Forecasting the GDP in the United States by Using ARIMA Model

This paper aims to give an overall view of the Gross Domestic Product (GDP) in the United States and determine the optimal model to predict the growth of GDP by using Autoregressive Integrated Moving Average Model (ARIMA). The ARIMA model was performed for 93 years from 1929 to 2022 of Gross Domestic Product, Billions of Dollars, Annually from Federal Reserve Economic Data (https://fred. stlouisfed.org). The researcher conclude that the estimated model of the first order difference for the logarithm of GDP (DLGDP) series is ARIMA (1,1,1) with coefficients: C = 0.057064, AR (1) = 0.489046 & MA (1) = 0.265583 where S.E. of regression equals 0.051529, R-squared value is about 0.412974, Durbin-Waston statistic (1.961008) and the probability of F-statistic equals (0.000000), which gives the forecast value 0.10436 of LGDP in 2022, while the actual value equals 0.8818 with very low relative error 1.617%, therefore, the forecast value is close to the actual value and indicates that the ARIMA (1,1,1) model has a good fitting effect.


INTRODUCTION:
GDP refers to Gross Domestic Product and is a criterion measure of the value added.It is created through the production of goods and services in certain country over a certain period of time, In this way, it also measures the yields and earnings which was gained from the production, as well as measuring the total amount spent on the final goods and services.The Gross Domestic Product (GDP) is the sum of all the final goods and services produced in the country within a specified period of time (usually one year).
The overall monetary value of these goods and services is taken together, which gives us the GDP.Various methods are used for computing GDP, such as value added method, expenditure methods.GDP is one of most important economic indicators that reflects the nature of the economic activities, and is a tool of evaluating the economic performance at the same time it helps as well in predicting some indicators such as inflation and unemployment (Islam and Alam, 2019; R. Carter Hill, 2015).
Although, GDP is single most significant indicator that seizes the economic activity.However, it lacks to supply a suitable measure of people's financial living and well-being making it less appropriate.Hence, using alternative indicators maybe more adequate.This indicator is based on symbolic GDP (known as GDP at current prices or GDP in value) and is available in various measures such as, US dollars and US dollars per capita.It is not an excellent option for the comparisons because progressing in developments is not only caused are real evolution but also requires variation in prices and PPPs (S.Dutta, 2022).The best way to the comprehend a country's economy is by looking at its Gross Domestic Product (GDP), it measures the country's total output, this includes everything produced by the public and all the companies in the country, it helps to follow economic fluctuations, the development of policies on the population and determining economic policies (S.Dutta, 2022).

MATERIALS AND METHODS:
The data of Gross Domestic Product, Billions of Dollars, Annual, (GDP) were obtained from Federal Reserve Economic Data (https://fred.stlouisfed.org).The MRIMA model was performed during 93 years from 1929 to 2022 by using Stationary test (Unit Root of Augmented Dickey-Fuller) which was performed on the GDP series, also autocorrelation and partial autocorrelation function graphs was performed to determine the laying of difference and the appropriate transformation should be used to be converted to stationary series.The researcher will deter-mine the appropriate model of ARIMA (p, d, q), by selecting the model that have a larger significant coefficient and highest R-squared value with smallest values of Akai Info Criterion, Schwarz Criterion and SIGMASQ (G.E.P. Box, 2015;Gujarati, 2009;H.H. Fan, 2009).
The data were analyzed with Econometrics Views (EViews) Release 10.

RESULTS AND DISCUSSION:
The GDP Data During 1929 -2022 is plotted in Fig.  Table 1 shows that the Augment Dickey-Fuller statistic is 6.611147 with P value (1.0000) is not statistically significant value at 1%, 5%, 10% level, so; we cannot reject the null hypothesis; that GDPA has a unit root, and we conclude that the series of GDP is no stationary.As in Fig. 1 the original series has exponential shape, so we should try to eliminate its nonstationary by using the logarithm of the GDP.Table 2 The LGDP Data During 1929 -2022 is plotted in Fig. 2. According to Fig. 2 and Table 2, the results show that the Augment Dickey-Fuller statistic of LGDP is -0.907100 with P value (0.7820) is not statistically significant value at 1%, 5%, 10% level, so; we cannot reject the null hypothesis; that LGDP has a unit root, and we conclude that the series of LGDP is still non-stationary.The Augment Dickey-Fuller statistic of D (LGDP) is (-5.084361) with P value (0.0000) is statistically significant value at 1%, 5%, 10% level, so; we reject the null hypothesis; that D (LGDP) a unit root, and we conclude that the series of D (LGDP) is stationary.The autocorrelation and the partial correlation function graphs of D (LGDP) series are plotted in the figure.In the below table the autocorrelation of the D (LGDP) series is significantly non zero when the lag order is q=1 or q=2, as it is basically in confidence band when the lag order is greater than 2. The same goes as well for partial auto-correlation where we take p=1 or p=2, hence the final order with 0, 1, 2 in autoregressive moving average pre-estimation is performed on the sample series.As shown in Fig. 3, the actual & fitted series are passing closely and the D (LGDP) has been fore-casted and is passing throw 50% confidence interval; so the forecasting of D (LGDP) is significant and the ability of forecasting the model is satisfactory.The autocorrelation and the partial autocorrelation function graphs of residual series in the above figure, show that the residual is white noise which indicates that the model is valid.Firstly, we do the forecast inside the sample to check the power of the model in forecasting (Hossain et al., 2020).
Table 8: Forecast inside the Sample.
The above graph shows that the forecast value of in 2022 is 0.10436 while the actual value is equal to 0.8818 with a very low relative error 1. 617%, so the forecasted value is close to the actual value which indicates that the model has a good fitting effect.Secondly, by using Box-Jenkies for forecasting GDP during the upcoming five years from 2023 to 2027, the results are shown in the table below:

ACKNOWLEDGEMENT:
With due respect and obeisance, I would like to express my utmost gratitude, indebtedness and appreciation to my husband Dr. Husham Hamadto for his immaterial support.

Fig. 1 :
Fig. 1: The above figure shows that the GDP series has exponential shape.

Table 1 :
Augment Dickey-Fuller Unit Root Test on GDP.

Table 5 :
The Results of Estimated Model of ARMA (p, q).

statistc) Akaike info criterion Schwarz criterion
The above table shows the results of ARMA (p, q) model for different parameters.To select the optimal model, we should compare the results of the signi-ficant for parameters: R-squared, Akai Info.Criterion, Schwarz Criterion and SIGMASQ.According to the above table, we found that the models ARMA

Table 9 :
Forecast outside the Sample: