kurnia, K., Gunawan., Miraj, P., Berawi, A.R.B., 2018. Forecasting the Land Value around Commuter Rail Stations using Hedonic Price Modeling. International Journal of Technology, Volume 9(7), pp. 1329–1337. DOI: https://doi.org/10.14716/ijtech.v9i7.2589

Chu, D.T., Vu Ngoc, S.M., Vu Thi, H., Nguyen Thi, Y.V., Ho, T.T., Hoang, V.T., Al-Tawfiq, J.A., 2022. COVID-19 in Southeast Asia: Current Status and Perspectives. Bioengineered, Volume 13 (2), pp. 3797–3809. DOI: 10.1080/21655979.2022.2031417

Cryer, J.D., Chan, K.-S., 2008. Time Series Analysis: with Applications to R. New York: Springer. http://dx.doi.org/10.1007/978-0-387-75959-3

Cucinotta, D., Vanelli, M., 2020. WHO Declares COVID-19 a Pandemic. Acta Biomed, Volume 91(1), pp. 157–160. DOI: 10.23750/abm.v91i1.9397

Damajanti, A., Yulianti, Y., Rosyati, R., 2018. The Effect of Global Stock Price Index and Rupiah Exchage Rate on Indonesian Composite Stock Price Index (CSPI) in Indonesian Stock Exchange (IDX). Economics and Business Solutions Journal, Volume 2(2), pp. 49–58. DOI:10.26623/EBSJ.V2I2.1206

Dhini, A., Surjandari, I., Riefqi, M., Puspasari, M.A., 2015. Forecasting Analysis of Consumer Goods Demand using Neural Networks and ARIMA. International Journal of Technology, Volume 6(5), pp. 872–880. DOI: https://doi.org/10.14716/ijtech.v6i5.1882

Fridayani, H.D., Iqbal, M., 2020. An Analysis: Indonesia’s New Normal Policy Implementation During COVID-19 and Its Impact on Economic Aspect. Jurnal Caraka Prabu, Volume 4(2), pp. 197–205. DOI: https://doi.org/10.36859/jcp.v4i2.293

Galbraith, J.K., 2015. The End of Normal: The Great Crisis and The Future of Growth. Simon and Schuster

Herlin, 2018. The Prediction of Bankruptcy Using Altman Z-Score Model (Case Study in BRI Bank, BNI Bank, Mandiri Bank, BTN Bank). Integrated Journal of Business and Economics, Volume 2(1), pp. 12–23

Hyndman, R.J., Koehler, A.B., Snyder, R.D., Grose, S., 2002. A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods. International Journal of Forecasting, Volume 18(3), pp. 439–454. DOI: https://doi.org/10.1016/S0169-2070(01)00110-8

Ministry of National Development Planning Republic of Indonesia (Ministry PPN RI), 2020. Laporan Perkembangan Ekonomi Indonesia dan Dunia Triwulan III Tahun 2020 (Indonesian and World Economic Development Report for the Third Quarter of 2020).  Volume 4(3). Ministry of National Development Planning Republic of Indonesia, Jakarta. Available online at: https://www.bappenas.go.id/files/5516/0819/5837/Laporan_Perkembangan_Ekonomi_Indonesia_dan_Dunia_Triwulan_III_2020.pdf, Accessed on December 24, 2021

Mofijur, M., Fattah, I.M.R., Alam, M.A., Islam, A.B.M.S., Ong, H.C., Rahman, S.M.A., Najafi, G., Ahmed, S.F., Uddin, M.A., Mahlia, T.M.I., 2020. Impact of COVID-19 on the Social, Economic, Environmental and Energy Domains: Lessons Learnt from A Global Pandemic. Sustain Prod Consum, Volume 26, pp. 343–359. DOI: 10.1016/j.spc.2020.10.016

Nicholson, W., Matteson, D.S., Bien, J. 2017. VARX-L: Structured Regularization for Large Vector Autoregressions with Exogenous Variables. International Journal of Forecasting, Volume 33(3), pp 627–651. DOI: 10.1016/j.ijforecast.2017.01.003

Ostertagova, E., and Ostertag, O., 2012. Forecasting Using Simple Exponential Smoothing Method. Acta Electrotechnica et Informatica, Volume 12(3), pp. 62–66. DOI: 10.2478/v10198-012-0034-2

Otoritas Jasa Keuangan (OJK), 2021. Stabilitas Sistem Keuangan (Financial System Stability). Otoritas Jasa Keuangan. Available at: https://www.ojk.go.id /id/kanal/perbankan/stabilitas-sistem-keuangan/Pages/Ikhtisar.aspx, Accessed on December 24, 2021

Parameswaran, S.K., 2007. Equity Shares, Preferred Shares and Stock Market Indices. New Delhi: Tata McGraw-Hill

Pradita, S.P., Ongkunaruk, P., Leingpibul, T.D., 2020. Utilizing an Intervention Forecasting Approach to Improve Reefer Container Demand Forecasting Accuracy: A Case Study in Indonesia. International Journal of Technology, Volume 11(1), pp. 144–154. DOI: https://doi.org/10.14716/ijtech.v11i1.3220

Puspasari, R., 2020. Pemerintah Waspada Dampak Pandemi Covid-19 Terhadap Ekonomi Indonesia (Government Wary of Impact of Covid-19 Pandemic on Indonesian Economy). Biro Komunikasi dan Layanan Informasi Kementerian Keuangan. Available online at: https://www.kemenkeu.go.id/publikasi/siaran-pers/siaran-pers-pemerintah-waspada-dampak-pandemi-covid-19-terhadap-ekonomi-indonesia/, Accessed December 24, 2021

