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Applied Mathematics & Information Sciences Applied Mathematics & Information Sciences
Volume 17
Issue 5
Sep. 2023
Article 8
9-1-2023
Forecasting Economic Growth and Movements with Wavelet Forecasting Economic Growth and Movements with Wavelet
Transform and ARIMA Model Transform and ARIMA Model
Omar Alsinglawi
Accounting Department, Business School, The University of Jordan, Amman, Jordan
,
O.alsinglawi@ju.edu.jo
Omar Alsinglawi
Accounting Department, Business School, The University of Jordan, Amman, Jordan
,
O.alsinglawi@ju.edu.jo
Mohammad Aladwan
Accounting Department, Business School, The University of Jordan, Amman, Jordan
,
O.alsinglawi@ju.edu.jo
Mohammad Aladwan
Accounting Department, Business School, The University of Jordan, Amman, Jordan
,
O.alsinglawi@ju.edu.jo
Saddam Alwadi
Finance Department, Business School, The University of Jordan, Amman, Jordan
, O.alsinglawi@ju.edu.jo
See next page for additional authors
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Recommended Citation Recommended Citation
Alsinglawi, Omar; Alsinglawi, Omar; Aladwan, Mohammad; Aladwan, Mohammad; Alwadi, Saddam; and
Alwadi, Saddam (2023) "Forecasting Economic Growth and Movements with Wavelet Transform and
ARIMA Model,"
Applied Mathematics & Information Sciences
: Vol. 17: Iss. 5, Article 8.
DOI: http://dx.doi.org/10.18576/amis/170508
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss5/8
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Forecasting Economic Growth and Movements with Wavelet Transform and Forecasting Economic Growth and Movements with Wavelet Transform and
ARIMA Model ARIMA Model
Authors Authors
Omar Alsinglawi, Omar Alsinglawi, Mohammad Aladwan, Mohammad Aladwan, Saddam Alwadi, and
Saddam Alwadi
This article is available in Applied Mathematics & Information Sciences: https://digitalcommons.aaru.edu.jo/amis/
vol17/iss5/8
Appl. Math. Inf. Sci. 17, No. 5, 817-828 (2023) 817
Applied Mathematics & Information Sciences
An International Journal
http://dx.doi.org/10.18576/amis/170508
Forecasting Economic Growth and Movements with
Wavelet Transform and ARIMA Model
Omar Alsinglawi1,∗, Mohammad Aladwan1, Saddam Alwadi2and Essa Alazzam3
1Accounting Department, Business School, The University of Jordan, Amman, Jordan
2Finance Department, Business School, The University of Jordan, Amman, Jordan
3Accounting Department, Tolledo College, Irbid, Jordan
Received: 17 Jun. 2023, Revised: 20 Jul. 2023, Accepted: 20 Aug. 2023
Published online: 1 Sep. 2023
Abstract: This study uses historical data and modern statistical models to forecast future Gross Domestic Product (GDP) in Jordan.
The Wavelet Transformation model (WT) and Autoregressive Integrated Moving Average (ARIMA) model were applied to the time
series data and yielded a best-fitting result of (2,1,1) for estimating GDP between 2022-2031. The study concludes that GDP is expected
to increase with a positive growth rate of around 3.22%, and recommends government agencies to monitor GDP, strengthen existing
policies, and adopt necessary economic reforms to support growth. Additionally, the private sector is encouraged to enhance production
tools to achieve economic growth that benefits all sectors of society.
Keywords: Prediction, WT, ARIMA, GDP, Time Series, Jordan.
1 Introduction
The capacity of the economy to generate products and
services at the local as well as global scale serves as a
barometer for measuring the development and economic
improvement of all nations. No matter what a nation’s
economy may look like—industrial, commercial,
agricultural, or even service-based—the volume of
revenue from domestic output is regarded as a sign of
economic strength. In order to raise their GDP, all nations
adopt various strategies and look for elements that
encourage production because doing so will certainly
have a positive ripple effect on the economy and the
overall well-being of society. When examining the
nation’s economy over the decades and years, it is seen as
its economic profile, which highlights the success factors
and the degree of development and growth that have
occurred in it over time. This review is essentially done to
identify the economy’s weaknesses and strengths, which
are either increasing or decreasing in importance [46] and
[1].
All economies and governments have seen throughout
history how GDP is impacted by numerous local or
external factors. While countries can control internal
variables and use them to their advantage, for the external
factors they have no power to alter them; instead, they can
only force them to adapt collectively [2] and [62]. The
ability of planners to develop plans based on useful
realistic numbers, to obtain these realistic figures, and to
achieve these objectives, it requires a thorough review of
previous results in order to build precise future forecasts,
this ability distinguishes random economic planning from
rational economic planning. Therefore, predicting future
economic effects is now one of the most crucial aspects of
effective planning and scheduling of policies [3] and [4].
