TX_1~ABS:AT/ADD:TX_2~ABS:AT 12 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 ReseaRch aRticle US Dollar/IQ Dinar Currency Exchange Rates Time Series Forecasting Using ARIMA Model Parzhin A. Mohammed1, Sami A. Obed1, Israa M. Ali1, Dler H. Kadir1,2 1Department of Statistics, College of Administration and Economics, Salahaddin University-Erbil, Kurdistan Region - F.R. Iraq., 2Department of Business Administration, Cihan University-Erbil, Iraq ABSTRACT The use of currency exchange estimation as a tool for economic planning is being researched as a technique for gaining economic stability. The main purpose of this study is to use the Autoregressive Integrated Moving Average (ARIMA) model to forecast monthly US dollar against IQ dinar exchange rates. The information was gathered from January 2010 to December 2020. We got the information from the website (sa.investing.com). The minimum value of root means square error and the Mean Absolute Error are used to select the optimal model. ARIMA (2, 1, 0) was found to be the best model for the US Dollar/IQ Dinar series. This is the forecasted meaning for the future of this exchange rate time series, which indicates a perpetual increase continuously in the next two years. Statgraphics version 15 was the statistical software package utilized to complete this project. Keywords: Exchange rate forecasting, US Dollar/IQ Dinar, time-series analysis, autoregressive integrated moving average model INTRODUCTION Time series analysis is used in a wide variety of fields. In economics, time series are used to represent the economy’s recorded history. The consumer price index, gross national product, and unemployment, as well as the population, products, and output, are all measured in the same time series. The statistical theory of time series has sparked a lot of interest in recent years. It is generally believed that the degree of financial transactions in and out of a country depends on several factors prevailing in that country. Since the advent of money, the world has always experienced the movement of money from one country to another due to economic, cultural, social, political, and other reasons. The Central Bank in every country usually keeps a record of such money transactions through various financial intermediaries. Every country has its own money, which can only be accepted for use within its territory. Hence, the establishment of foreign money became necessary. Foreign money is the money of other countries of the world which serves as money in the foreign exchange market. The researcher’s study time-series data to attempt to establish a strong statistical way for forecasting a future rate of exchange of the US dollar over the Iraqi dinar basis on previous data here on the exchange rate of the US dollar and the Iraq dinar. Using the historic date of the exchange rate of the local currency against the foreign currency, this statistical tool can be used to forecast the rate of exchange of any foreign currency. The most common technique in time series is Box-Jenkins modeling. The other name of it is Autoregressive Integrated Moving Average (ARIMA) modeling. Recent work on ARIMA forecasting has revealed an apparent accuracy for forecasting. ARIMA models have been applied for US Dollar/IQ Dinar Currency Exchange Rates time series forecasting. In this work, the original dataset has 132 observations. ARIMA modeling was used to forecast two years ahead of data. The rest of the paper is structured as the following: Section 2 describes the methodology of Box Jenkins and provides a brief introduction to the theory of ARIMA model building. Section 3 introduces the data used in this study and follows the ARIMA procedure for building an adequate model for the forecasting exercise and discusses the results. Finally, section 4 is devoted to conclusions.