Putri, A.M.H., 2022. Sangat Dominan! Ini Bank Penyalur KUR Terbesar Hingga 2022 (Very Dominant! These Are the Largest KUR Distributing Banks Until 2022). Available online at: https://www.cnbcindonesia.com/research/20221226115913-128-400096/ sangat-dominan-ini-bank-penyalur-kur-terbesar-hingga2022#:~:text=Bank%20Penyalur%20Kredit%20Usaha%20Raky
at%20(KUR) Penyalur%20Kredit%20Usaha%20Rakyat%20(KUR)%20dengan%20Nilai%20Akad%20Terbesar&text=Dalam%20periode%202014%20hingga%2026,akad%20Rp%20899%2C07%20triliun, Accessed on February 7, 2023

Rahmayanti, I.A., Andreas, C., Ulyah, S.M., 2021. Does US-China Trade War Affect the Brent Crude Oil Price? An ARIMAX Forecasting Approach. In: AIP Conference Proceedings, Volume 2329(1), p. 060010. DOI: 10.1063/5.0042359

Robiyanto, R., Santoso, M. A., Atahau, A. D. R., & Harijono, H. 2019. The Indonesia Stock Exchange and Its Dynamics: An Analysis of The Effect of Macroeconomic Variables. Montenegrin Journal of Economics, Volume 15(4), pp. 59–73. DOI: 10.14254/1800-5845/2019.15-4.5

Setianto, Kurniawan, P.A., 2020. Pertumbuhan Ekonomi Indonesia Triwulan I-2020 (Indonesia's Economic Growth in Quarterly1-2020). Available online at: https://www.bps.go.id/pressrelease/2020/05/05/1736/ekonomi-indonesia-triwu lan-i-2020-tumbuh-2-97-persen.html, Accessed on December 24, 2021

Smolak, K., Kasieczka, B., Fialkiewicz, W., Rohm, W., Si?a-Nowicka, K., Kopa?czyk, K., 2020. Applying Human Mobility and Water Consumption Data for Short-Term Water Demand Forecasting Using Classical and Machine Learning Models. Urban Water Journal, Volume 17(1), pp. 32–42. DOI: https://doi.org/10.1080/1573062X.2020.1734947

Tsay, R.S., 2013. Multivariate Time Series Analysis: with R and Financial Applications. New Jersey: John Wiley & Sons, Inc

Ulyah, S.M., 2019. Forecasting Index and Stock Returns by Considering the Effect of Indonesia Pre-presidential Election 2019 Using ARIMAX and VARX Approaches. Journal of Physics: Conference Series, Volume 1277(1), p. 012053. DOI: 10.1088/1742-6596/1277/1/012053

Ulyah, S.M., Andreas, C., Rahmayanti, I.A., 2021. Forecasting Gold and Oil Prices Considering US-China Trade War using Vector Autoregressive with Exogenous Input. AIP Conference Proceedings, Volume 2329(1), p. 060020. DOI: https://doi.org/10.1063/5.0042362

Ulyah, S.M., Susilaningrum, D., Suhartono, 2014. Peramalan Volume Penjualan Total Sepeda Motor di Kabupaten Bojonegoro dan Lamongan dengan Pendekatan Model ARIMAX dan VARX (Forecasting Total Motorcycle Sales Volume in Bojonegoro and Lamongan Regencies Using ARIMAX and VARX Model Approaches). Jurnal Sains dan Seni ITS, Volume 3(2), pp. D230–D235. DOI: 10.12962/j23373520.v3i2.8148

Vaithilingam, C.A., Natesan, S., Rajalaxmi, R.R., Tamilarasi, K., Praveena, N.G., Abdul Karim, S.A. 2022. Evolution of Outbreaks, Lessons Learnt and Challenges Towards “New Normalcy”—Post COVID-19 World. In: Shifting Economic, Financial and Banking Paradigm. Studies in Systems, Decision and Control, Volume 382, pp. 1–22

Warsono, Russel, E., Wamiliana, Widiarti, Usman, M., 2019. Vector Autoregressive with Exogenous Variable Model and its Application in Modeling and Forecasting Energy Data: Case Study of PTBA and HRUM Energy. International Journal of Energy Economics and Policy, Volume 9(2), pp. 390–398. DOI: https://doi.org/10.32479/ijeep.7223

Wei, W.W.S., 2019. Multivariate Time Series Analysis and Applications. New Jersey: John Wiley & Sons, Inc

Worldometers, 2021. COVID Live - Coronavirus Statistics. Worldometer. Available online at: https://www.worldometers.info/coronavirus/, Accessed on December 24, 2021

Zhang, D., Hu, M., Ji, Q., 2020. Financial Markets Under The Global Pandemic of COVID-19. Finance Research Letters. Volume 36, pp. 1–6. DOI: https://doi.org/10.1016/j.frl.2020.101528

Zhao, C., Hu, P., Liu, X., Lan, X., Zhang, H., 2023. Stock Market Analysis Using Time Series Relational Models for Stock Price Prediction. Mathematics, Volume 11(5), pp. 1–13. DOI: https://doi.org/10.3390/math11051130

Zubakin, V.A., Kosorukov, O.A., Moiseev, N.A., 2015. Improvement of Regression  Forecasting Models. Modern applied science, Volume 9 (6), pp. 344–353. DOI:10.5539/mas.v9n6p344