INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 916
Predictive Modelling of Health Expenditure in Italy: Using GARCH
Techniques
Dr. Shyam Charan Barma
Head (Assistant Professor), Department of Economics, Kalipada Ghosh Tarai Mahavidyalaya (Under
University of North Bengal, W.B, India)
DOI: https://dx.doi.org/10.51244/IJRSI.2025.1210000080
Received: 20 October 2025; Accepted: 27 October 2025; Published: 04 November 2025
ABSTRACT
This study analyses Italy’s monthly data about health expenditure from January 2012 to October 2022, sourced
from International Financial Statistics (IMF). Augmented Dickey-Fuller (ADF) tests confirm the series is non-
stationary at levels, exhibiting random walk behaviour, but achieves stationarity after first differencing,
indicating integration of order one [Et ~ I(1)]. Regression analysis reveals a significant 12-month lagged effect,
where a 1% increase in prior health expenditure growth raises the current growth rate by 0.19%, reflecting annual
seasonality (e.g., fiscal budgets, winter health costs). The constant term indicates a robust 4.26% monthly growth
rate, driven by Italy’s aging population, rising medical costs, and universal healthcare system (SSN), consistent
with 8–9% of GDP spending. ARIMA forecasting shows a 0.284% increase in current growth per 1% prior
growth, while GARCH(1,1) modelling indicates a marginally significant 0.169% effect from 5-month lagged
growth and persistent volatility from shocks like COVID-19. The small value of R2 and insignificant F-stat.
value suggested unmodeled factors (e.g., GDP, inflation) drive variability. The 2012–2022 period, marked by
economic recovery and the pandemic, underscores volatility, necessitating refined models and flexible budgeting
for Italy’s healthcare system.
Keywords: Stationarity, ADF Test, ACF, PACF, Angel-Granger Cointegration, ARIMA, ARCH, GARCH. JEL
Classification: H51, H52, H53, H75, I15, I150, I180
INTRODUCTION:
The healthcare system in Italy is renowned for its universal coverage and high-quality services. Over the period
from 1980 to 2022, Italy’s health expenditure and the development of healthcare facilities have undergone
significant transformations influenced by economic, demographic, and policy changes. This essay examines the
evolution of health expenditure and facilities in Italy, focusing on key trends, challenges, and policy responses
during this period. The 1980s marked a period of consolidation for Italy's National Health Service (Servizio
Sanitario Nazionale, SSN), established in 1978. Health expenditure during this decade grew steadily as the
government aimed to ensure universal access to healthcare services. Public health spending increased as a
percentage of GDP, reflecting the government's commitment to building a robust healthcare infrastructure.
However, the system faced challenges such as regional disparities in service quality and efficiency.In the 1990s,
Italy implemented several reforms aimed at enhancing the efficiency and effectiveness of the SSN. The most
significant reform was the 1992 legislation, which decentralized healthcare administration to regional
governments. This shift aimed to address regional disparities and promote more efficient allocation of resources.
Despite these efforts, the decade also saw growing concerns about rising healthcare costs, driven by an aging
population and increasing demand for healthcare services.The early 2000s were characterized by efforts to
contain healthcare costs while improving service quality. The introduction of the National Health Plan in 2001
set priorities for the healthcare system, including reducing hospital beds, promoting primary care, and improving
preventive services. Health expenditure continued to rise, but at a slower pace, due to cost-containment measures
such as budget caps for regional health authorities and the promotion of generic drugs. Despite these measures,
regional disparities in health expenditure and service quality persisted.The global financial crisis of 2008 had a
significant impact on Italy's economy, leading to austerity measures that affected healthcare funding. Between
2010 and 2015, public health expenditure as a percentage of GDP decreased, prompting concerns about the
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 917
sustainability of the SSN. Austerity measures included cuts to healthcare budgets, reductions in hospital beds,
and increased co-payments for services. These measures led to increased pressure on healthcare facilities and
staff, as well as longer waiting times for patients.The COVID-19 pandemic, which began in 2020, posed
unprecedented challenges to Italy's healthcare system. The initial outbreak in Lombardy exposed weaknesses in
the system, including insufficient ICU capacity and inadequate protective equipment for healthcare workers. In
response, the government increased health expenditure significantly to strengthen the healthcare infrastructure,
enhance testing and tracing capabilities, and support the rollout of vaccination programs. The pandemic
underscored the need for a resilient healthcare system capable of responding to public health emergencies.
Development of Healthcare Facilities
From the 1980s to the 1990s, Italy invested heavily in expanding and modernizing healthcare facilities. New
hospitals were built, and existing ones were upgraded to improve service delivery. The decentralization of
healthcare administration in the 1990s aimed to enhance regional healthcare infrastructure and address disparities
in access and quality of care. However, this period also highlighted the challenges of coordinating healthcare
services across regions with varying levels of resources and expertise. The 2000s saw significant technological
advancements in healthcare facilities. Investments in medical technology, such as MRI machines, CT scanners,
and minimally invasive surgical equipment, improved diagnostic and treatment capabilities. Specialized
healthcare centres were established to provide advanced care for complex conditions. Despite these
advancements, the uneven distribution of facilities and resources across regions remained a challenge. During
the 2010s, Italy faced the dual challenges of an aging population and budget constraints. To address these
challenges, the healthcare system increasingly focused on primary care and community-based services.