Modern economies started to review past economic
results from previous periods and establish future
expectations based on these results. The gross domestic
product for all countries turn into main concern in how to
measure, develop and increase it so as country rises it to a
higher economic level. The effective future financial
planning requires considering all economic variables at
the local level and at the external level of the state
because future financial success requires the ability to
increase future resources by taking advantage of past
historical financial practices. Therefore, forecasting the
macro factors of the economy such as gross domestic
income, inflation, interest rates, consumption, investment,
tax is one of the reasons for the success of the economy
∗Corresponding author e-mail: O.alsinglawi@ju.edu.jo
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since these forecasts is regarded as essentials for
decision-making process [3] and [5].
The problem of the study crystallizes in the failure of
many of the financial and monetary policies followed by
the state in improving the economic level by increasing
the gross domestic product due to the weakness in the
Orientalism of the financial future for the state; several
observation by many researches and international
organizations were concentrated on gross national
product as the most crucial factor that reflects the
economy growth. i.e. [6,7,8,9,10,11,47,62]. since it
embraces the total value of economy goods, services,
personal consumption, government procurement, in
addition to the public and private inventory of country
[12,13]. Recently, forecasting of GDP has come to be of
great importance to all economies around the world due
to the fact that economic growth indicators are vital for
the both of government and community, as well as to
other countries that are dealt with country economically
[13,14]. The lack of attention and interest of
policymakers and in modern and advanced scientific
mathematical methods in forecasting GDP, that serve
policy-making, this study mainly assembled to prove the
ability of past financial results in extrapolating future
results so that policies are developed and implemented on
a clear ground to achieve these future goals. Forecasting
future GDP nowadays is realized as the superior measure
for the wealth of the nation, thus countries with high GDP
are considered rich countries, while countries with low
GDP are seen as poor countries and they harness all their
resources to rise to wealthy countries.
In view of the importance for measuring and
forecasting GDP annually, studies on this subject will be
inspired as long as the economy continues since
decision-makers must continually be provided with
up-to-date numbers and forecasts that serve their
decisions concerning the percentage of GDP growth. The
current study is motivated by the continuous need for our
country as emerging economy to be updated with all
information concerning the level of progress in GDP and
whether the future expected trend satisfy policy makers
expectations. Moreover, the study is regarded to be a
complementary one to other similar studies worldwide in
follow-up the recent developments in GDP for developed
countries. What gives this study originality is its
employment for advanced and more accurate data about
future trend of GDP by modern mathematical and
statistical models; also this study is distinguished by its
invented ability to provide more up-to-date information
on future GDP position, which is helpful and supportive
to the decision-making process for economists whom
search to reduces the cases of future economic
uncertainties; furthermore, the study can establish an
evidence to be a reference for government economic
agencies and legislators about the anticipated future
development of the country’s economy as a whole.
The organization of the paper after the introduction
will be as follows: the second part is for the theoretical
framework and the literature review of the study, the
methodology and methods will be in the third section, the
fourth section will be for data, analysis and discussion,
and the last part will be for conclusions and
recommendations.
2 Theoretical Background and Related
Literature
2.1 Gross Domestic Product (GDP)
When we examine the historical development of the GDP
scale, we discover that Willian Beatty was responsible for
its invention before 1700 AD. This measure was
straightforward and developed to combat the greed of
land and farm financiers who imposed unfair taxes during
the Dutch and English wars between 1654 and 1676.
Charles Defenat created this metric in 1695, and Simon
Kzench introduced the first modern notion of GDP in
1934. Kzentech stated in a U.S. Congressional Economic
Report that this measure can be used to assess the
well-being of society. In 1991, the United States of
America adopted Kzench’s ideas that were embodied in
world economics by measuring economic growth in total
domestic production rather than total national production.
The GDP measure had been adopted as the primary
method for gauging economic development in any nation
following the Bretton Conference in 1944 [53].
