Forecasting Inflation using the ARIMA Approach

(Case of Albania)

INGRID KONOMI, BLISARD ZANI

Department of Finance, Faculty of Economics,

University of Tirana,

Rruga e Elbasanit,Tirana

ALBANIA

Abstract: Traditionally, macroeconomic statistics have played a major role in creating the framework for analyzing

economic phenomena. Price changes are one of the most worrying situations where individuals, firms, and

government tend to keep in control as much as possible. Even if the economic effect could be negligible, the

psychological effect could be more considerable. Inflation creates a touchable impact in the vast majority of

economic sectors. Meanwhile, empirical studies of inflation have shown a very correlative relationship between

inflation and other macroeconomic indicators such as unemployment, GDP growth, net exports, etc. Albanian

economy has suffered from time to time from inflation consequences. Simultaneously, inflation in Albania has

created a cyclical form and a significant trend. Due to these conditions, simple econometric models such as ARMA

or ARIMA can be used to forecast future inflation, especially at the moment when inflation is the focus of the

Albanian economy. This paper aims to create an ARIMA econometric model of inflation in the time frame from

2009-2022. It also creates a quantitative approach for forecasting inflation in the Republic of Albania. Furthermore,

this paper tries to explain some phenomena linked with inflation giving some qualitative data. ARIMA model will

be used to forecast future inflation in Albania. Lastly, as explained in the paper, it is shown that the ARIMA model

should be taken under consideration in policymaking processes.

Keywords: - Inflation, ARIMA model, forecasting

Jel Code: E27, E31, E37

Received: December 22, 2022. Revised: May 16, 2023. Accepted: June 1, 2023. Published: June 8, 2023.

1 Introduction

Macroeconomic statistics have historically been

crucial in developing the foundation for examining

economic phenomena. Due to their significance in

the overall economy, macro indicators (including

unemployment, inflation, economic growth, imports,

and exports) have been at the core of economic

theories. One of the most unsettling circumstances is

when prices change, and people, businesses, and the

government all try to maintain as much control as

they can. The psychological impact of inflation could

be greater even if the economic impact can be

minimal.

In the vast majority of economic sectors, inflation

has a palpable effect. Price fluctuations can

occasionally turn deadly as a result of the domino

effect they generate. Prices of final goods increase as

a result of rising costs of production in the industries

and sectors they affect. A very strong correlation has

been found between inflation and other

macroeconomic indicators including unemployment,

GDP growth, net exports, etc. in empirical studies of

inflation.

Occasionally, the effects of inflation have

impacted the Albanian economy. In the previous

three decades, the focus of fiscal policy and the

macroeconomic framework have included inflation as

a key indicator. Additionally, the central bank of

Albania's key monetary policy goals has been price

stability and targeted inflation. Prices rose by double

digits in the first decade of the 1990s, taking into

consideration the structural change in the Albanian

economy. Meanwhile, they started to normalize in the

second decade after previous fluctuations and shocks.

This normalization was accompanied by the

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intervention of central government institutions, the

central bank, and the improvement of other

macroeconomic indicators.

Albanian inflation seems to be a useful indicator

to examine in terms of its trend and form. Some

industries are largely responsible for inflation, while

other economic sectors maintain more stable pricing.

Recent years show high inflation in developing

sectors like construction, and food and beverage

industry, etc. In Albania, inflation has simultaneously

resulted in a strong trend and a cyclical form. These

factors make it possible to predict future inflation

using straightforward econometric models like

ARMA or ARIMA, particularly currently when

inflation is a key concern for the Albanian economy.

The purpose of this study is to develop an

ARIMA econometric model of inflation for the

period from 2009 to 2021. Furthermore, it develops a

quantitative technique for forecasting inflation in the

Republic of Albania. There are no recent papers or

studies that forecast inflation in Albania with

econometric models that analyze the process of

inflation forecasting in Albania and explain its

cyclical trend. Besides that, by providing some

qualitative data, this research attempts to explain

several occurrences connected to inflation. The

ARIMA model will be employed to estimate

Albanian inflation in the future. Additionally, this

study extends to the ongoing discussion on inflation

and its consequences for the Albanian economy.

