key: cord-0684158-qsitv9yn
authors: Ahmar, Ansari Saleh; del Val, Eva Boj
title: SutteARIMA: Short-term forecasting method, a case: Covid-19 and stock market in Spain
date: 2020-04-22
journal: Sci Total Environ
DOI: 10.1016/j.scitotenv.2020.138883
sha: 1af8c29bad31660642145c6a514fa91e7143c6fc
doc_id: 684158
cord_uid: qsitv9yn

Abstract The purpose of our research is to predict the short-term of confirmed cases of covid-19 and IBEX in Spain by using SutteARIMA method. Covid-19 Spanish confirmed data obtained from Worldometer and Spain Stock Market data (IBEX 35) data obtained from Yahoo Finance. Data starts from 12 February 2020–09 April 2020 (the date on Covid-19 was detected in Spain). The data from 12 February 2020–02 April 2020 using to fitting with data from 03 April – 09 April 2020. Based on the fitting data, we can doing short forecast for 3 future period (10 April – 12 April 2020 for Covid-19 and 14 April – 16 April 2020 for IBEX). In this study, the SutteARIMA method will be used. For the evaluation of the forecasting methods we applied forecasting accuracy measures, mean absolute percentage error (MAPE). Based on the results of ARIMA and SutteARIMA forecasting methods, we conclude that the SutteARIMA method is most suitable than ARIMA to calculate the daily forecasts of confirmed cases of Covid-19 and IBEX in Spain. The MAPE value of 0.1905 (smaller than 0.04 compared to MAPE value of ARIMA) for confirmed cases of Covid-19 in Spain and 0,0202 for IBEX stock. At the end of the analysis, using the SutteARIMA method, we calculate daily forecasts of confirmed cases of Covid-19 in Spain from 10 April 2020 until 12 April 2020 and Spain Stock Market from 14 April until 16 April 2020.

explained that in 2017, world growth has strengthened to 3.8 percent and has significantly increased in a global trade. Global growth was projected to rise to 3.9 percent in 2018 and 2019 before 3.8 percent in 2017. This growth was driven by an increase in the projected growth in developing markets and developing economies as well as rapid growth in developed countries. IMF also expected growth for 2018 and 2019 to increase by 0.2 percent annually compared to World Economics Outlook (WEO) in October 2017. In addition, IMF explained that the increase was also driven by the recovery in investment in developed countries, strong economic growth in developing countries in Asia, progress in developing countries of Europe, and signs of recovery in some commodity exporters. Furthermore, this growth was also supported by a strong impetus, the good market sentiment, the accommodative financial conditions, as well as domestic and international impact of the expansionary fiscal policy in the United States. Recovery in some commodity prices should allow a gradual increase in commodity exporters.

Today, the world is shocked by the epidemic called Covid-19. Covid-19 is a contagious and deadly disease that currently exists in the world by WHO. Covid-19 was first reported in Wuhan, Hubei Province, China in December 2019. Covid-19 is an infectious disease caused by a new coronavirus (SARS-CoV-2) discovered in China (Yang et al., 2020) . Based on WHO (2020) data, as of 6 April 2020, there were 1210956 confirmed cases and 67594 confirmed deaths. In Spain, Covid-19 cases began to be detected on 12 February 2020. The J o u r n a l P r e -p r o o f 3 people recovered and was the second highest country in the world with confirmed cases of covid-19 (Worldometer, 2020) .

To anticipate the many confirmed cases of Covid-19, Spain began lockdown on 14 March 2020 (France24, 2020) , this lockdown also resulted in all restaurants, bars, hotels, schools and universities all being closed and of course this will have an impact on the economy of the Spanish country especially Spain Market Index (IBEX 35) which experienced a decline of up to 14% at the closing of shares (McMurtry, 2020) .

To see more about the impact of lockdown and Covid-19, it is necessary to forecast the data. Time series data changes from time to time and sometimes in an abruptly manner. To view these changes from time to time, estimates of the data need to be done. Forecasting or predictions related to Covid-19 have been studied by various researchers: (Fanelli and Piazza, 2020) studying the forecasting of the spread of covid-19 in China, Italy, and France using the SIRD model, (Roosa et al., 2020) studying about Covid-19 real-time forecast in China with generalized logistic growth model (GLM), (Benvenuto et al., 2020) examines the forecast of Covid-19 using ARIMA, and (Koczkodaj et al., 2020) predicts Covid-19 outside of China by using a simple heuristic (exponential curve). Zt  define stationarity (or weak stationarity) as follows (Brockwell and Davis, 2016; Montgomery et al., 2015) :

(1) the expected value of the time series does not depend on time,   t EZ is independent of t, where t = time.

(2) the autocovariance function defined as

for any lag k is only a function of k

 is independent of t for each k.

Definisi 2.2   t a process define white noise with mean 0 and variance 2  , (Brockwel and Davis, 2006) :

If and only if   t a meets:

(2.1) (Wei, 1994) added that white noise process  t a stationary with autocorrelation function:

and partial autocorrelation function:

The autoregressive model is a form of regression that links the observations of a particular moment with the values of previous observations at a specific time interval.

J o u r n a l P r e -p r o o f 5 The generally, form of autoregressive process the data order p (AR(p)) formulate as (Wei, 1994) :

The moving average process is a process that the time series value at time t is influenced by the current error element and may be weighted in the past.

The general form of the process of moving average order q is expressed by MA (q) (Wei, 1994) :

,

The ( t Z ) process are an autoregressive-moving average or ARMA (p, q) model if it fulfilled (Wei, 1994) :

(for AR(p)) and 2 12

If there is a differencing then the ARIMA model becomes as follows:

(for differencing non seasonal) and

(for MA(q)).

α-Sutte Indicator was developed using the principle of the forecasting method of using the previous data . A was also developed using the adopted moving average method. The moving average method is used to predict the trend history of the data. The α-Sutte Indicator uses 4 previous data ( 1 t Z  , 2 t Z  , 3 t Z  , and 4 t Z  ) as supporting data for forecasting and making the decision (Ahmar, 2018) .

The equation of the α-Sutte Indicator method are as follows (Ahmar, 2018) :

where: 

If equation (2.5) we reduce using backward shift operator  

If we define: 

and the equation (2.4) we can simplify: 

Short-term daily estimates are important for making strategic decisions for the future. In the case of Covid-19, daily forecasting can provide information to decision makers to find a way to prevent Covid-19 from spreading. Daily New Cases of Covid-19 in Spain (12 February 2020 -09 April 2020) Figure 1 shows that the confirmed cases of Covid-19 in Spain will continue to grow until this curve is sloped. One of the weaknesses of time series forecasting uses previous data experience as predictive data to be data so that predictions that are suitable for the case are short forecasting for 3-5 future periods. Figure 1 also show the addition of confirmed cases of Covid-19 in Spain every day seems to be stabilizing in around 5000 cases.

J o u r n a l P r e -p r o o f 11 Since Covid-19 is established as a pandemic by WHO and the existence of lockdown or social restrictions will affect the economic development of a country. One thing that is influential is the stock market because with the existence of this pandemic, investors are starting to panic buying, so selling stock has resulted in a drop in stock prices. Moreover, based on WHO data on 9 April 2020, Spain became the second highest country with a confirmed cases of Covid-19 in the world. 

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