Traditionally, GDP is suggested by many historians,
i.e. [3,4,15,16,17,18,47,48] as the representative of the
market monetary value for all goods and services
produced during a specific period of time, usually a year,
this measure is constantly adopted to compare living
standards in different countries, as it has been proven that
the use of GDP per capita (nominal) does not reflect
differences in social welfare between countries and does
not accurately measure inflation levels, so GDP at the
gross level is more accurate and appropriate than GDP at
the individual level. Thus, when the value of the GDP of
countries is reported each year, details are made about the
contributions of the different sectors of industry, trade or
services to this output, which may appear in the annual
reports of government agencies per capita at the country
level of GDP. The Organization for Economic
Cooperation and Development (OECD) defined GDP as a
total measure of production that covers the total loads
added by the population, institutions, and participants in
production and services, with the addition of any taxes
and the introduction of any support provided by the
government. This is just one example of the many
national and international economic institutions that have
provided a set of definitions of GDP. The International
Monetary Fund noted that the GDP reflects the monetary
value of all consumer goods and services purchased by
consumers and generated in a particular country
throughout a year [8,9,19]. For many years, economists
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have used the GDP as the benchmark for global
comparisons and as a primary measure of economic
advancement, describing it as the most reliable and
powerful indication of a nation’s progress and
development [20,21,22,47,53]. The modernization of the
economy, however, resulted in numerous critiques of this
indicator, demonstrating that it ignores a number of other
factors, including resource investment, environmental
effects, and unpaid labor. As a result, critics have
proposed alternative economic models to measure
economic growth and development, such as the Donut
economy, which incorporates additional indicators of
economic success, such as the Better Life Index, which is
published by the Organization for Economic Cooperation
and Development [19]. Theoretically, every notion of
GDP that has been developed and every one of its
measurements have the same effect on GDP; these
measurements can be divided into three categories: The
first reflects the value of all finished goods and services
generated by society over a specific time period, typically
a full year [2,53,62]. The second represents the value of
the total increased value of all economic sectors plus
taxes, minus any gifts or other forms of financial or
in-kind assistance given to the government. Regarding the
third, it reflects the entire income from output in the state
after deducting wages for employees and production tax it
is the total amount of output income in the state, less
employee pay and production taxes [14,22]. These three
measurements were highlighted as the methods for
calculating GDP; the first was categorized as the cost or
expenditure method, the second as the production
method, and the third as the revenue method [53,63].
2.2 Future Prediction of GDP
The concept of economic forecasting is the creation of
methodologies and techniques to predict anticipated
future economic results. Economic forecasting can be
made at the aggregate level for all elements of the
economy combined, such as forecasting GDP or gross
national product, or it can be allocated to specific
economic factors like inflation, unemployment, or fiscal
deficit, and it can be allocated to a specific economic
sector such as the financial sector [3,4,17,23,47].
Economic forecasting generally aims to determine the
level of economic prosperity or growth of a country or a
particular sector. There are many interested in economic
forecasting’s results such as government agencies, central
banks and international funds such as the International
Monetary Fund or the Organization for International
Cooperation and Economics [8,9,19]. In addition to
increasing individual awareness, numerous local and
international study centers are also interested in GDP
forecasting. Academics and economic scholars are also
drawn to this topic of study. Because the indications that
arise from these forecasts need to be revised on a regular
basis, these projections are typically ongoing and
unstoppable.
During the last five decades, those interested in
forecasting such as economic researchers and
mathematicians have developed many methods of future
economic forecasting, where all these methods have been
used in data analysis of economic variables, and a
methodology with similar steps has been adopted in most
forecasting methods. When the researcher makes a
forecast, he begins to determine the scope, which includes
identifying the variables and economic topics to be
researched based on the needs of the target group that
benefit from the forecasts. In the second step, literary
sources, studies and points of view that help in
interpretation, commentary and comparison of forecasting
results are reviewed, in the third step accurate and reliable
data are collected about the economic variables targeted
for forecasting from databases or from any appropriate
sources. In the fourth step, the researcher determines the
relationships between the variables studied, such as
identifying independent variables and dependent or
intermediate variables, but in the fifth step, these
relationships are translated into models through
mathematical equations that clarify the assumed
relationships between the variables, and in the last step,
the results are drawn, the results are interpreted and
discussed, and comparisons are made to the results [24,
25,26,47,49].
Because its well known that the gross domestic
product is made up of a number of elements, including
consumer spending, government spending, total
investment, and foreign trade, forecasting benefits should
be used to support plans and policies relating to these
components. In addition, forecasting generally has a
number of advantages and benefits that benefit all groups
at all levels of the state, society, or even other nations, as
well as any groups that gain from the outcomes of
economic forecasting [8,9,19]. At the individual level,
forecasts can show the stability of the economy, and this
encourages members of society to spend their incomes on
consumption and reduce savings, which increases
productivity to meet society’s consumption. Therefore, it
is clear that confidence in income stability is a strong
indicator of economic stability and this reduces the
burden on the government on societal spending [3,27].
The results of economic forecasting also benefit
government agencies to develop financial plans and
determine their programs better to face any possible
economic fluctuations indicated by future forecasts;
prediction of future economic numbers are suggested as
an appropriate guide for the movement of investment in
the country, moreover, forecasts serve government and
community in several economic issues such as trade
balance, unemployment, taxes and inflation [3,17,19].
Future forecasting benefits companies operating in the
country in reducing future uncertainties, which enhances
their ability to avoid or reduce risks related to future
changes and better control the conduct of their business
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by developing appropriate business strategies and making
decisions that support the company to achieve its goals by
adapting its resources to the future [9,22]. Develop a
comprehensive vision of future work, re-evaluate costs
and types of future products and services, in addition to
building future budgets for sales and profits [8,19].
Many methods of future economic forecasting have
been developed over the last fifty years by those with an
interest in forecasting, such as economists and
mathematicians. All of these methods have been used in
the data analysis of economic variables, and the majority
of forecasting methodologies have adopted a
methodology with similar steps. When a forecast is made,
the researcher first establishes the scope, which entails
choosing the variables and economic areas that should be
investigated in light of the requirements of the target
audience that will gain from the forecasts. The second
step involves reviewing literary works, studies, and points
of view that aid in the interpretation, commentary, and
comparison of forecasting results. The third step involves
gathering accurate and reliable data about the economic
variables targeted for forecasting from databases or other
suitable sources. In the fourth step, the researcher
establishes the relationships between the variables under
study, such as identifying independent and dependent or
intermediate variables; however, in the fifth step, these
relationships are translated into models through
mathematical equations that clarify the assumed
relationships between the variables; and in the final step,
the results are drawn, the results are interpreted and
discussed, and comparisons are made to the results. As
accuracy is considered one of the most crucial criteria for
the success of the economic forecasting process, a set of
statistical tests have also been adopted by researchers to
ascertain the level of accuracy of information collection,
the accuracy of the tools used to predict, and the accuracy
of the results.
In general, the accuracy of the results is affected by
the variety of future forecasting methods, this can be
utilized in addition to the prediction makers’ expertise
and knowledge [47,49,54]. The methods and techniques
for future economic forecasting vary between qualitative
methods and short- or long-term quantitative methods
according to the need for these forecasts. Qualitative
methods depend on survey methods, opinion polls,
interviews, questionnaires or observation method, these
methods aim to design relational models for the opinions
of experts and specialists in certain economic fields in
order to determine future trends in these areas [47]. As for
the other type, which is quantitative methods, it depends
on real numerical data from the past and uses statistical
quantitative models through which the direction of future
numbers can be predicted based on historical numbers,
and the quantitative method usually depends on time
series for multiple periods of time, where they can be
examined and predicted using statistical methods such as
correlation and simple and multiple regression, and more
advanced methods with high accuracy have recently
appeared to predict time series data such as
Autoregressive Integrated Moving Average (ARIMA)
[28,46,47].
2.3 Formal Studies on Autoregressive Integrated
Moving Average (ARIMA)
[47] pointed out the criticism of many statistical methods
for their inaccuracy in predicting the future is accurate
and appropriate for time series has encouraged many
mathematicians and statisticians to search for highly
accurate statistical methods in forecasting, including
Autoregressive Integrated Moving Average (ARIMA).
This method has been adopted by many researchers, i.e.
[3,4,7,10,11,25,29,30,46] when predicting the direction
of GDP due to the urgent need for high-accuracy figures
that can be used as a basis for understanding the evolution
of GDP and its fluctuations, and since GDP appears in
numbers for several years as a time series, ARIMA has
proven highly effective in predicting its future accuracy.
GDP is usually volatile in nature, but its temporal
results may appear in several directions, it may be in a
trend upward or downward or stable, and the ARIMA
model can accurately predict these three cases, whether
they are annual, quarterly, monthly or even on daily basis.
There are many statistical forms of ARIMA but in this
study, the methodology of [47] and later developed by
[31,32] will be employed to reach an accurate forecast
about the GDP in Jordan.
It is noteworthy that many researchers such as [2,3,4,
23] after multiple experience in using several statistical
measures to measure economic growth, suggested that
ARIMA found one of the best statistical measures capable
for predicting future growth with high accuracy and with
a slight deviation from the expected, and the researchers
also showed that the moving average depends on partial
autocorrelation and autocorrelation functions; moreover,
the [48] framework was suggested as the best automatic
algorithm that was also applied by the deployed both of
[33] and [61] whom focused on time series data as the
major determinant for estimation the ARIMA parameters.
Some researchers, like [34] also employed time series that
were extracted from the financial markets and created a
multi-factor dynamic proposed system (VAR) to measure
growth in GDP; similarly, [35] also succeeded in using
ARIMA model to estimate GDP in china environment
after predicting china GDP from 2007 to 2011 relying on
data on GDP from 1978 to 2006. Equal results were
found on ARIMA accuracy by [38] when they used data
from 1952 to 2007 and revealed that ARIMA predicted
future GDP with variance of only 5% between actual
GDP and predicted GDP. Similar results were also
achieved by [20,21,22,36,37].
