CC BY
56Математические и имитационные модели экономики Mathematical and simulation models of the economy
УДК 311.174+336.761.5 DOI 10.29141/2782-4934-2023-2-1-1 EDN VWIFAL
Abdo Ali Nasser Aldine1
Belarus State Economic University, Minsk, Republic of Belarus
Forecasting Lebanese stocks using ARIMA models
Abstract. This paper presents method of building ARIMA model for stock price prediction. The experimental results obtained with best ARIMA model to predict stock exchange on short-run basis with aim to guide investors in stock market, to create profitable investment selections. In this article our analysis and forecasting are focused on the price of three shares of three different sectors, SOLA (Solidere Company, development and reconstruction sector), BYB (Byblos bank, Banking sector) and HOLC (Holcim Liban, industrial sector). The three companies were selected based upon the market capitalization by sectors of activities in the Beirut Stock Exchange (BSE) and their role on Lebanese economic development. The taken data of the price of three shares of three different sectors from 29th April 2021 to April 29, 2022, and predict the future prices until the end of May 5, 2022, using ARIMA model. Using the standard model selection criteria such as AIC, BIC, log-likelihood and SigmaSQ we diagnosed the forecasting performance of various ARIMA models with a view to determining the best ARIMA model for predicting stock market in each sector under investigation. The outcome of the empirical analysis indicated that ARIMA (1,1,1), ARIMA (1,1,1) and ARIMA (1,1,2) models are respectively the best forecast models for BYB and HOLC and SOLA.
Key words: time series analysis; modeling; autoregressive integrated moving average (ARIMA); forecasting; stocks. Paper submitted: February 27, 2023
For citation: Nasser Aldine A. A. Forecasting Lebanese stocks using ARIMA models. Digital models and solutions. 2023. Vol. 2, no. 1. DOI: 10.29141/2782-4934-2023-2-1-1. EDN: VWIFAL.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Абдо Али Насер Альдин1
белорусский государственный экономический университет, г. Минск, Республика Беларусь
Прогнозирование цен акций в Ливане с использованием моделей ДШМД
Аннотация. В статье представлен метод построения модели ARIMA для прогнозирования цен акций на ливанском фондовом рынке. Экспериментальные результаты, полученные с помощью лучшей модели ARIMA для краткосрочного прогнозирования, позволяют направлять инвесторов и создавать выгодные инвестиционные ре-
тл « «
шения. В этой статье анализ и прогнозы сосредоточены на цене трех акций трех разных секторов: SOLA (компания Solidere, сектор развития и реконструкции), BYB (Byblos bank, банковский сектор) и HOLC (Holcim Liban, промышленный сектор). Три компании были выбраны на основе рыночной капитализации по секторам деятельности на Бейрутской фондовой бирже (BSE) и их роли в экономическом развитии Ливана. Данные взяты за период с 29 апреля 2021 г. по 29 апреля 2022 г., прогноз сделан до 5 мая 2022 г. Эффективность прогнозирования различных моделей ARIMA с целью определения лучшей модели в каждом исследуемом секторе диагностировалась на основе стандартных критериев выбора модели (AIC, BIC, логарифмическое правдоподобие и SigmaSQ). Результаты эмпирического анализа показали, что модели ARIMA (1,1,1), ARIMA (1,1,1) и ARIMA (1,1,2) являются лучшими моделями прогноза для BYB и HOLC и SOLA соответственно.
Ключевые слова: анализ временных рядов; моделирование; авторегрессионное интегрированное скользящее среднее (ARIMA); прогноз; акции. Дата поступления статьи: 27 февраля 2023 г.