[1-5] Corresponding Author: Parzhin A. Mohammed, Department of Statistics, College of Administration and Economics, Salahaddin University - Erbil, Kurdistan Region - F.R. Iraq,. E-mail: Parzhin.mohammrd@su.edu.krd Received: November 29, 2021 Accepted: January 02, 2022 Published: February 10, 2022 DOI: 10.24086/cuesj.v6n1y2022.pp12-19 Copyright © 2022 Parzhin A. Mohammed, Sami A. Obed, Israa M. Ali, Dler H. Kadir. This is an open-access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0). Cihan University-Erbil Scientific Journal (CUESJ) Mohammed, et al.: Time series forecasting using ARIMA Model 13 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 METHODOLOGY This section introduces some basic definitions and concepts. Time Series A time series is a collection of correlated observations made in a specific order across time. A discrete-time series is one in which the set T 0 of times at which observations are taken is discrete, such as when they are conducted at fixed intervals. When observations are recorded continuously across a time interval, such as when T 0 = [0, 1], a continuous-time series is obtained. If we want to emphasize that observations are recorded continuously, we’ll use the notation (t) rather than X.[6,7] Stationary Time Series The first and second moments of a stochastic process X t are deemed stationary although they are time-invariant. To put it another way, if the first criterion is met, X t is stationary, meaning that all members of a stationary stochastic process have the same constant mean. For example, a time series generated by a stationary stochastic process must vary around a constant mean and not show a trend. The variances are often time-invariant due to the second requirement. The variance σ µ2 2x t xE X= −[ ( ) ] =0 is independent of t when k = 0. Furthermore, the covariance E [(X t −μ x ) (X t−k −μ x )] = γ k depends only on the distance in time k between the two members of the process, not on t.[8,9] Time Series Models A time series model for observed data X t is a description of the joint distributions (or, in some cases, just the means, and covariance) of a set of random variables X t , where X t is supposed to represent a realization.[10] Autoregressive (AR) Model A process {X t } is said to be an AR model of an order p, abbreviated AR (p), is of the form. X t =∅ 1 X t−1 + ∅ 2 X t−2 +….+ ∅ p X t−p +ϵ t (1) Where it X t is stationary, ∅ 1 , ∅ 2 ,…., ∅ p , are constants (∅ p ≠0).[11] Moving Average (MA) Model A process {X t } is called to be the MA model of order q, or MA (q) model, is identified to be X t = ϵ t −θ 1 ϵ t−1 −θ 2 ϵ t−2 −…− θ q ϵ t−q (2) Where there are q lags in the MA and θ 1 , θ 2 ,….θ p (θ p ≠0) are parameters.[11] ARMA Model The process {X t , t = 0, ± 1, ± 2.,}is said to be an ARMA(p, q) process if {X t } is stationary and if for all the t, X t −∅ 1 X t−1 − −∅ p X t−p = ε t + θ 1 ε t−1 + +θ q ε t−q (3) where {ϵ t } ~ N (0,σ2). We say that {X t } is an ARMA (p, q) process with mean μ. If X t −μ} is an ARMA (p, q) process.[7] ARIMA Model If the dth difference Z t = ∇dX t is a stationary ARMA process, a time series {X t } is said to follow an integrated ARMA model. We state that {X t } is an ARIMA (p, d, q) process if {Z t } follows an ARMA (p, q) model. Fortunately, we can typically take d=1 or 0 greater than for practical purposes.[9] Consider an ARIMA (p, 1, q) process. With Z t = X t −X t−1 , we have Z t = ∅ 1 Z t−1 + ∅ 2 Z t−2 +…+ ∅ p Z t−p +ϵ t −θ 1 ϵ t−1 –θ 2 ϵ t−2 … −θ q ϵ t−q (4) Stages of Time -Series Model Building The process of a three-step adaptive approach is used to build an ARIMA model. First, previous data analysis helps to identify a probable model of a time series model class. Second, the model’s unknown parameters are approximated. Finally, diagnostics checks are carried out through residue left models to analyze the model’s appropriateness or to predict possible developments. Then, we will go through each of these processes in any further context.