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Predicting Jordanian's GDP Based on ARIMA Modeling
Omar Alsinglawi, S. AL Wadi, Mohammad Aladwan, Mohammad H. Saleh
Faculty of Management and Finance, The University of Jordan, Jordan
O.alsinglawi@ju.edu.jo
Sadam_alwadi@yahoo.co.uk
Msm_Adwan@ju.edu.jo
Mohsaleh1966@yahoo.com
Abstract.
Gross Domestic Product (GDP) is the market value of the all goods and services that are
produced within the country's national borders in a year, Our study aims to estimate and predict
Jordanian's GDP using a time series data for the period from 1978 till 2017, the data has been
taken from Jordanian's department of statistics, Minitab and Matlab statistical software's are
used , we deploy a wavelet transform (WT) model to decomposes the time series data then
detecting the fluctuations and outliers values, also an ARIMA (autoregressive integrated moving
average) is established, the fitted ARIMA (2, 2, 1) time series model is the best for modeling the
Jordanian's GDP according to the recognition rules and stationary test of time series. The results
show that the predicted values are within the range of 5%, and the prediction capability of this
model is relatively adequate and efficient in modeling the annual GDP for the next 20 years,
Thus, the prediction accuracy is considered high. It is concluded that Jordanian's GDP is in
upward trend for upcoming 20 fascial years, Furthermore Jordanian's government has to follow
more comprehensive economic policies and should implement key growth-enhancing reforms to
strength its economy,also it has to stimulate job-creating growth and creates conditions to
increase private investment and improve country's competitiveness.
Key words: Prediction, WT, ARIMA, GDP
INTRODUCTION
Gross Domestic Product (GDP) is the market value of the all goods and services that are
produced within the country's national borders in a year. GDP is a measure that is used to
evaluate overall economic performance of a country, it includes all goods and services produced
by the economy including personal consumption, government purchases, private inventories,
paid in construction costs and the foreign trade balance (net exports). The subject of GDP
became of high importance among macro economy variables. Data on GDP is regarded as an
important indicator for evaluating the national economic development and growth of entire
macro economy (Ahmad & Harnhirun,1996)
Most popular definitions of GDP conceptually identical and can be categorized in three ways:
First, it is equal to the total expenditures for all final goods and services produced within the
country in a specified period of time (a fascial year). Second, it is equal to the sum of the value
added at every phase of production by all the industries in a country, plus taxes less grants on
products in a fascial year. Third, it is equal to the sum of the income generated by production in
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the country in the fiscal year, that is compensation of employees, taxes on production and
imports less grants, and profits(Ahmad & Harnhirun,1996). GDP aggregates the entire economic
motion. It is frequently used as a finest measure of how is the performance of the economy. GDP
is generally measured in one of a three approaches. First, the Expenditure approach, it involves
the market value of all domestic expenditures made on final goods and services of the year,
including consumption expenditures, investment expenditures, government expenditures, and net
exports the domestic purchases of goods and services and net exports. Second, the Production
approach, it is involving the summation of all value-added activities at every phase of production
by all industries inside the country, plus taxes and product's subsidies of the period. Third is the
Income approach, it is the summation of all aspect of the income made by production within the
economy as remuneration of employees, capital income, and gross operating surplus of
enterprises i.e. profit, taxes on production and imports less grants of the period (Den,2010)
The aim of this research is to estimate and predict future Jordanian's GDP, using a time series
data for the period from 1978 till 2017, this study is supposed to offer a valuable understanding
for the Jordanian's expected GDP. Prediction of GDP involves application of statistical and
mathematical models to predict upcoming developments in the economy. It allows to review
previous economic movements and predict how current economic changes will amend the
patterns of previous trend, therefore, a more accurate prediction would provide a significance
help to the government in setting up economic development goals, strategies and policies.
Consequently, an accurate GDP prediction presents a leading insight and an understanding for
future economics' trend.
The research question addressed in this study: "Is the ARIMA model a significant model for
predicting the future GDP values? ", consequently, we need to attain the subsequent objectives:
• To know the Jordanian's GDP trend.
• To select the best ARIMA model that fits the Jordanian's GDP.
• To predict the Jordanian's GDP.
• To develop ARIMA model for predicting future GDP of the Jordanian's economy.
This paper is organized as follows. Section 2 describes the literature review. Section 3 introduces
the methodology and framework. Sections 4 describes the data descriptions and analytical
results. Finally, Section 5 presents the conclusions.