Для цитирования: Nasser Aldine A. A. Forecasting Lebanese stocks using ARIMA models. Digital models and solutions. 2023. Vol. 2, no. 1. DOI: 10.29141/2782-4934-2023-21-1. EDN: VWIFAL.
introduction
Over the past years, the researchers have been interested in studying of stock market performance and its trends to predict various outcomes by means of statistical modeling The most efficient way to forecast is to understand the present scenarios. The mathematical and statistical method of time series analysis is used to explain natural events and their behavior through time. Forecasting financial time series such as stock market has drawn considerable attention among applied researchers because of the vital role which stock market play on the economy of any nation. Forecasting stock indices is very difficult because the market indices
Математические и имитационные модели экономики Mathematical and simulation models of the economy
are highly fluctuating as result of increase or decrease that characterize the stock price. Fluctuations are affecting the investor's belief. Determining more effective ways of stock market index prediction is important for stock market investors to make more informed and accurate investment decisions.
To date, autoregressive integrated moving average (ARIMA) model is the mostly widely used time series model for forecasting stock market series. The key factor behind the proposed method is the lack of a statistically significant correlation between market parameters and the target price of closing. Perhaps because of the reality that if the prospect market worth of the stocks is effectively expected, the depositors can be driven, the idea of forecasting stock market return has become very popular.
Looking to the literature review of ARIMA models, we can easily see that ARIMA models are applied to analyze and forecast time series data in much empirical research. Paul et al. [1] seek to determine the best ARIMA model for forecasting the average daily share price indices for shares of a pharmaceutical company in Bangladesh, their study utilized AIC, SIC, AME, RMSE and MAPE as the selection criteria. Upon testing several models, the study found ARIMA (2,1,2) to be the best model for forecasting the shares of the pharmaceutical company. Likewise, Wahyudi [2] attempted to predict stock price volatility of equities that are listed on the Indonesia Stock Exchange using the ARIMA model. Whilst using the Indonesia Composite Stock Price Index, results of the empirical analysis evidenced that the best ARIMA model was (0, 0, 1). This model was determined based on the AIC criterion.
Also, from an agricultural perspective, Jadhav et al. [3] applied univariate ARIMA techniques to forecast and validate farm prices of cereals in Karnataka state, India. Upon analysis, the study made pragmatic findings that suggested that the ARIMA model is empirically applicable for forecasting and validating farm prices of cereal crops. Similarly, Fattah et al. [4] seek to model and forecast the sales demand for the products sold by a food company, using a time series approach. The study which utilized past demand information of customer purchases, tested several ARIMA models to forecast and anticipate future demand. Based on the AIC, SBC, maximum likelihood and standard error criteria, the study found the ARIMA (1,0,1) as the best model to predict future demand for food products of the company.
From a macroeconomic perspective, Abonazel & Abd-Elftah [5] sought to develop an appropriate ARIMA model to forecast and validate the Egyptian annual gross domestic product (GDP). Upon utilizing the Box-Jenkins approach, the researchers noted the ARIMA (1,2,1) as the most suitable model for forecasting and validating Egyptian annual GDP. Alsharif et al. [6] utilized ARIMA models for both daily and monthly solar radiation in Seoul, South Korea, using solar radiation data. Through a critical empirical analysis, the findings of the study suggested that while ARIMA (1,1,2) model can be used to predict daily solar radiation, ARIMA (4,1,1) model can be effectively used to predict monthly solar radiation.
Eke [7] asserted that the ARIMA (2,0,3) is the best fit model for predicting the Nigerian Stock Exchange monthly stock market returns over a ten-year period. This assertion was based on the use of the Box-Jenkins technique, as well as the AIC and MSE performance criteria. In a similar study, Mustapa & Ismail [8] sought to develop an appropriate ARIMA
Математические и имитационные модели экономики Mathematical and simulation models of the economy
model that best fits the S&P 500 monthly stock prices for a 17-year period to enhance portfolio and investment decision making. Upon testing several models, the study found the ARIMA (2,1,2) and GARCH (1,1) as the most appropriate models for predicting the S&P 500 monthly stock prices.