[12] Identification To make the data stable, it may have to be pre-processed. Some of the other four stages below must be followed to achieve stationarity: 1- Start by looking at it. 2- Rescale it using a logarithmic or exponential transform, for example. 3- Take out the deterministic elements. 4- And that is the distinction. To put it another way, take ∇(B)d X until you reach a stop. In most cases, d = 1,2 will enough. The autocorrelations decline to zero exponentially fast, indicating that the system is stationary. We can try to fit an ARMA (p, q) model when the series is stationary. The correlogram � 0  ˆ  /kkr γ γ= and partial autocorrelations ˆ kk∅ are considered. The following observations have previously been made. Both the sample ACF and PACF, as previously mentioned, have a standard deviation of around 1/N, where N is the length of the series. A good rule of thumb is that ACF and PACF values between ±2/√N are inconsequential. for k > max (p, q), the kth order sample ACF and PACF decay geometrically in an ARMA (p, q) process, as shown in Table 1.[13,14] Estimations of parameters Various methods, such as the moment method, least squares, maximum likelihood, and Yule-Walker estimate, can also Table 1: Theoretical ACF and PACF properties for stationary processes Process ACF PACF AR (p) Tails off as exponential decay or damped sine wave Cuts off after lag p MA (q) Cuts off after lag q Tails off as exponential decay or damped sine wave ARMA (p, q) Tails off after lag (q-p) Tail off after lag (q-p) Mohammed, et al.: Time series forecasting using ARIMA Model 14 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 be used to predict the values as in the tentatively defined model.[12] Verification of the model The box-Jenkins methodology’s confirmation procedure is rather extensive. The predicted model’s compliance with the examined data must be confirmed using various diagnostic tests.[15] Forecasting[12] Once a suitable time series model has been fitted, it may be used to create forecasts of observations in the future. If the current time will be is denoted by T, the forecast for X T +τ is named the τ -period-ahead forecast, then denoted by ( ) ˆ TTX τ+ . The mean squared error, which is the averaged value of the squares prediction error, is the conventional criterion to use in getting the best forecast, ( ) 2    2ˆE[( T ) ] E [  ( ) ]T TTX eX τ τ τ+ +− = is minimized. It can be seen that the best forecast in the mean square sense is the conditional expectation of X T +τ given current and previous observations, that is, X T , X T−1 ,…. X X X XT T T T� |) ( , ,...)�� + + −=τ τ(T E 1 (5) Consider, for example, an ARIMA (p, d, q) process at time T+τ (i.e., τ a period in The future): X Xt i p d i t i T i q i T+ = + + − + = += + −+ ∅∑ ∑τ τ τ τδ θ 1 1   (6) And Box Jenkins described the flow chart shown in Figure 1.[16] The Dependable Statistical Standards to Test Forecasting Model Mean absolute error (MAE) ( ) ( ) N 1t 1 1 | |e 1      N ˆ |  |ˆ N t t N t t t t t Y Y NMAE Y Y N N == = − = = = − ∑∑ ∑ (7) Where t = time period, N = total number of observations, and e t = (observed value - forecasted value) at time t.