Literature suggests that ARIMA models are one of

the best and most practical methods for explaining

the economic phenomenon of inflation.

2 Literature Review

The focus of economists has always been on

inflation, just like it is with all macroeconomic

measures. Some theoretical frameworks make an

effort to explain how inflation affects the economy

and how prices affect supply and demand. Other

economists have developed streamlined models to

describe the roots of inflation and predict their

effects. In general, inflation takes into consideration

the stable growth of the prices in a certain economy,

[5], [6].

One of the major concerns about inflation is how

it affects economic growth. The ability to measure

how inflation affects economic growth can be

somewhat limited at times. Due to the additional

effects of inflation, it is very hard to quantify the real

impact. Inflation affects all equilibrium sides. Due to

changes in the cost of the end products themselves as

well as the production factors, demand and supply

chains experience significant volatility. Hernando

and Andrés have examined how inflation affects

economic growth, [1], [8], [4]. They concluded that

inflation typically forces the economy to contract

because higher prices constrain both supply and

demand. Controversially, the first economic theories

sought a positive correlation between growth and

inflation [7], [15].

Numerous studies examine how inflation affects

investments. “Price inflation is associated with

increased price volatility, and it can lead to future

investment insecurities”, [12], [13]. As investments

are frequently associated with significant cash flow,

inflation may be detrimental to the climate for

investments. In the meanwhile, inflation is being

targeted at concerns about future cash flows. The

inflation rate has a greater impact on the general

equilibrium than unemployment or the other macro

indices.

Different perspectives on the economic structure

resulted in various solutions. Monetarists have

examined the crucial part that monetary expansion

plays in determining the rate of inflation. Other

schools of economic thinking, such as the

Neoclassicals, have developed ideas that attempt to

explain how inflation affects capital accumulation

and investment, which in turn influences how it

affects growth, [6], [9]. Since the economy is

temporarily transitioning into a new stable potential

growth level, the short-term inflation brought on by

an increase in aggregate demand is seen as beneficial

for the economy. While Keynesians define long-term

inflation as a troubling phenomenon in the long run.

A "lazy dog" could best describe inflation; it stays at

a certain level until there is a disturbance.

One of the most important questions regarding

inflation is linked with the level of inflation that

causes economic growth to be negative. What level

of inflation is harmful to economic growth? Various

studies have made a lot of empirical reviews of

different levels of inflation in different stages of

growth. In addition, cross-data about different

countries have been analyzed together. Authors like

Ghosh and Philips, Khan, and Senhadji concluded

that reducing inflation by 1 percent could raise output

by between 0.5 and 2.5 percent. They also found that

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there is a nonlinear relationship between inflation and

economic growth, [15], [19], [11].

The econometric modeling of inflation has been the

subject of many recent studies. We may use these

measures to design an inflation forecasting

framework by taking into account new models of

auto-regressive vectors and the concepts of moving

averages. According to mathematical reasoning, we

can clearly describe inflation as one of the self-

explanatory phenomena that can "repeat itself". We

can accurately anticipate future inflation utilizing

econometric tools in addition to analyzing the

historical time series of inflation. In light of the

above, this paper's goal is to examine Albania's

inflation rate and predict future inflation using

ARIMA models, [2], [14], [17], [20].

The first discussion linked with the level of

inflation determines which type of inflation should be

considered. Other countries with similar economic

typologies as the Albanian economy suggest that the

core inflation should be the right level to be

considered, [4], [10]. The inflation rate taken into

consideration in this paper will be the inflation rate

measured in the Republic of Albania by the

Consuming Price Index (Core-CPI) (monthly data),

[19], [16].

3 Methodology

This section outlines an ARIMA modeling and

forecasting framework. The rigorous collection and

assessment of data serve as the foundation for the

ARIMA forecasting process, [18]. The generalized

ARIMA model can be used as a tool to predict future

inflation rates if it is developed under theoretical

assumptions. Figure 1 serves as a synopsis of the

general process and the key steps.

Fig. 1: Arima forecasting steps

3.1 Data Collection and Examination

This paper examines the Republic of Albania's

inflation data over the last 13 years (2009 – 2022).