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2.4 Economic Environment in Jordan
Jordan is classified economically as a developing country,
and its geographical location imposed on it the status of
unstable countries due to the political conditions
surrounding it and because of the ongoing regional
conflicts in the Middle East, which made it economically
affected by these political, economic and social tensions
that occur in the region [9,55,56]. Despite the continuous
attempts and efforts by the Jordanian government and the
investment sectors, Jordan has suffered since
independence in the forties of the last century with
fluctuating in economic results such as prices of goods
and services, production and various resources [8]. Jordan
has for several decades developed economic strategies
and plans aimed at increasing economic growth, and
many of these policies have succeeded in improving the
economic level in the country, and Jordan has established
several economic partnerships with Western countries
such as the United States of America, the United
Kingdom and many European countries, and has also
created economic links and partnerships with neighboring
countries in the Middle East, North African countries and
East Asian countries, as these links contributed to
improving the balance of payments and led to acceptable
economic growth despite the scarcity of economic
resources in Jordan [9].
During the last two decades, the Jordanian
government has made fundamental changes to the
composition of the Jordanian economy in order to
increase openness to global markets and began to
liberalize markets and follow the open economy
approach, where the government has taken a set of
economic measures aimed at raising the level of the
economy and increasing its productivity, as it has
privatized many sectors such as the industrial and health
sectors, energy and communications sectors, and
promoted private education and health by encouraging
private schools, universities and private hospitals [9]. The
official authorities also conducted a comprehensive
review of legal and economic legislation, as they
amended the Tax Law and the Social Security Law, made
amendments to commercial laws and regulations, and
established private investment zones and industrial cities
in all big cities of the country [8,57]. However, despite all
the economic measures taken by the official authorities,
the Jordanian economy continued to suffer, as it faced
many crises and external influences such as the first and
second Gulf wars, the Iraq crisis and the war in Syria,
where these influences led to a rise in production inputs, a
decrease in exports, an increase in the cost of living and a
rise in energy prices, which affected the Jordanian
economy by appearing very slow [9]. Despite some
assistance and support provided by Western countries and
Gulf countries through grants and aid, the Jordanian
economy as a developing country lacking basic resources
and wealth has remained at a modest growth level [59].
In order to improve the GDP, many international
institutions and organizations, especially the World Bank
and International Monetary Fund provided advice and
recommendations to carry out many economic reforms by
changing economic policies, raising government
intervention in many internal economic activities such as
energy, water and electricity prices, and raising the sales
tax [60]. the results of the statistics of the GDP that
shown in figure 1 show that the average growth was 7.6%
from 1965 to 2021, and the results that appear indicate
that there is a decrease in the growth rate, as the rate of
Growth 3.6% in the last 10 years and 2.5% in the last five
years; this decrease in the last two years might be justified
by the pandemic of Covid-19 [8,9].
Fig. 1: GDP Annual Growth Rate
3 3. Methodology of The Study
The methodology for the study is shown in Figure 2. It
consists of a number of steps, beginning with the
collection of time series data on GDP that will be used for
forecasting, followed by an explanation of the
methodology using the appropriate mathematical models
(Wavelet Transform formula) and, finally, the analysis of
the data using statistical software to determine the best
ARIMA model for prediction.
Fig. 2: framework of the study
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3.1 ARIMA model
ARIMA model is an auto regression (AR) model and
viewed as a process applied on lagged values of time
series data, this model is equated as follows:
Yt =
α
0+
α
1Yt −1+
α
2Yt −2+... +
α
pYt −p(1)
The moving average (MA) of the framework is
correlated if AR have other mechanisms that generates Y
value; but it must contain past values with its error terms.
The MA (q) is assembled as:
ε
t=
β
1
ε
t+
β
2
ε
t−2+
β
3
ε
t−3+... +
β
qY
ε
t−q(2)
This model has inaccuracies resulted from white
noise; this is donated to as ARMA (p, q) process when Y
retains both of AR and MA qualities. The methodology of
[45,50] is followed which basically derived from
(Box-Jenkins model) in order to label and predict the
proper statistical model that can be applied to represent
how the sampled data were formed. However, because of
the non-stationary nature of time series numbers, a
differences of time series will result in a stationary time
series data thus, the model assumes that if the selected
data was stabilized after multiplication with (d), we
donate (I) to the date series. Therefore, the initial time
series is ARIMA but only if ARMA (p, q) was functioned
to the series of data that is I(d), (p,d,q). Moreover, this
equation for ARIMA model assumes the use of
correlogram in order to identify the values for p, q that
used in AR and MA. The framework also assumes that
the ordering for the moving average q, ACF stops or dies
down beyond lagging q at the same time the
autoregressive for the order of p, and PACF also stop or
dies down post the lagging of p for the AR (p) methods.