[17] Root mean square error (RMSE)[1] This is simply the square root of MSE: 2 1 )    ˆ( n t t t Y Y RMSE MSE n = − = = ∑ (8) APPLICATION ON REALDATA Data Description The dataset used in this analysis is monthly US Dollar/IQ Dinar Currency Exchange rates time series forecasting using the ARIMA model. All the data were collected from the website (sa.investing.com).data were collected for the period January 2010 to December 2020. There were overall 132 observations. The statistical analysis was computationally implemented in the Stat graphics 15 software, as shown in Table 2. Time Series Plots The monthly exchange rate between the US Dollar/IQ Dinar is depicted in the data set’s time series plot. Because the variation in the size of the fluctuations with time is referred to as non- stationary in the variance, the plot reveals that the data is clear of being non-stationary in the mean and variance, seasonal, and trend patterns with an increasing variety of variance, as shown in Figure 2. Randomness Test First of all, the randomness test of the one series should be made using the Box-Pierce test. The null hypotheses are the time series are random, versus the alternative hypotheses of non-randomness, to know that the data has a certain behavior than having a random behavior. As explained in Table 3 for the series; as P < 0.05 to every series, therefore null hypotheses were rejected, meaning that the one-time series are not random series. The hypothesis was as follows for the exchange rate US dollar/IQ dinar the series. Figure 1: Depicts the Box-Jenkins model-building methodology Figure 2: Time series plot of the original monthly exchange rate USD/IQD data from 1 January 2010 to 31 December 2020 Mohammed, et al.: Time series forecasting using ARIMA Model 15 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 Table 2: Monthly average US Dollar/IQ Dinar Currency Exchange Rates data for the period 1 January 2010–31 December 2020 Years 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 January 1169.00 1166 1163.5 1163.25 1163.8 1164 1175.9 1181 1184.05 1186.43 1189.4 February 1165.9 1175 1163 1163 1163 1165 1196.44 1175 1184.05 1186.43 1189 March 1170 1175 1160.9 1160 1163.55 1163 1170 1166 1184 1189 1187.62 April 1170.1 1165 1160.9 1157 1162 1164 1165.7 1166 1185.24 1186.43 1187.62 May 1168 1166 1162.25 1145 1162.5 1165 1169.4 1167 1186.43 1186.43 1189 June 1168 1166 1162 1160.5 1162.9 1162 1167.2 1166 1190 1186.4 1187.62 July 1170.03 1166.05 1162.05 1162.5 1164.2 1156 1168 1167 1186.43 1186.43 1187.62 August 1171 1166 1162 1164 1161.3 1145 1162.7 1177.73 1186.43 1186.2 1187.62 September 1169.2 1166 1162 1163.8 1163.05 1131 1162.7 1166.1 1186.43 1186.43 1187.62 October 1169.05 1167 1162 1164 1162 1122 1164 1166 1186.43 1189 1189 November 1169.47 1167 1162 1160.8 1160 1108 1160.3 1182.8 1186.43 1187.62 1187.62 December 1166.5 1166.3 1163 1163.8 1142 1095 1181 1184 1186.43 1187.62 1459 Figure 3: Exchange rate USD/IQD series plot after non-seasonal differencing of orders one H 0 : The series is random H 1 : The series is not random Data Transformation After proving the non-randomness of the exchange rate US Dollar/IQ Dinar time series, it can be concluded that all the data series have a certain behavior, so to overcome this behavior we will try to transform the data series, each according to its behavior. Then, the data were transformed, for instance, a non-seasonal difference of order one for the variable. Then, the series was tested again to test the existence of randomness. The hypotheses were accepted when P > 0.05 as shown in Table 4. The hypothesis for the exchange rate USD/IQD series was as follows. H 0 : The series is random H 1 : The series is not random. It can be noticed that all the data series were accepted to be random after the transformations made on the series. Stationary The series under consideration must satisfy the condition of being stationary; that is, the mean and variance are independent of time throughout the series. The original series needs to be differentiated to make the series stationary around meaning and to get stationary around variance for the series, we make transformations The rest original series exchange rate US dollar/IQ dinar is needed non-seasonal differencing of order one transform to achieve stationary, Figure 