Initiatives such as the Casa della Salute (Health House) model aimed to integrate primary care, specialist
services, and social care under one roof, enhancing coordination and access to care. Telemedicine and digital
health technologies also gained traction, offering new ways to deliver healthcare services more efficiently. The
Covid-19 pandemic highlighted the critical importance of resilient healthcare facilities. Italy's healthcare system
faced immense pressure, particularly in the early months of the pandemic. The government responded by rapidly
increasing ICU capacity, converting non-healthcare facilities into temporary hospitals, and mobilizing additional
healthcare workers. Investments in telemedicine and digital health solutions accelerated, enabling remote
consultations and monitoring to reduce the burden on hospitals. The pandemic underscored the need for flexible
and adaptable healthcare facilities capable of responding to emergencies.
REVIEW OF LITERATURE:
John Bryant, Audrey Teasdale, Martin Tobias, Jit Cheung and Mhairi McHugh (2004) they explained through
the simulation model assesses population ageing’s impact on New Zealand’s government health expenditures
(acute and long-term care) from 1951 to 2051. Ageing, including disability and proximity to death, increases the
elderly’s expenditure share from 29% to 63%. However, non-demographic factors (e.g., treatment expansion,
wage increases) drive most expenditure growth. Restraining expenditure to 6-12% of GDP requires significantly
lower non-demographic growth rates.
Paraskevi Klazoglou and Nikolaos Dritsakis (2018) they developed an ARIMA (0,1,1) model using the Box–
Jenkins method to forecast US health expenditure from 1970 to 2015. The model minimizes the difference
between predicted and observed values, employing static one-step ahead forecasting for accurate projections. It
effectively captures structural trends and innovations, providing a robust tool for predicting health expenditure
dynamics.
Ulf-G. Gerdtham, Bengt Jönsson (2000) they suggested the comparative analyses of aggregate health
expenditure across countries, highlighting the role of institutional regimes and explanatory variables. The
regression analyses using cross-section and panel data identify aggregate income as the primary driver, with
income elasticity often exceeding unity, suggesting healthcare as a luxury good. Primary care gatekeepers and
capitation systems reduce expenditure compared to fee-for-service. Future research needs stronger
macroeconomic theory and updated, unified empirical studies.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 918
Section: I
Test of Stationary of health expenditure through Correlogram Study:
The nature of stationarity and integrability of health expenditure have been enquired into through the study of
their respective correlograms. The Figure 1 present correlograms of health expenditure at level and at first
difference respectively. Again Figure 2 present the correlograms of the health expenditure series at level and at
first difference respectively.
Figure:1 Correlogram of Health Expenditure at Level Data
Figure:2 Correlogram of Health Expenditure at 1st Difference Data
Findings from The Figures 1 And 2
(A) It is observed from the correlogram of health expenditure given by the Figure 1 that
the ACF of health expenditure displays a long ladder-like dying out pattern of solid spikes as the lag
length increases.
the PACF contains only one significant spike (even at 1% level) at lag one and all other lags contain very
insignificant spikes.
All these features of the correlogram confirm the non-stationarity of the health expenditure series at level.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 919
(B) The integrability of health expenditure series is being enquired into through the examination of the
correlogram of health expenditure series at first difference as given by the Figure 2.
It is observed from the Figure 2 that for the first differenced filtered series of health expenditure.
the ACF is marked by the absence of any dying out pattern of spikes.
no singularly significant large spike appears at the first lag of the corresponding PACF.
These features of the correlogram, as given in the Figure 2, confirm that the first differenced series of health
expenditure is stationary. Consequently, health expenditure series is I (1).
Augmented Dickey Fuller Unit Root Test
In order to test for the existence of unit roots, and to determine the degree of differencing necessary to induce
stationarity, the Augmented Dickey-Fuller test is used.
The results of the Augmented Dickey-Fuller test (ADF) determine the form in which the data should be applied
in any econometric analyses. The test is based on the following equations:
∆���� = ��1 + ��1����−1 + ��1�� ∑ ∆��
��=1 ����−1 + ��1�� …………………………..(1)
where ∆���� = (���� − ����−1) ��1��~��������(0,������
2 )
Table:1
Results of the Augmented Dickey Fuller (Unit Root Test)
(Automatic based on SIC, MAXLAG=12) [Sample:- 2012:I -2022:XI]
Country Variable
ADF Test
Stat.