[49] noted that this model diagnose is mostly applied
basing on Mean Absolute Percent Error ((MAPE) and
also applied by Root Mean Square Error (RMSE) by
value of (MAPE).
3.2 Wavelet Transform Equation
In order to realise the accurate estimation for future data,
the initial observation of time series data is changed to
time scale domain by application of a mathematical
model known as Wavelet Transform (WT). Since the
majority of financial data are non-stationary, the model
works extremely well with this type of data. Discrete
Wavelet Transform (DWT) and continuous Wavelet
Transform are two sub-types of WT (CWT) as pointed
out by Several researches such as [39,40,41,49,51]. The
properties of each of these functions are the same across
all applications. The WT’s equation for each function will
be described in this paper. These suggestions are equally
originated by the work of [42,52].
The wavelets methods and assumptions are structured
on Fourier enquiry, this theory adopts the fact that any
function is the total value for both of sine and cosine
scores. The WT is generally the function of time
represented by t which follows a simple law, identified as
wavelet admissibility state [52]:
C
ϕ
=Z∞
0
(|
ϕ
f|
f)d f <∞(3)
The QF is donated to the transformation of Fourier
function for frequencies of (f, for Q(t)). The WT is
donated to method mean that might be applicable to
several applications; for instance, the analyzing image
and the signals processes. This method was formalized to
overcome the complications allied to Fourier
transformations in the case of confronting non stationary
data signals that could confined in interval of time or
space and frequencies. The most common forms of WT
are function-family; the wavelet father type represents the
smooth and low frequencies fragments for particular
signals; on the hand the mother wavelet type define the
details for high frequented parts; the formula in equation
3 demonstrate the two types of wavelet propositions,
where, j= 1,2, 3. . . . . . ..., j for the J-level [ 52]:
Φ
j,k=2−j
2
φ
(t−2jk
2j)(4)
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:
Z
φ
(t)dt =1and Z
ϕ
(t)td =0 (5)
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 byS=2j, j=1,2,3,. . .J.
Referring to formula 4 the f (t) function is donated to
the input of wavelet analysis, that is used to be
constructed up for the sequence of both mother and
mother of wavelet index, that represented by k, when k=
0,1,2. . . . . . . and defined by S in eq uation 5 when S=2j, j
1,2,3. . . . j. The analysis for the reality of d esecrated
sample of data involves generating lattice in order to
conduct the necessary calculations. Scientifically its more
suitable to apply a dyadic development as represented in
formula 4, this expansion is assembled in equation 6 as:
SJ,K=Z
φ
(t)dt =1(and)dJ,K=Z
ϕ
(t)td =0 (6)
The orthogonal for wavelet framework is an estimation
for f (t) as:
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F(t) = ∑SJ,K
Φ
J,K(t) + ∑dJ,K
ϕ
J,K(t) + ∑dJ−1,K
ϕ
J−1,K(t)
... +∑d1,K
ϕ
1,K(t)··· (7)
SJ(t) = ∑SJ,K
Φ
J,K(t)(8)
DJ(t) = ∑dJ,K
Φ
J,K(t)(9)
The coefficients for the estimations of WT series is
equated in equation 6, particularly for the discrete signal;
the Sj (t) and Dj (t) are representative for both of smooth
and details [43]. In the case that data pattern is found
highly irregular, the wavelet should repeatedly apply in
order to decrease the errors for the root mean (RMSE)
among the signal prior and post transforming; thus, any
noise obtained from the original series can be discharged,
consequently we intended to apply WT for two times on
the data.
3.3 Accuracy of Mathematical Model
As the aim of the study is to obtain the best estimation
results; therefore, before starting discussion for
comparison of framework a discussion will be firstly
undertaken on the criteria’s that were applied to warranty
the fair comparison. The three selected criteria for
accuracy are Mean square error (MSE), Root mean square
error (RMSE) in addition to the Mean absolute error;
these categories were formally experimented by several
historians and found fit to equate performance differences
among models [42,44,62].
4 Results
4.1 Data description
The study’s data set included Jordan’s gross domestic
product (GDP), which was taken from the Central Bank
of Jordan’s (CBJ) annual reports and the general
department of statistics. The data set, which was chosen
as a time series, encompassed the years 1965 to 2021.
The data were examined using Matlab and Mini-tab
statistical software, which is recommended as the best
suitable software for using ARIMA, in order to estimate
the future GDP. The research hypothesis, dependent and
independent variables, as well as the anticipated statistical
tests, are all shown in Table 1.