At the early period of the Covid-19, Alzahrani et al. [9] sought to forecast the daily increases of cases in Saudi Arabia and the possibility of the Umrah & Hajj Pilgrimages 2020. The researchers utilized four different prediction models: the AR model, MA model, ARMA model and ARIMA model. Upon testing all models, the study found the ARIMA model to explicate the best predictive power amongst other models. The ARIMA model further predicted the suspension of the Umrah & Hajj Pilgrimages, 2020.
In a likewise context, Singh et al. [10] utilized the ARIMA model to predict the spread trajectories as well as mortalities of COVID-19 in the top 15 countries as of April 2020. The study utilized the model to forecast the spread of the virus and its associated mortalities for the subsequent two months. The findings suggested a decline in both cases and associated mortalities in China, Switzerland, and Germany. However, it was predicted that countries such as the United States, Spain, Italy, France, and the United Kingdom will witness increases in the spread of the virus as well as its associated mortalities Singh et al. [10].
Research Methodology
A quantitative research design was adopted for this study and the data used was collected from the investing website on Stocks prices series within 29th April 2021 to 29th April 2022 in Beirut Stock Exchange. The selected stocks data were based on data availability and the sampling technique is purposive. The method of data analysis for this paper is descriptive statistics (using mean and standard deviation for the data summary) and time series using unit root test to test for stationarity of the Stock's price series and the autoregressive integrated moving average (ARIMA) to predict the future values of the Stock's price rate in Beirut Stock Exchange. The ARIMA model was developed by Box and Jenkins. It is also known as the Box-Jenkins methodology which consists of some major steps as identifying, estimating, and diagnosing.
In financial forecasting, the model is one of the most widely used approaches Pai & Lin [11]; Merh et al. [12]. ARIMA models have demonstrated their efficient ability to produce short-term predictions. In terms of short-term prediction, it consistently outperformed complicated structural models Meyler et al. [13]. The ARIMA model consists of several steps such as identification, estimation, diagnostic and forecast.
Identification of the model, this involves selecting the most appropriate lags for the AR and MA parts, as well as determining if the variable requires first-differencing to induce stationarity. The ACF and PACF are used to identify the best model. (Information criteria can also be used).
Estimation, this usually involves the use of a least squares estimation process.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Diagnostic testing, which usually is the test for autocorrelation. If this part is failed then the process returns to the identification section and begins again, usually by the addition of extra variables.
Forecasting, the ARIMA models are particularly useful for forecasting due to the use of lagged variables.
The statistical software used for the analysis of this paper is EViews version 12.0.
The unit root test, also known as the stationarity test, indicates the presence of a unit root when the series lacks stationarity and may lead to spurious results and the absence of a unit root when there is a presence of stationarity in the series. To resolve the problem of spurious results, the unit root test is accomplished using the augmented Dickey-Fuller test (ADF). The hypothesis to accomplish the unit test can be stated as:
H0: there is a presence of a unit root (series is not stationary) vs Ha: there is no unit root (the series is stationary). The ADF test can be presented mathematically as:
AYt = 0 + yY - 1 + I = 1PY - i + ©t.
Where, 0 is a constant, y is the coefficient of process root, P/ coefficient in time tendency, p is the lag order and ©t is the disturbance (error) term.
Model specification
ARIMA model is generally expressed in the form (p, d, q) which was built from the combination of three building blocks, namely, p for Autoregressive (AR), d for Integration order term (I) and q for Moving Average (MA) for modeling the serial correlation in the disturbance. This means that ARIMA considers both the past values (AR) and the mean residuals of the error term (MA).