The inflation rates data are collected from the Bank

of Albania

and show monthly data about the core

inflation of a time series with 166 data rows. We can

see some inflation shocks from time to time by taking

a quick look at the data (Figure 2) Meanwhile, the

inflation rate has become more stable and less

volatile in recent years. As can be seen, by the figure

below, the core inflation in Albania has been under

the targeted level of 4% for more than 12 years.

Meanwhile, the highest inflation before 2022 has

been in 2011 as the world crisis began to affect the

Albanian economy. Continuously, for approximately

three years (2013 – 2016), the economy of Albania

was accompanied by deflation and then it stabilized

between the interval 2% - 4%. Nowadays, the core

inflation has peaked at almost 10%. In addition, the

last months have shown a new trend of rising

inflation in almost all the important economic sectors

of Albania. Moreover, the Russo – Ukrainian war and

the energetic crisis have been the main contributors

to inflation. Foods and beverages, input prices,

transportation, and real estate sectors have been the

most affected by inflation.

Bank of Albania is the official central bank of the Republic of

Albania.

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-2

09 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Inflation (%)

Fig. 2: Monthly core inflation data (%)

(2009 -10M2022) Generated by: EViews 10

3.2 Stationarity of Time Series

In the autoregressive models and regressive models

in general which create time series, econometric

diagnosis, and tests must be in consideration to assess

the effectiveness and relevance of these models.

Stationarity of the time series is one of the most

important initial points to complete, and it serves as a

pre-test for creating the autoregressive models. A

stationary process has the property that the mean,

variance, and autocorrelation structure do not change

over time. Stationarity can be defined in precise

mathematical terms. Still, for our purpose, we mean a

flat-looking series, without trend, constant variance

over time, a constant autocorrelation structure over

time, and no periodic fluctuations. If the time series is

not stationarity, usually the data of the time series can

be different (in the first or second level). That is,

given the series Lt we create the new series Yi = Δ Lt

= Li – Li-1. The differenced data will contain one less

point than the original data. Although we can

differentiate the data more than once, one difference

is usually sufficient.

Before evaluating the stationarity of data

collected, the general form of the ARIMA model is a

simple ARMA model (autoregressive moving

average model). If the time series is root stationary,

then we can create an ARMA model. Whereas the

time series fail to be originally stationary, we

differentiate (usually at the first level) data and take

into consideration an ARIMA model. A generalized

ARMA (p; q) model can be described below:

 



  



  

Generally, an ARIMA (p,d,q) is a nonseasonal model

where:

 p is the number of autoregressive terms,

 d is the number of nonseasonal differences

needed for stationarity, and

 q is the number of lagged forecast errors in

the prediction equation.

Let y denote the dth difference of Y, which means if

time series are stationary at the first difference (as our

model explained below), then yt = Yt - Yt-1. The

primary ARIMA model should now be as:

 



  



  

Analyzing inflation rate data (on monthly basis) we

conclude that they are not unit root stationary, and

they are being converted into stationary ones at the

first level.

The augmented Dickey-Fuller test for stationarity of

time series is presented in Table 1.

Table 1. Augmented Dickey-Fuller test for

stationarity of time series

Null Hypothesis: D(INF) has a unit root

t-Statistic

Prob.*

Augmented Dickey-Fuller test statistic

-8.759156

0.0000

Test critical

values:

1% level

-3.470427

5% level

-2.879045

10% level

-2.576182

Evaluating the probability coefficient [0.00] (p <

0.05), we conclude that the data are now stationarity

in the first difference. The Augmented Dickey-Fuller

is one of the most used tests for stationarity, so the

model passes the stationarity test, [3], [21]. Inflation

data series can now be used to create an Arima

model.

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4 Model Parameters and Estimation

The evaluation of the Arima models begins with

determining the terms p and q. To determine the

autoregressive order and the level of moving average

terms, the correlogram of the data series must be

analyzed. We must determine the correct order of

autoregressive terms by checking whether any of the

autoregressive terms exceeds the limits of partial

correlations. The same logic is used to determine the

best moving average terms. The autocorrelation and

partial correlation of the inflation time series are

shown in Figure 3.