As the figure screen has a non-linear route, the results
for the Histogram, Accumulated Histogram, and
Descriptive Statistics for the Study Time Series are shown
in Figure 2. Because the data is non-stationary in nature,
it is classified as random data that varies from year to
year.
Table 1: Data analysis Matrix
Fitted ARIMA Model
Research hypothesis Modelling and prediction of GDP
Dependent variable GDP
Independent variable Time (year)
statistics His, Acc.His, des.stat, WT, ARIMA
Fig. 3: Data Description of GDP
4.2 Decomposition of Time Series Data
There are a Consensus among analysts that time series
data consists of three elements; trend, noise and
seasonality [3,4,17,23,25,46]. Thus decomposition aims
to separate these three elements in order to read and
explain the results properly. The trend component show
the volatility of data in states of increase and decrease;
whilst the seasonal component aims to decrease the
volatility of data by repeating processing of data to the
time series, as for the third element Noise its aimed to
reduce the noise state of data through randomization [21,
22].
The results in figure 4 the decomposition of data using
WT, but pre proceeding in sample decomposition its
worthy to point out that the sampled time series has been
reformed by the log function since high volatility is
noticed in time series. As shown in the figure the
decomposition represented of: a1 as the approximated
coefficients that assemble for the appropriate estimation;
d1, illustrates the volatility or fluctuation of data;
accordingly, the mathematical equation can be assembled
as S= a1 + d1, where S donated to the original data.
When screening the results displayed in figure 4, we
see that the timing plots for GDP exhibit random
fluctuations. This result indicates that the data are
non-stationary in nature and volatile across the analyzed
time, and as a result, are not constant in terms of mean or
variance. The spectral analysis of WT must be used when
the data are in a non-stationary state since they typically
exhibit a seasonal tendency. Since the primary
characteristics and volatility of time series data are
clarified by d1, the non-stationary nature of time series
allows the transformation process of data from random
trend to linear trend. There are several oscillations that are
mixed in with the GDP results across the study period, as
the findings of d1 in the figure also demonstrate.
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Fig. 4: Data Description of GDP
Once the decomposition steps applied on time series
data, an ARIMA methodology is applied to allocate the
suitable model for predicting Jordanian GDP, the results
are shown in table 3.
Table 2: ARIMA forecasting models
Fitted ARIMA Model
Model (2,1,1)
MASE 0.3708
RMSE 0.0699
Table 2 show the models of ARIMA that detected by
means of MASE and RMSE; by performing Gaussian
MLE criterion, both of ARIMA models parameters were
predicted; grounding on ARIMA frameworks the best
fitted models that selected is those with the lowest score
of MASE which is (0.6878) and the lowest value of
RMSE that is (0.0699) with the most fitted ARIMA with
value of (2,1,1). Based on articulated ARIMA fitted
model, the results in figure 5 that show the GDP trend
from 1965 to 3031, the figure suggests that the Jordanian
economic growth represented by GDP is estimated to be
upward sloping trend; this results is supportive to
economy by such optimistic results. As the figure
illustrate that the upcoming ten years in Jordanian
economy tend to be compensational for the previous
declined years.
Fig. 5: GDP original and forcasted
5 Conclusion
The study was driven by the need to forecast the future
trend of the GDP in Jordan by utilizing time series data
from earlier periods and incorporating them into
high-precision mathematical prediction models to
forecast GDP growth in the future. Time series data on
GDP covering the years 1965 to 2021 were gathered from
databases at the Central Bank of Jordan and the
Department of Statistics. These time series data will be
used as a foundation to forecast GDP growth over the
following 10 years, from 2022 to 2031. The study
adopted the model WT in the first stage to build data and
identify oscillations and outliers. In the second stage, the
ARIMA model was employed, which was agreed upon by
most researchers as one of the best models for predicting
future data, as it was used to predict GDP. The study used
the quantitative research approach, which depends on the
analysis of real data derived from the market.
After gathering the study’s original time series-based
data and testing them using the study model, it was
discovered that the data were non-stationary by nature; as
a result, they were transformed into stationary data to
better suit the study. During the process of model
development, the initial data is found to be non-stationary
and is then modified to become stationary. The ARIMA
(2,1,1) model, which has the lowest BIC values of all the
early ARIMA models, is chosen for analysis and GDP
forecast. The findings demonstrate that for the appropriate
framework, the fitted model’s effect R square value is
high (95%) and its mean absolute percent error is quite
small. As a result, the estimation’s accuracy was high.
Therefore, it has been determined that during the next ten
years, Jordan’s GDP will continue to rise at a level
consistent with its recent development trend; the
anticipated average growth rate would be close to 3.22%.