The general Autoregressive (AR (p)) of orderp can be expressed below as:
yt = Yt + OY- 1 + ®2 Yt- 2 + ... ®P Yt- p + £/. (1)
While MA (q) is specified as:
yt = ^t + ©1£t - 1 + ©2£t - 2 - ... + ©q £t - q. (2)
While MA (q) is specified as:
Therefore, ARMA (p, q) is given as:
yt = Yt + ®1Yt - 1 + O2Yt - 2 + ... OpYt - P + £t + ©1£t - 1 + ©2£t - 2 - ... + ©q£t - q. (3)
Hence, ARIMA process of order (p, d, q) can be specify using backward shift operator as:
O(£) Ad yt = 5 + 0(£)et; (4)
O(B) = 1 - 91B - 91B2 - ••• ... - 9pBp; (5)
0(B) = 1 - B1B - B2B2 - ••• ... - 02B2. (6)
Where O(B) is the autoregressive operator while 0 (B) is the moving average operator
Математические и имитационные модели экономики Mathematical and simulation models of the economy
However, ARIMA (p, d, q) can also be expressed as:
Yt = Ifi = 1 Ф/ yt - 1 + Xq = 1 0Q -j + e/r
(7)
Results and Discussion
The official daily data of stocks prices of Beirut Stock Exchange between 29th April 2021 and 29th April 2022 has a total number of 253 observations which are used to estimate and forecast the model. It must be noted that the stocks are divided into three parts: first part is SOLA construction stock, BYB bank stock (Byblos bank) and HOLC cement stock. The data contain missing data because each stock was not trade in every day. The data used in the study is provided by investing website. Table 1 displays the descriptive statistics of the Beirut stock exchange for the selected period studied. It shows positive skewness in each stock which refers to the degree to which the data are asymmetric. Furthermore, BYB and HOLC have high positive kurtosis greater than 3, indicating that the distributions are leptokurtic, have larger tails than the normal distribution while the kurtosis of SOLA is less than 3 which indicates platykurtic distribution. And, according to the Jarque-Bera statistics, the distribution of HOLC and SOLA is normal at the 99 % confidence level since the probability is more than 0.01, while for BYB is not normal.
Table 1. Descriptive statistics
BYB PRICE HOLC PRICE SOLA PRICE
Mean 0.891028 19.10008 29.59885
Median 0.890000 19.04000 30.06000
Maximum 1.040000 22.99000 37.71000
Minimum 0.780000 15.90000 24.32000
Std. Dev. 0.043613 1.446810 3.049640
Skewness 0.368960 0.145975 -0.220849
Kurtosis 4.442960 3.051708 2.557996
Jarque-Bera 27.68936 0.926704 4.116144
Probability 0.000001 0.629171 0.127700
Sum 225.4300 4832.320 7488.510
Sum Sq. Dev. 0.479333 527.5014 2343.677
Observations 253 253 253
Stationarity test
The Stock's price series during 29th April 2021-29th April 2022 are plotted is Figure 1. It shows that all the stocks maintain unstable pattern in their stock's growth. The result of the stationarity test (ADF test and KPS test) on the data is given in Table 2.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Figure 1. The Stock's price series during 29th April 2021-29th April 2022
Table 2. ADF and KPS tests results
Variables Testing for the Stationary of the data
ADF test Ho: Unit roots KPS test Ho: Unit roots
(assumes common unit root process) (assumes common unit root process)
Indicator At level First differences of log At level First differences of log
BYB PRICE Test statistic -2.0397 -10.8253* 1.664 0.2019*
1% level -3.457 -3.457 0.739 0.739
5% level -2.873 -2.873 0.463 0.463
10% level -2.573 -2.573 0.347 0.347
HOLC PRICE Test statistic -2.2923 -8.1552 1.1037 0.0579*
1% level -3.457 -3.457 0.739 0.739
5% level -2.873 -2.873 0.463 0.463
10% level -2.573 -2.573 0.347 0.347
SOLA PRICE Test statistic -2.073 -19.3330* 1.2167 0.0881*
1% level -3.456 -3.456 0.739 0.739
5% level -2.873 -2.873 0.463 0.463
10% level -2.573 -2.573 0.347 0.347
ADF and KPS test is greater than the critical value of the significance level of 0.01, 0.05 and 0.1, It should be highlighted that both the ADF test and the KPS test fail to reject the null hypothesis at the original data, that is to say, the original stocks sequence is non-stationary. The observed time series were transformed to bring them to the stationary process. Since there is an anomalous value in this series because the series contain missing value which was replaced by interpolation methods to prevent the results from being distorted.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
However, ADF and KPS are less than the three critical values of the test level. That is to say, the AlogBYB and AlogHOLC and AlogSOLA sequence after the logarithmic change and the first-order difference is a stationary series, and the significance test of the stationarity is passed.