3 show the differenced series. To identify the entire order of the models for the series, we investigate the Autocorrelation Function (ACF) and Partial ACF (PACF) for the original data. The ACF and PACF plots are displayed in the Figure 4 series. The estimated autocorrelations and PACF between corrected data values at various lags are shown in this table. The auto-correlation coefficient lag k determines between Table 3: Hypothesis of randomness test and P-value for data Series Box-pierce test P-value Decision Exchange rate USD/IQD 0.000 (SNR) Table 4: Hypothesis of randomness test and P-value for transformed data Series Box-Pierce test P-value Decision Exchange rate USD/IQD 1 (SR) the residuals at time t-k and time t is related and The partial autocorrelation coefficient measures the correlation between the residuals at time t and time t+k having accounted for the correlations at all lower lags 95.0% probability bounds around 0 are also indicated. There is a statistically significant association at the 95.0% confidence level if the probability bounds for a certain lag do not contain the calculated coefficient. The 95.0% probability bounds around 0 are also indicated. There is a statistically significant association at the 95.0% confidence level if the probability bounds for a certain lag do not contain the calculated coefficient. At the 95.0% confidence level, none of the 24 partial autocorrelation coefficients are statistically significant. The same procedure was conducted for the series; Table 5 through Table 6 contain that. Mohammed, et al.: Time series forecasting using ARIMA Model 16 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 Table 5: Estimated Autocorrelations for adjusted exchange rate USD/IQD Lag Autocorrelation Standard Error. Lower 95.0%Probability. Limit Upper 95.0%Probability. Limit 1 0.260945 0.087038 -0.170593 0.170593 2 0.211871 0.092776 -0.181839 0.181839 3 0.189218 0.096372 -0.188886 0.188886 4 0.174333 0.099146 -0.194324 0.194324 5 0.16255 0.101442 -0.198824 0.198824 6 0.160989 0.103397 -0.202654 0.202654 7 0.16544 0.105279 -0.206343 0.206343 8 0.16592 0.10723 -0.210168 0.210168 9 0.167997 0.109158 -0.213946 0.213946 10 0.178883 0.111099 -0.217751 0.217751 11 0.187412 0.11326 -0.221986 0.221986 12 0.170011 0.115586 -0.226544 0.226544 13 0.140489 0.117465 -0.230227 0.230227 14 0.1297 0.118731 -0.232709 0.232709 15 0.127231 0.119799 -0.234803 0.234803 16 0.128438 0.120819 -0.236801 0.236801 17 0.127931 0.121849 -0.23882 0.23882 18 0.132377 0.122862 -0.240806 0.240806 19 0.131391 0.123938 -0.242914 0.242914 20 0.119234 0.124989 -0.244974 0.244974 21 0.126591 0.125847 -0.246657 0.246657 22 0.120522 0.126808 -0.24854 0.24854 23 0.10901 0.127673 -0.250235 0.250235 24 0.0940275 0.128376 -0.251614 0.251614 Figure 4: The original monthly ACF and PACF for the US Dollar/IQ Dinar exchange rate data After we take the differenced series for the exchange rate, which is transformed into a stationary series of the mean and the variance, the ACF and PACF plots of the differenced series show that all the lags are within the confidence limits as shown in the mentioned Figure 5. Choosing Appropriate Model After checking for stationary of the time series’ mean and variance, the model identification process is used to determine the adequate model given the ACF and PACF. The appropriate model for the series is shown in Table 7. At least the RMSE and MAE are used to determine the best models. Model Identification After getting on the stationary for the time series study, the ACF and PACF are shown in the table accordingly for stationary data. We will examine the data in ACF and PACF. The ARIMA model for the exchange rate variable is obtained (2,1,0) 12 . Estimation It was found that the best model describing the exchange rate US Dollar/IQ Dinar series mentioned