5.1 Implications, limitations and future research
The present study is acknowledged by its contribution to
previous research regarding the use modern estimation
mathematical model in forecasting the expected future
enhancement in economic growth represented by GDP;
the little research on this issue specifically in emerging
countries was a motivating factor to conduct this analysis.
The study brought more insight and shed more light on
how to policy makers can utilize the results of such
forecasting’s in formulating plans, polices and strategies
on a clear sight for future upcoming results. The study
also concentrated in to the ability for adaptation of policy
makers and government agencies to future trend of GDP;
moreover, the results directed to interested parties on how
to overcome any probable risks attained from future
economic situation, for example governments might seek
for local or external support for funding economy.
The study linked the past results with future results
which is crucial for decision makers to point out any past
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deficiencies in monetary or financial results and correct
them in future action; such practices guide the policy
makers on the country level or on corporate level for more
efficacy in utilizing available resources that participates in
production or service. Promoting the tools and techniques
of measurement is also an implication for researchers,
analysts which enables them to obtain accurate,
appropriate and transparent numbers for both past and
future results. The results achieved from such foresting’s
increases the level of cooperation between all country
sectors whether private or public institutions enhance any
future unsatisfied expected future results.
The outcomes of our research offers some
implications that are helpful for applying forecasting in
different settings. The desire to obtain reliable relevant
financial information mandates government to plan and
execute based on this forecasting’s. Therefore, adopting
such methods in planning helps government in general
and public in particular. Furthermore, the modern
forecasting techniques empower policymakers in
convincing official and public with their strategies and
plans. The provision of new planning methods without
benefit from such methods regarded as a weakness point
in countries that hardly seek to enhance their economic
position. The emergence of forecasting methods also can
be used as controls for effective use of resources in order
to achieve the desired goals. The real value of forecasting
methods will not be achieved unless the ideal
employment of these methods by competent persons
whom have the required knowledge in utilizing future
trends in present actions.
Without a doubt, it has become known to everyone
that government cannot continue with traditional planning
old systems, in an accelerated world and an economic
environment with high competition that has exceeded the
borders of countries, it has become necessary for
government and even companies in private sectors have to
insert these forecasting methods into financial culture.
This activity will result in unlimited transparent and
reliable information useful for making economic
decisions; hence, if government and companies want to
maintain their growth and continuity, they are obliged to
provide efficient, effective and figures to all interested
parties. Therefore, it is recommended that the officials
and government agencies to continue monitoring the
gross domestic product, strengthen existing policies,
plans, and laws, and adopt the necessary economic
reforms to support the anticipated economic growth. It
also needed to encourage the private sector to enhance
and develop all production tools to assist the government
in achieving distinguished economic growth whose
consequences are mirrored in all sectors of society.
In scientific research, there is no study without
limitations, similar to other studies conducted on this
topic this study faced several limitations, including the
time period on which the study was conducted, as this
study covered a forcasted period of 10 years; for some
professionals and researchers the period is too short and
that this study may need longer periods of time. Also, one
of the limitations is related to the type of forecasting
method (ARIMA), some could argue that other methods
are more efficient in the field of forecasting such as
(SARIMA, ARIMAX) or artificial neural networks
(ANNs) and recurrent neural networks (RNNs). The third
limitation is related to the selected variables for the study;
most of forecasting research focused on GDP, but still
there are many indicators for economic growth such as
Consumer Price Index (CPI), or unemployment figures,
analysts might claim that these indicators are better than
GDP. Future research on this topic can develop the study
through the use longer time periods for forecasting
example more than 10 years, also future researchers can
use other growth indicators such as (CPI) or
unemployment; also future researcher can employ another
types of forecasting methods other than ARIMA.’
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Omar AlSinglawi,
Associate Professor
Accounting Department
/ University of Jordan,
His research interest
in economic, accounting
and financial prediction,
he has published several
research articles in reputable
international journals.
Mohammad Aladwan
Associate Professor,
Accounting Department
/ University of Jordan,
educated accounting in
several Jordanian universities,
his research interests in
accounting fields, sustainable
development and future
forecasting, published several
research’s in high ranked international journal.
Sadam Alwadi
Associate Professor, Finance
Department / University
of Jordan, His research
interest in finance, economy
and mathematics, accounting
and financial prediction,
he has published numerous
researches in reputable
international journals.
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828 O. Alsinglawi et al.: Deployment of Mathematical WT and ARIMA Modelling
Essa Alazam Assistant
Professor,Dean of Toledo
College, His research
interest in Accounting
and finance, he has published
many researches in reputable
international journals.
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2023 NSP
Natural Sciences Publishing Cor.