Model identification
With the EViews software, the autocorrelation and partial autocorrelation function graphs of the series are plotted in Figure 2.
Figure 2. ACF and PACFplots
From the autocorrelation and partial autocorrelation function graphs of the series. For AlogBYB price, the 1st and 2nd lag in partial autocorrelation graph are above the confidence band so p = 1 or p = 2. To determine the order of the autoregressive component,the 1st lag is greater than confidence band in autocorrelation graph so q = 1. In order to determine the order of moving average component for AlogHOLC price, the 1st lag in partial autocorrelation is above the confidence band so p = 1 to determine for autoregressive component, 1st lag is greater than confidence band in autocorrelation graph so q = 1, while for AlogSOLA price, the 1st and 2nd lag in partial autocorrelation are above the confidence band so p = 1 or p = 2 in order to determine the order of the autoregressive component, and 1st and 2nd lag are greater than confidence band in autocorrelation graph so q = 1 or q = 2 in order to determine the order of moving average component. Considering that the judgment is very subjective, to establish a more accurate model, the range of values of p and q is approximately relaxed and multiple ARMA (p, q) models are established. The order with 0, 1, 2 in autoregressive moving average pre-estimation is performed on the processed samples data. Table below lists the test results of ARMA (p, q) for different parameters. Adjusted ^-squared, AIC value, SC value and S.E. of regression are all important criteria for selecting models. The AIC criterion and the SC criterion are mainly used for ranking and select the optimal model. Generally, the larger the
Математические и имитационные модели экономики Mathematical and simulation models of the economy
coefficient of determination, the smaller the AIC value and the SC value, and the residual variance, the corresponding ARMA (p, q) model is superior.
It should be emphasized that although the appropriate ARIMA model is usually selected using the AIC value and the SC value. However, the minimum AIC value and the SC value are not sufficient conditions for the optimal ARMA model, therefore I must go further with uses of SigmaSQ (volality measure) and log-likelihood. I take smallest value in SigmaSQ (volality measure) and biggest value for log-likelihood.
In Table 3, the model that did pass the parameter significance test and the residual randomness test was identified by "*". Finally, it is preferable to prefer the ARMA (1,1) model in AlogBYB and AlogHOLC time series and ARMA (1,2) model in AlogSOLA time series.
Table 3. AIC and SC criterion
Variables (pq) SigmaSQ AIC SC Log-likelihood
AlogBYB price (1,1)* 0.000282* -5.282298* -5.22628* 669.5696*
(0,1) 0.000294 -5.272451 -5.244440 666.3288
(1,0) 0.000381 -5.018534 -4.990523 634.3353
(1,2) 0.000290 -5.27009 -5.21407 668.0312
(2,1) 0.000293 -5.26048 -5.20446 666.8205
(2,2) 0.000458 -4.81989 -4.76386 611.3056
AlogHOLC price (1,0) 0.000038 -7.306264 -7.278253 922.5893
(1,1)* 0.000053 -7.341898* -7.285876* 929.0792*
(0,1) 0.000038 -7.330693 -7.302681 925.6673
(1,2) 0.000037* -7.32054 -7.267032 926.7048
(2,1) 0.000038 -7.320109 -7.264086 926.3338
(2,2) 0.000041 -7.224685 -7.168662 914.3103
AlogSOLA price (1,1) 0.000297 -5.250195 -5.194172 665.5245
(1,0) 0.000318 -5.198271 -5.170260 656.9822
(0,1) 0.000313 -5.216174 -5.188162 659.2379
(1,2)* 0.000296* -5.253168* -5.197147* 665.8992*
(2,1) 0.000304 -5.227915 -5.171893 662.7173
(2,2) 0.000305 -5.223585 -5.167562 662.1717
Model establishment and inspection The final model of the stocks sequence for the specific form of the models are present below and y = Yt + - 1 + ®2 Yt - 2 + ... + ®pYt - p + 8/ + ©18/ - 1 + ©26/ - 2 - ... + ©q8t - q.