Literature review:
Gross Domestic Product (GDP):
Economic size is measured by its output, the most widely-used measure of economic output is
the GDP, it is generally measured using one of a three approaches, these approaches of
measuring GDP should result in the same number, with some possible discrepancies caused by
usual mathematical and statistical figures rounding. These approaches as follow:
First, the Expenditure approach, it involves the domestic purchases of goods and services plus
net exports.
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Second, the Production approach, sometimes called Net Product or Value-added method, it
involves the summation of all value-added activities at every phase of production by all
industries inside the country, plus taxes and product's subsidies of the period.
Third is the Income approach, it is the summation of all aspect of the income made by production
within the economy as remuneration of employees, capital income, and gross operating surplus
of enterprises i.e. profit, taxes on production and imports less grants of the period (Ahmad &
Harnhirun,1996).Predicting GDP is a vital issue if it is able to understand and capture the future
developments of the economy, so it is meaningful to review the economic trends and predict the
effect of current economic circumstances on the future GDP trend. This can be done through
using time series data of GDP, which consists of observations consecutively generated over time.
Such data are ordered with respect to the time, which shows the trend related to the time period
observed. The trend may be increasing, decreasing, constant or having a cyclical fluctuation an
ups and downs pattern the over time. Also, the data may show that the underlying process has
periodic fluctuations of constant length, which is seasonal behavior. therefore, Modeling would
capture this underlying process using the observed time series data so that it could be possible to
forecast what would likely be realized at a specific point in time in the future. In predicting
macroeconomic time series variables like GDP, there are many possible types of models that are
used in literature, in our study we will use ARIMA (Litterman,1986, Stockton &
Glassman,1987).
In predicting a time series data of GDP as a macroeconomic variable, ARIMA model has been
proven to be reliable and an accurate model. (Tsay and Tiao,1985) used ARIMA modeling, they
fitted a non-seasonal data by identifying autoregressive and moving average terms with the help
of partial autocorrelation and autocorrelation functions (Box &Jenkins,1970). Also (Topolewski,
et al. 1995) deployed automatic methods were developed to identify as well as estimate the
parameters of ARIMA model by utilizing time-series data for a single variable. Furthermore
(Mait & Chatterjee,2012) used similar methodology to model macroeconomic variable like GDP.
however, both the studies were limited to only non-seasonal time series and such modeling needs
a long time-series data on the macroeconomic variable in question.
(Mei, et. al,2011) constructed a multi-factor dynamic system VAR prediction model of GDP by
selecting six main economic indicators, using time series data extracted from the Shanghai
region in China,also (Wang & Wang ,2011) deployed ARIMA for predicting the GDP of China
based on time series data. They set up an ARIMA model of the GDP of China from 1978 to
2006. They then choose the best ARIMA model based on statistical tests and predict the GDP
from 2007 to 2011. The result shows that the error between the actual value and the predicted
value is insignificant which shows that the ARIMA model is highly accurate, Additionally ( Wei,
Bian and Yuan ,2010) used ARIMA model for GDP data series from 1952 to 2007 to predict the
GDP of the Shanxi province in China, they found that error between the real GDP value and the
predicted value is within 5% range .
Jordanian's Economy:
Jordan is existing in the most volatile regions in the world. Given the country’s high exposure to
exogenous shocks, it has been affected by the regional conflicts, the fluctuations of commodity
prices, and shifts in geopolitical relations which all compound the country’s existing
vulnerabilities. A combination of rising external and internal pressures challenges Jordan’s
balance, like a tightrope walker subject to gusts of winds. Over the past decade, Jordan has
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pursued structural economic reforms in many sectors like education, health, as well as
privatization and liberalization. The Government of Jordan has introduced social protection
systems and reformed subsidies, creating the circumstances for public-private partnerships in
infrastructure and making tax reforms. However, further progress is needed so that reforms
aimed at enhancing the investment climate and ease of doing business can lead to enhance
economic growth and increase its GDP.A major challenge facing Jordan remains to strengthen
the economy in the context of a challenging external environment. Adverse regional
developments, in particular the Syria and Iraq crises, remain the largest recent shock affecting
Jordan. Continued regional uncertainty and reduced external assistance will continue to put
pressure on Jordan. Additionally, a High unemployment rate, high dependency on grants and
declining remittances from Gulf economies pose a serious challenge. More comprehensive
economic policies and the quick implementation of key growth-enhancing reforms is necessary
to reduce the country’s sensitivity to external shocks and help strengthening the economy, also
creating conditions for increased private investment and improve country's competitiveness will
remain crucial for Jordan to stimulate job-creating growth(World bank ,2018).