above, the parameters were estimated, as shown in Table 8. Mohammed, et al.: Time series forecasting using ARIMA Model 17 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 Model Diagnostic Checking The residuals for the fitted model should be just white noise for forecasting a good model; in other words, the chosen model has exhausted the whole behavior of the series. As a result, we compute and plot the ACF and PACF of the residuals; we want to find no significant ACF or PACF. Furthermore, the fitted model should accurately predict the future. Autocorrelation and partial autocorrelation of residual test The residual ACF and PACF of the models that we develop will be checked. Also, the model needs to pass the test for randomness of the residuals to prove that the model chosen has exhausted the data and that there are no significant remaining to be explained in the data. After the model diagnostics Figure 5: ACF and PACF of exchange rate time series after non-seasonal differencing of order one Table 6: Estimated Partial Autocorrelations for adjusted exchange rate USD/IQD Lag Partial autocorrelation Standard. Error Lower 95.0%Probability. Limit Upper 95.0%Probability. Limit 1 0.260945 0.0870388 -0.170593 0.170593 2 0.154285 0.0870388 -0.170593 0.170593 3 0.112343 0.0870388 -0.170593 0.170593 4 0.0880657 0.0870388 -0.170593 0.170593 5 0.0712356 0.0870388 -0.170593 0.170593 6 0.0682761 0.0870388 -0.170593 0.170593 7 0.0702673 0.0870388 -0.170593 0.170593 8 0.0654201 0.0870388 -0.170593 0.170593 9 0.0633015 0.0870388 -0.170593 0.170593 10 0.0712627 0.0870388 -0.170593 0.170593 11 0.073625 0.0870388 -0.170593 0.170593 12 0.0458525 0.0870388 -0.170593 0.170593 13 0.0129112 0.0870388 -0.170593 0.170593 14 0.00989309 0.0870388 -0.170593 0.170593 15 0.0141497 0.0870388 -0.170593 0.170593 16 0.0192469 0.0870388 -0.170593 0.170593 17 0.0192278 0.0870388 -0.170593 0.170593 18 0.0242387 0.0870388 -0.170593 0.170593 19 0.0214791 0.0870388 -0.170593 0.170593 20 0.00718463 0.0870388 -0.170593 0.170593 21 0.0199373 0.0870388 -0.170593 0.170593 22 0.0126535 0.0870388 -0.170593 0.170593 23 0.00311673 0.0870388 -0.170593 0.170593 24 -0.00737107 0.0870388 -0.170593 0.170593 Table 7: Evaluation of ARIMA models No. Model RMSE MAE 1 ARIMA (1,1,0) (2,1,2) 12 27.219 7.557 2 ARIMA (1,1,1) (1,0,1) 12 25.798 5.959 3 ARIMA (1,1,2) ( 2,0,1) 12 25.717 6.122 4 ARIMA (1,1,2) (1,0,1) 12 25.615 6.121 5 ARIMA (2,1,2) (2,0,1) 12 25.845 6.020 6 ARIMA (0,1,1) (1,0,1) 12 25.698 5.965 7 ARIMA (0,1,1) 12 25.549 5.733 8 ARIMA (1,1,1) 12 25.648 5.736 9 ARIMA (2,1,0) 12 25.494 5.664 10 ARIMA (1,1,0) 12 25.549 5.729 Mohammed, et al.: Time series forecasting using ARIMA Model 18 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 process, we can do further forecasts. Plots are displayed in the Figure 6 series. Goodness of fit test It is possible to know the adequate model ARIMA (2,1,0) for the exchange rate USD/IQD time series repeatedly using the Box and Pierce test. The null hypothesis is not rejected because the P-value is more than 0.05 and the model above is acceptable, implying that the residuals are also random and that the forecast will be adequate and dependable, as shown in Table 9. Forecasting After diagnosing the fitted model and selected as the best one, the final step comes forward forecasting. It is time to use the specified model for forecasting future values starting from January 2021 until December 2022, as shown in Table 10 and Figure 7. Table 8: Function Model, Parameter Estimate for Series Model Series Model Function Model Parameter Estimate θ1 � θ2 � ∅1 � ∅2 � Θ1 � Θ2 � Φ1 � Φ2 � Exchange rate ARIMA (2,1,0) 12 − −∆ = ∅ ∆ + ∅ ∆ +1 1 2 1t t t tZ Z Z e -0.28 -0.01 Table 9: Hypothesis and P-value for the residual series model Series Model Hypothesis P-value Exchange Rate ARIMA (2,1,0) 12 Null