The data in parentheses below the equation is the t-test statistic of the corresponding estimate value.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Dependent Variable: D(LOG_BYB_)
Variable Coefficient Std. Error t-Statistic Prob.
С -0.000168 2.07E-05 -8.127645 0.0000
AR(1) 0.204789 0.059749 3.427494 0.0007
MA(1) -1.000000 53.93544 -0.018524 0.9852
SIGMASQ 0.000232 0.000373 0.756600 0.4500
R-squared 0.392253 Mean dependentvar 7.93E-05
Adjusted R-squared 0.384901 S.D. dependentvar 0.021598
S.E. of regression 0.016939 Akaike info criterion -5.282298
Sum squared resid 0.071161 Schwarz criterion -5.226276
Log likelihood 669.5696 Hannan-Quinn criter. -5.259756
F-statistic 53.35486 Durbin-Watson stat 1.994008
Prob(F-statistic) 0.000000
Figure 3. Output ofthe ARMA (1,1) model in AlogBYB
For the
A logBYBt = -0.000168 + 0.2047897/ _ 1 - 1.0008/ _ 1 + 8t;
(-8.1765) (3.427493) (-0.018386)
CTBYB = 0.016939. (8)
The estimated value of the variance of the corresponding error term is 0.016939. It can be seen from the t statistic of the model coefficients and AR(1) and its P value of the parameter estimates are significant at the significance level of 0.01 while the MA(1) and its parameter isn't significant.
Dependent Variable: D(LOG_HOLC_)
Method: ARMA Maximum Likelihood (OPG - BHHH)
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000529 0.000664 0.797839 0.4257
AR(1) -0.345179 0.103039 -3.349968 0.0009
MA(1) 0.707713 0.089254 7.929186 0.0000
SIGMASQ 3.67E-05 1.44E-06 25.46706 0.0000
R-squared 0.129879 Mean dependentvar 0.000520
Adjusted R-squared 0.119353 S.D. dependentvar 0.006508
S.E. of regression 0.006107 Akaike info criterion -7.341898
Sum squared resid 0.009250 Schwarz criterion -7.285876
Log likelihood 929.0792 Hannan-Quinn criter. -7.319356
F-statistic 12.33926 Durbin-Watson stat 1.960504
Prob(F-statistic) 0.000000
Figure 4. Output ofthe ARMA (1,1) model in AlogHOLC
A logHOLQ = 0.000529 - 0.3451797/ _ 1 + 0.707713et _ 1 + et;
(0.797839) (-3.349968) (-7.929186)
oholc = 0.006107. (9)
Математические и имитационные модели экономики Mathematical and simulation models of the economy
The estimated value of the variance of the corresponding error term is 0.006107. The P value of AR(1) and MA(1) parameters estimates are significant at the significance level of 0.01 while the constant parameter isn't significant.