As seen in figure (1 ) the annual growth of GDP during the period between 1978 -2017, the
average growth rate was 7.6%, and it seems that in the last 10 years the growth is declining due
to political instability in the surrounding countries, the 2017 growth rate declined to 3.6%.
Figure(1 ) GDP Annual Growth Rate
Methodology:
This section consists of the research framework, the mathematical model that is used to achieve
the purpose of this research and mathematical criteria used.
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RESEARCH FRAMEWORK:
Figure (2) The flowchart of the paper
ARIMA MODEL:
An Auto regressive (AR) process is a series depends on its lagged values. The AR(p)model is a
regression model which defined as :
Yt = α0 + α1Yt-1 + α2Yt-2+… +αpYt-p
Moving average (MA) model is related if the AR process is not the only mechanism that
generates Y , but it contains past values with its error terms. MA (q) process is defined:
εt=β1εt + β2εt-2 + β3εt-3 + … +βqεt-q
which contains the white noise errors. When Y has both the features of AR and MA, it is called
as ARMA (p, q) process. (Gujarathi, et, al.,2012) ARIMA (Box-Jenkins model) is to classify and
estimate a statistical model which can be explained as having generated the sample data. Since
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the financial time series data are type of non-stationary, therefore differencing the series will
yield a stationary time series.
If the financial data becomes stationary when differenced d times, we name the series as I(d).
Consequently, if ARMA(p,q) is applied to a series financial data which is I(d), then the original
time series is ARIMA(p, d, q). The ARIMA methodology proposed that finding the values of p
and q for AR and MA respectively by referring to the correlogram. In MA (q) model, moving
average of order q, ACF Dies Down or Cuts off after lag q while for AR (p), autoregressive of
order p PACF Dies Down or Cuts off after lag p. (Princeton,2008). Model diagnosis can be
applied based on the values of Root mean Square Error (RMSE) and Mean Absolute percent
Error (MAPE).
Wavelet Transform Formula:
WT is a mathematical model employed to convert the original observations into a time-scale
domain. The model is very appropriate with the non-stationary data since most of the financial
data are non-stationary. WT can be divided into Discrete Wavelet transform (DWT) and
continuous wavelet transform (CWT). DWT consists of many functions such as Haar,
Daubechies, Maximum overlapping Wavelet transform (MODWT) and others. All of these
functions have the same properties with different applications. In this article, the WT will be
presented with its equation for all functions. For more details please refer to (Daubechies,1992;
Chiann & Morettin,1998; Gençay, et, al., 2002; Al Wadi, 2010)
Wavelets theory is based on Fourier analysis, which represents any function as the sum of the
sine and cosine functions. A wavelet is simply a function of time t that obeys a basic rule, known
as the wavelet admissibility condition ( Gençay, et, al., 2002):
(2)
where is the Fourier transform and a function of frequency f, of . The WT is a
mathematical tool that can be applied to numerous applications, such as image analysis and
signal processing. It was introduced to solve problems associated with the Fourier transform,
when dealing with non-stationary signals, or signals that are localized in time, space, or
frequency.
There are two types of wavelets within a given function/family. Father wavelets describe the
smooth and low-frequency parts of a signal, and mother wavelets describe the detailed and high-
frequency components. Equation (3) represents the father wavelet and mother wavelet
respectively, with j=1,2,3,..., J in the J-level wavelet decomposition( Gençay, et, al., 2002):
(3)
where J denotes the maximum scale sustainable by the number of data points and the two types
of wavelets stated above, namely father wavelets and mother wavelets and satisfies:
(4)
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time series data, i.e., function f(t), is an input represented by wavelet analysis, and can be built
up as a sequence of projections onto father and mother wavelets indexed by both {k}, k = {0, 1,
2,...} and by{S}=2j, {j=1,2,3,. . .J}.
Analyzing real discretely sampled data requires creating a lattice for making calculations.
Mathematically, it is convenient to use a dyadic expansion, as shown in equation (4). The
expansion coefficients are given by the projections:
(5)
The orthogonal wavelet series approximation to f (t) is defined by:
(6)
and
(7)
The WT is used to calculate the coefficient of the wavelet series approximation in Eq. (6) for a
discrete signal, where and are introducing the smooth and details coefficients
respectively. The smooth coefficients dives the most important features of the data set and the
details coefficients are used to detect the main features in the dataset. For more details about the
WT and its functions please refer to(Al-Khazaleh et,al.,2015). When the data pattern is very
rough, the wavelet process is repeatedly applied. The aim of preprocessing is to minimize the
Root Mean Squared Error (RMSE) between the signal before and after transformation. The noise
in the original data can thus be removed. Importantly, the adaptive noise in the training pattern
may reduce the risk of over fitting in training phase. Thus, we adopt WT twice for the
preprocessing of training data in this study.