Fig. 3: Autocorrelation and partial correlation of

inflation time series

The partial autocorrelation defines the AR terms of

the ARIMA model, so it is determined that is it

suggestable to use AR (1). Meanwhile, the

autocorrelation test tells us that the right terms of

moving average should be MA (12). In conclusion,

the full ARIMA model used in this paper will be

ARIMA (1,1,12).

Let’s take into consideration the general ARIMA

(1,1,12). The equation should be as it follows:

Δ yt = c + φ1 Δ yt-1 + εt + θ1 εt-1 + θ2 εt-2 + …+ θ11 εt-11

+ θ12 εt-12

(1)

4.1 ARIMA Equation Estimation

As it is shown by the estimation of the model, all the

variables are statistically significant and have

statistical importance [for AR (1), MA (12)] because

the p. value < 0.05. Meanwhile, the whole model is

statistically important, and this is proved by the fact

that p.(F-stat) < 0.05. As a first step to model

estimation, the ARIMA (1,1,12) can now be tested

for other econometrical proofs.

The ARIMA inflation model used is presented in

Table 2.

Table 2. ARIMA inflation model Generated by

EViews10

4.2 White Noise Test

Dependent Variable: D(INF)

Method: ARMA Maximum Likelihood

Variable

Coefficient

Std. Error

t-Statistic

Prob.

0.019538

0.027534

0.709597

0.4790

AR (1)

0.410206

0.096172

4.265347

0.0000

MA (12)

-0.516693

0.148626

-3.476462

0.0007

SIGMASQ

0.076603

0.003759

20.37674

0.0000

R-squared

0.240867

Mean dependent var

0.036909

Adjusted R-

squared

0.226722

S.D. dependent var

0.318628

S.E. of

regression

0.280190

Akaike info

criterion

0.340947

Sum squared

residuals.

12.63951

Schwarz criterion

0.416243

Log-likelihood

-24.12816

Hannan-Quinn

0.371512

F-statistic

17.02801

Durbin-Watson stat

2.122275

Prob(F-statistic)

0.000000

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The ARIMA model can be used only if it passes

some econometric tests. One of the most important

tests is the White Noise Test (Ljung – Box Q

Statistic). A time series is white noise if the variables

are independent and identically distributed with a

mean of zero. This means that all variables have the

same variance (σ2) and each value has a zero

correlation with all other values in the series. Our

monthly data shows that the white noise test is passed

successfully (as all the values of probability are

greater than 5%) [p > 0.05], affirming that the

residuals of the model (εi terms) are white noised. As

all the tests have been completed, the model

estimation continues with the evaluation of

covariance stationarity and invertibility. The next

analysis consists of analyzing the ARMA roots

covariance and invertibility.

4.3 ARMA Covariance Stationarity and

Invertibility

Conducting the ARMA roots test about the

covariance stationarity shows us that AR roots should

be inside the circle graph (as presented below). This

confirms the covariance stationarity. At the same

time, the invertibility test shows that also the MA

root is inside the ARMA structure circle, so the

model can now be used normally. The ARMA roots

are illustrated in Figure 4

Fig. 4: ARMA roots

In conclusion, after testing the stationarity of the time

series, white noise test (Q-correlogram), and ARMA

structure, the model can be used to forecast future

inflation.

4.4 Forecasting the Inflation in Albania

Regarding the model used in this paper, the final

ARIMA model is described below:

Δ yt = 0.019 + 0.41 yt-1 – 0.517 εt-12 + εt (2)

Equation (2) shows the correlative relationship

between autoregressive terms and moving average

terms with the inflation defined by the equation.

 Theoretically, there will be a 0.019% level of

inflation, ceteris paribus.

 If the previous monthly inflation changes by

1%, we can expect a 0.41% change in the

monthly actual inflation (this is shown by the

auto-regressive (AR) part of the equation).

 A change in the moving average part (MA)

contributes to the hammering of the effects of

the previous year’s inflation into the actual

monthly inflation with 0.517%. This is

explained by the effects of the moving

average concept as the previous inflation

caused in any sector is expected to impact

less in previous months (periods) due to the

intervention of the central bank and other

institutions.