Dependent Variable: D(LOG_SOLA_)
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000571 0.000642 0.889146 0.3748
AR(1) -0.236412 0.046055 -5.133212 0.0000
MA(2) -0.346929 0.037797 -9.178769 0.0000
SIGMASQ 0.000296 1.40E-05 21.20038 0.0000
R-squared 0.095245 Mean dependent var 0.000673
Adjusted R-squared 0.084301 S.D. dependent var 0.018135
S.E. of regression 0.017354 AkaiKe info criterion -5.253168
Sum squared resid 0.074687 Schwa (z criterion -5.197146
Log likelihood 665.8992 Hannan-Quinn criter. -5.230626
F-statistic 8.702470 Durbin-Watson stat 1.890062
Prob(F-statistic) 0.000016
Figure 5. Output of ARMA (1,2) model in AlogSOLA
A logSOLAt = 0.000571 - 0.236412Yt _ 1 - 0.346929et _ 1 + et;
(0.889146) (-5.133212) (-9.178769)
osola = 0.017354. (10)
The estimated value of the variance of the corresponding error term is 0.017354. The P value of AR(1) and MA(1) parameters estimates are significant at the significance level of 0.01 while the constant parameter isn't significant.
The model is used to fit the data, and the result is shown in Figures 6-8. In the figures, the fitted data is very closed to actual data and residual are far from the actual data this indicated that the models fitted the data.
ActL^I, Fitted and Residual graph of ARIMA(1,1,1] of LogBYB series
25 SO 75 100 125 1SD 175 200 225 250
—w— Residual —■— Actual —Fitted
Figure 6. Residuals, Actual and fitted data ofALogBYB series
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Figure 7. Residuals, Actual and fitted data of ALogHOLC series
Figure 8. Residuals, Actual and fitted data ofAlogSOLA series
However, after I have selected the best models, I ensured that the model satisfies the requirements to forecast and predict the future values, therefore the model satisfied the following:
• No autocorrelation, i. e. Residual of the model are white noise (Ljung-Box Q statistic) (Figure 9).
• Satisfied stability condition, i. e. the inverse roots must lie inside the unit circle (Figure 10). A white noise test is performed on the residual after fitting the models. The autocorrelation
and partial autocorrelation function graphs of the residual series show that the residual is a white noise since all the graphs are within the confidence bound, this indicating that the model is valid for estimation and forecasting.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Figure 9. ACF and PACF Graphs of ALogBYB, ALogHOLC, ALogSOLA residual
Figure 10. Inverse roots of AR/MA Polynomials
Also, by plotting the inverse roots we can see that all the inverse roots lie inside the unit circle. The models satisfied the stability conditions, and the error terms are white noise.
Data forecasting
Under the graphical interface in EViews software, Dynamic forecast mode is used to predict the Stocks values from 1-May-2022 to 5-May-2022. The results are listed in Table 7.
From the plot above we can conclude that HOLC and SOLA stock exchange will be increasing as the days go, while BYB stock price will be decreasing as the days go.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
Table 7. Forecasting value
Day, month HOLC stock price BYB stock price SOLA stock price
1-May-2022 21.618110 0.782946 37.999200
2-May-2022 21.640721 0.782601 38.039632
3-May-2022 21.663330 0.782256 38.080067
4-May-2022 21.689470 0.781912 38.120503
5-May-2022 21.708561 0.781567 38.160938
Conclusion
The study aims to investigate the application of autoregressive integrated moving averages (ARIMA) for forecasting the prices of some stocks of Beirut Stock Exchange. The outcome of the empirical analysis indicated that ARIMA (1,1,1), ARIMA (1,1,1) and ARIMA (1,1,2) models are the best forecast models for BYB (Byblos bank, Banking sector), HOLC (Holcim Liban, industrial sector) and SOLA (Solidere Company, development and reconstruction sector) respectively.
It was suggested that the Lebanese stock market performance made it possible to forecast the stock prices. However, the suggestion made here may has certain limitation because the data in the study has many missing values, which was auto filled with uses of interpolation method and the results obtain may not reliable since the data isn't original data. The high requirements for forecast results and the uncertainty of the situation have led to the need for adaptive forecasting methods and will prompt a significant amount of further additional research in the Lebanese stock market.