Accuracy Criteria:
This section consists of two subsections. Firstly, we will present the criteria which have been
used to make a fair comparison, and then the framework comparison will be presented with more
details. The researchers have been adopted to compare the performance of the models within
three types of accuracy criteria which are Mean square error (MSE), Root mean squared error
(RMSE) and Mean absolute error (MAE). For more details about the mathematical model refer
to (Aggarwal,et,al.,2008;Wadia,et,al.,2011).
RESULTS
Data Description
In this research, we use a time series data that represent the Jordanian's GDP for the period from
1978 till 2017, the data has been taken from Jordanian's department of statistics. The Matlab and
Minitab statistical software were used to analyze the data.
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Table(1). Data analysis matrix.
Research
hypothesis
Independent
Variable
Dependent
Variable
Statistics
Modeling and
Predicting GDP
Time
GDP
Histogram, accumulated
histogram and descriptive
statistics, WT, ARIMA
As shown in the figure (3) a histogram, accumulated histogram and descriptive statistics of the
time series show a non-linear path; therefore, it is none stationary homogenous type,
characterized by random changes from one period to another.
Figure (3) Data Description Of GDP
Decomposing time series:
A time series generally has three components that are a trend, noise and seasonal components.
Decomposition of the time series means separating original time series into these components:
First-Trend: The increasing or decreasing values in any time series.
Second-Seasonal: The repeating cycle over a specific period in any time series.
Third-Noise: The random of values in any time series.
Figure (1) shows the decomposition based on WT. Before proceed to make data decomposition
the data has been transformed using the log function in second order since the data is highly
fluctuated, the decomposition procedure consists of a1, which is the approximated coefficients
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used for the proper forecasting and d1 which shows the fluctuations of data. Mathematically, the
equation can be represented as S= a1+d1 where S is the original data.
Figure (4) WT decomposition
Refer to the figure (4) a visual inspection of the time plots shows that GDP data time series has a
trend of random fluctuations, which means that the data are non-stationary and it is not constant
around mean and variance. This type of non-stationary time series data contains a seasonal trend
can be carried out by spectral analysis function which is WT. which lead to transform a random
trend into a linear trend. Since d1 explains the main features and fluctuations of the time series
data, it has been clear that there were much fluctuations that the Jordanian's economy faced
during the study period.
After we have done the decomposing process of time series data, we applied the ARIMA
forecasting process,
TABLE 3..
ARIMA Model for
Jordanian's GDP
Model
(2,2,1)
MASE
0.7089
RMSE
0.0709
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The fitted ARIMA models were diagnosed using MASE and RMSE. Parameter estimation for
the ARIMA models was done using the Gaussian MLE criterion. The ARIMA models fitted
based on the lowest value of MASE (0.7089)and RMSE(0.0709),with a fit ARIMA is
ARIMA(2,2,1).
According to the fitted ARIMA model respectively, the best model can be re-written as follows:
Where; represents the value of GDP.
Figure (5), GDP, Billions of JD
Figure (6),GDP orgional & forcasted
Figures (5,6) show the GDP original and predicted values, the data series-stationary from (1978
till 2017) and the forecasted values of GDP for the coming twenty years (years 2017 till 2036),
this suggests that the GDP long term trend is up ward slopping, which gives an indication that
Jordanian's economy long-term view considered positive and will continue its growing.
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CONCLUSION:
In this paper we deployed a WT model to decomposes the data to detect the fluctuation and
outlier values, then we utilized ARIMA model in predicting Jordanian's GDP, using GDP time
series of the years 1978 to 2017. it is clear that ARIMA model offers an excellent technique to
predict any single data variable like GDP as an important macroeconomic indicator. It is strength
lies in its fitting varieties of different types of time series with any pattern. In the process of
model building, the original data is found a non- stationary then stransformed to be stationary.
An ARIMA (2,2,1) model is developed for analyzing and predict GDP among all of various
tentative ARIMA models as it has lowest BIC values. From the results, it can be observed that
influence R Square value is (95%) high and Mean Absolute Percentage Error is very small for
the fitted model. Therefore, the prediction accuracy is high. It is concluded that Jordanian's GDP
will continue growth in the same growth pattern in the coming 20 years, Jordanian's government
has to follow more comprehensive economic policies and implement key growth-enhancing
reforms to strengthen the economy, also it has to stimulate job-creating growth and creates
conditionsto increase private investment and improve country's competitiveness.
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