The forecasting process shows the result of future

foreseen inflation in Albania for the end of the year

2022 and the first half year of 2023. Figure 5 below

shows the tendency and trend of a dynamic forecast

of the actual time series (M11-2022 – M6-2023):

M11 M12 M1 M2 M3 M4 M5 M6

2022 2023

INFF ± 2 S.E.

Fig. 5: Forecasted inflation in Albania

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As it is forecasted by the model, the core

inflation rate in Albania will increase for the next

four months and then gradually decrease in the other

next months. In addition, the inflation will stay stable

at the level of 8% - 9%, due to the stabilization

instruments used all these months. Furthermore, other

macroeconomic indexes like GDP growth and

unemployment also indicate a decline in the level of

inflation. In the same logic as above, nominal shocks

are also expected during these months.

5 Conclusions

Due to its major role in the economy, inflation does

impact not only the general level of prices but almost

all the other macro indexes like economic growth,

unemployment, trade balance, current account, etc.

Inflation is neither a reason nor a consequence. It is a

complex indicator that measures the oscillation of

prices in the economic situation overall. It must not

be studied as an isolated index but concerning

inflation and other macro indicators.

Regarding the econometric model, we can

conclude that the econometric model of ARIMA is

one of the models that can create a satisfactory

framework to predict inflation and to create

forecasting models for phenomena like inflation.

ARIMA models work especially for time series of

data in developing countries due to the lack of

stationarity of their data in the unit roots. So, inflation

in Albania can be forecasted and used as a

policymaking tool. As a matter of fact, the next three

years are expected to be with more stable inflation,

but most of the time below the expected inflation rate

defined by the Bank of Albania.

The last recent years show data on high levels of

inflation due to covid-19 effects on the Albanian

economy. Henceforth the econometric models

(especially the models that use autoregressive terms)

may be used accompanied by some qualitative data

and explanations. Some “unusual shocks” of

inflation can derive from some situations that are

hard to explain just by quantitative data and statistical

models.

Consequently logically, we recommend that the

Bank of Albania and other government institutions

involved in policymaking should be more aware of

the consequences coming from an unpredictable

inflation rate in the Albanian economy. Moreover,

the objective of the central bank for core inflation can

be revised in adaption to the changes caused by the

earthquake and Covid-19 pandemic situation. The

central bank of Albania should intervene in the

Albanian economy with direct and indirect

instruments in case of hyperinflation during the next

months. The Bank of Albania (BoA) has increased

the level of treasury bonds sold in the Albanian

financial market as a measure to decrease the level of

cash in the economy. In addition, BoA has increased

the level of interest rate to 2.75% as a direct operative

instrument.

While the inflation level is a very important topic

nowadays in Albania, the analysis should go deeper

into understanding the changes in core inflation. At

the same time, it is recommended to focus on the

main sectors and industries that cause inflation. A

deeper analysis may be concentrated into sectors like

construction, real estate, or some parts of the food

supply chain due to their importance in the Albanian

economy.

A sustainable economy and the challenges posed

by solutions require modern approaches to study the

impact of important indicators like inflation.

Additional studies should be made to create a full

framework of studies for typical indexes like inflation

in Albania. This paper suggests that for important

macro topics, these studies should be conducted from

time to time to affirm or change some viewpoints or

to enrich the studies file as frequently as possible.

Structural autoregressive models can be very useful

in determining the importance of nominal and real

shocks in the economy. Throughout this model,

additional interpretations can be made to understand

specific consequences of inflation in the overall

economic performance. We also invite other authors

to improve the theoretical and practical framework

with valuable studies.

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Volume 20, 2023

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Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

-Ingrid Konomi has worked on the literature review

and economic analysis of the data’s statistical

processing results.

-Blisard Zani has worked the statistical processing

using EViews 10 software.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflict of interest to declare

that is relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_

WSEAS TRANSACTIONS on BUSINESS and ECONOMICS

DOI: 10.37394/23207.2023.20.111

Ingrid Konomi, Blisard Zani

E-ISSN: 2224-2899

1259

Volume 20, 2023