hypothesis (H0): Adequate Model Alternative hypothesis( H1): not Adequate Model 0.241 Table 10: Forecasting monthly average exchange rate USD/IQD Series for the 24 Months using ARIMA (2,1,0) 12 model Years Months Forecast LCL UCL 2021 January 1456.25 1405.81 1506.69 February 1379.31 1308.39 1450.24 March 1380.98 1301.65 1460.32 April 1402.79 1315.71 1489.86 May 1402.06 1306.26 1497.86 June 1395.88 1292.15 1499.62 July 1396.16 1285.46 1506.87 August 1397.91 1280.63 1515.19 September 1397.81 1274.21 1521.41 October 1397.32 1267.71 1526.93 November 1397.35 1262.02 1532.68 December 1397.49 1256.67 1538.31 2022 January 1397.48 1251.38 1543.58 February 1397.44 1246.23 1548.65 March 1397.44 1241.3 1553.58 April 1397.45 1236.53 1558.38 May 1397.45 1231.88 1563.02 June 1397.45 1227.36 1567.54 July 1397.45 1222.96 1571.94 August 1397.45 1218.67 1576.24 September 1397.45 1214.48 1580.43 October 1397.45 1210.38 1584.53 November 1397.45 1206.37 1588.54 December 1397.45 1202.44 1592.46 Mohammed, et al.: Time series forecasting using ARIMA Model 19 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (1): 12-19 CONCLUSION The results of the analysis show that the time series data was not stationary around the mean and the variance. This means that almost all data of this kind should be different to remove any sort of trend influence on the data. Because such series deal with metrology, fluctuations in the data for monthly US Dollar/IQ Dinar currency exchange rates are to be expected. The RMSE and MAE are being used to select the best model. The ARIMA model was found to be the better model for the series data ARIMA (2,1,0) 12 . This is the forecasted means for the future of this US Dollar against IQ Dinar time series which indicates a perpetual increase in the exchange rate. REFERENCES 1. J. E. Buet, G. M. Barber and D. L. Rigby. Elementary Statistics for Geographers. 3rd ed. New York: The Guilford Press, 2009. 2. W. A. Fuller. Introduction to Statistical Time Series. 2nd ed. Canada: John Wiley and Sons, Inc., 1996. 3. A. K. Farhan and M. R. Fakhir. Forecasting the exchange rates of the Iraqi Dinar against the US Dollar using the time series model (ARIMA). 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Chan. Time Series Analysis with Applications. 2nd ed. USA, New York: Springer Science and Business Media, LLC, 233 Spring Street, 10013, 2008. 10. P. J. Brockwell and R. A. Davis. Introduction to Time Series and Forecasting. 2nd ed. New York: Springer-Verlag, Inc.; 2002. 11. R. S. Shumway and D. S. Stoffer. Time Series Analysis and its Applications with R Example. 3rd ed. USA, New York: Springer Science and Business Media, LLC, 233 Spring Street, 2011. 12. D. C. Montgomery, C. L. Jennings and M. Kulahci. Introduction to Time Series Analysis and Forecasting. 2nd ed. Canada, Hoboken, New Jersey: John Wiley and Sons. Inc., 2016. 13. W. Wei. Time Series Analysis: Univariate and Multivariate Methods. 2nd ed. USA: Greg Tobin, 2006. 14. A. Omer, H. Blbas and D. Kadir D. A comparison between brown’s and holt’s double exponential smoothing for forecasting applied generation electrical energies in Kurdistan Region. Cihan University Erbil Scientific Journal, vol. 5, no. 2, pp. 56-63, 2021. 15. T. Cipra. Time Series in Economics and Finance. Nature, Switzerland, AG, 2020. 16. G. E. P. Box, G. M. Jenkins and G. C. Reincel. Time Series Analysis Forecasting and Control. 3rd ed. Hoboken, New Jersey: Prentice- Hall, Inc., 1994. 17. R. A. Yaffee and M. McGee. Introduction to Time Series Analysis and Forecasting with Applications of SAS and SPSS. Tokyo, Toronto: Academic Press, Inc.; 1996. Figure 6: ACF and PACF of residuals model Figure 7: Original USD/IQD series, forecasted values, and confidence limits using ARIMA (2,1,0) 12 model for the Period January 2021–December 2022, Forecast (24 Months)