Источники
1. Paul, J. C., Hoque, M. S., & Rahman, M. M. (2013). Selection of best ARIMA model for forecasting average daily share price index of pharmaceutical companies in Bangladesh: a case study on Square Pharmaceutical Ltd. Global Journal of Management and Business Research, 13(3), 14-26.
2. Wahyudi (2017). Time series model and forecast of GDP per capita in Tianjin. Northern Economy, 3, 44-46.
3. Jadhav, V., Chinnappa, R. B., & Gaddi, G. (2017). Application of ARIMA model for forecasting agricultural prices. Journal of Agricultural Science and Technology, 19, 981-992.
4. Fattah, J., Ezzine, L., Aman, Z., El Moussami, H., & Lachhab, A. (2018). Forecasting of demand using ARIMA model. International Journal of Engineering Business Management, 10, 1-9. https://doi.org/10.1177/1847979018808673.
5. Abonazel, M. R., & Abd-Elftah, A. I. (2019). Forecasting Egyptian GDP using ARIMA models. Reports on Economics and Finance, 5(1), 35-47. https://doi.org/10.12988/ ref.2019.81023.
Математические и имитационные модели экономики Mathematical and simulation models of the economy
6. Alsharif, M. H., Younes, M. K., & Kim, J. (2019). Time series ARIMA model for prediction of daily and monthly average global solar radiation: the case study of Seoul, South Korea. Symmetry, 11(2), 240. https://doi.org/10.3390/sym11020240.
7. Eke, C. N. (2019). Time series analysis on monthly stock market returns of the Nigerian stock exchange: an ARIMA modeling approach. Asian Journal of Economics, Business and Accounting, 11(4), 1-9. https://doi.org/10.9734/AJEBA/2019/v11i430138.
8. Mustapa, F. H., & Ismail, M. T. (2019). Modelling and forecasting S&P 500 stock prices using hybrid Arima-Garch Model. Journal of Physics: Conference Series, 1366, 012130. https://doi.org/10.1088/1742-6596/1366/1Z012130.
9. Alzahrani, S. I., Aljamaan, I. A., & Al-Fakih, E. A. (2020). Forecasting the spread of the COVID-19 pandemic in Saudi Arabia using ARIMA prediction model under current public health interventions. Journal of Infection and Public Health, 13(7), 914-919. https:// doi.org/10.1016/j.jiph.2020.06.001.
10. Singh, R. K., Rani, M., Bhagavathula, A. S., Sah, R., Rodriguez-Morales, A. J., Kalita, H., Nanda, C., Sharma, S., Sharma, Y. D., Rabaan, A. A., Rahmani, J., & Kumar, P. (2020). Prediction of the COVID-19 pandemic for the top 15 affected countries: advanced autoregressive integrated moving average (ARIMA) model. JMIR Public Health and Surveillance, 6(2), e19115. https://doi.org/10.2196/19115.
11. Pai, P. F., & Lin, C. S. (2005). A hybrid ARIMA and support vector machines model in stock price forecasting. Omega, 33(6), 497-505. https://doi.org/10.1016/j.omega.2004.07.024.
12. Merh, N., Saxena, V. P., & Pardasani, K. R. (2010). A comparison between hybrid approaches of ANN and ARIMA for Indian stock trend forecasting. Business Intelligence Journal, 3(2), 23-43.
13. Meyler, A., Kenny, G., & Quinn, T. (1998). Forecasting Irish inflation using ARIMA models. Dublin.
Information about the authors
Abdo Ali Nasser Aldin, PhD student. Belarusian State Economic University, 220070, Republic of Belarus, Minsk, Partizansky Ave., 26. E-mail: [email protected].
Информация об авторах
Абдо Али Нассер Альдин, аспирант. Белорусский государственный экономический университет, 220070, Республика Беларусь, г. Минск, Партизанский проспект, 26. E-mail: [email protected].