Prob*
Value
Mackinnon Critical Value
Remarks
1% 5% 10%
Italy
���� 2.189 0.999 -3.481 -2.884 -2.579 Non-Stationary
∆����
-11.309
0.000 -3.481 -2.884 -2.579 Stationary
Where ���� stands for Health Expenditure at level and ∆Et stands for Health Expenditure at 1st difference.
Review of the Findings:
The findings in our study through ADF Unit Root Tests and through the examinations of relevant correlograms
of the variables confirm that over the period 2012: I - 2022: XI.
health expenditure series is non-stationary at level and therefore, exhibit random walk processes.
The health expenditure series attain stationarity upon filtering through first differencing Consequently,
the series is integrated of order one i.e, Et~ I(1) .
ARIMA Model:
ARIMA is a popular time series forecasting method that combines three components:
1. Autoregressive (AR)
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 920
2. Integrated (I)
3. Moving Average (MA)
ARIMA models are denoted as ARIMA (p, d, q) where we consider
I. p is the number of lag observations included in the model (AR part).
II. d is the number of times that the raw observations are differenced (I part).
III. q is the size of the moving average window (MA part).
Now AR(p) model is
���� = ��1����−1 + ��2����−2 + ⋯ … … … . …��������−�� + ����………………..(2)
I(d)differencing:
����
′ = ���� − ����−1……………………………………………..………..(3)
(Repeated d times if d>1)
MA(q) Model:
���� = ���� + ��������−1 + ��2����−2 + ⋯ … … … … . . +��������−��………….…….(4)
So the ARIMA(p, d, q)model can be written as
����
′ = ��1����−1
′ + ��2����−2
′ + ⋯ … … … . +��������−��
′ + ���� + ��1����−1 + ��2����−2 +
⋯ … … .��������−��…………………………………………………………..…….(5)
Where y
t
′ is differenced series.
Section: II
Estimated model: AR(12) structure of health expenditure is
∆���� = ��1 + ��2∆����−12 + ����………..………..(6)
Estimated model of the equation (6)
∆���� = ��1 + ����∆����−12…………………………..(7)
Coefficient 0.033 0.191
t- Stat. 4.011 2.331
S.E. 0.008 0.082
Prob. 0.000 0.021
R2 = 0.045 Adj R2 = 0.036 AIC = -2.094
SIC = -2.048 S. E of Regression = 0 .084 F- stat. = 5.436
Prob(F- stat.) = 0.021 SSR = 0.822 D .W. stat. = 1.918
Findings from the AR (12) model: This variable represents the health expenditure from 12 months prior. The
positive coefficient indicates a significant positive relationship between health expenditure in the current period
and that from twelve month ago. A 1-unit increase in health expenditure from the twelve-month results in a 0.191
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 921
unit increase in the current period. The value of R2 indicates that approximately 4.48% of the variance in health
expenditure is explained by the model. Similarly, the Adj. R2 value indicates that the number of predictors in the
model, suggesting a slightly lower explanatory power. When we consider the degrees of freedoms of regression
implies that the standard error of the regression, indicating the average distance that the observed values fall
from the regression line. The SSR indicates that the Measure of the discrepancy between the data and the
estimation model. The values of Log Likelihood suggested that a higher value indicates a better fit of the model
to the data.
Again, the value of AIC indicates that used for model selection; lower values indicate a better model fit and for
SIC Similar to AIC but penalizes for the number of parameters; used for model selection. Both F-stat. and
Prob(F-stat.) indicates that the model is statistically significant at the 5% level. Similarly, D.W stat. values means
that there is no autocorrelation of health expenditure of Italian Economy.
Figure: 3
Correlogram of Residual
It is observed from the correlogram of residual series is given by the figure 3 that
I. the ACF of the residual series is free from any dying out pattern of spikes, and
II. the PACF of the series is marked by the absence of any singularly significant spike at lag one.
III. Here the residual series is stationary at level i.e residual is I(0).
and these observations testify for MA(0) structure for ∆E��. ARIMA (12,1,0) forecasts for E��. The estimated
model becomes
∆���� = ��1 + ��2∆����−12 + ��3����
+ ����………………..(8)
ARIMA(12,1,0) model as given by the equation (8) has been used for generating one period ahead forecast for
E��. The time plots of health expenditure ( E��) and the corresponding ARIMA forecast (����) are being presented
through the figure 4. E�� is found to be coincident with ���� over the period concerned.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 922
Figure:4
ARIMA (12.1.0) forecasting of Health Expenditure
The graph illustrates the ARIMA forecasting of health expenditure in Italy from 2012 to 2022. Time Period (X-
axis) covers the years from 2012 to 2022, marking the timeline over which the health expenditure data and the
ARIMA forecasts are plotted. Expenditure Level (Y-axis) indicates the level of health expenditure, ranging from
-0.4 to 0.4. The scale is likely normalized or differenced, a common practice in time-series forecasting to stabilize
variance and better identify patterns.
Here Health Expenditure (solid Line) represents the actual health expenditure in Italy over the time period. It
shows the real data, highlighting the fluctuations, peaks, and dips in spending. ARIMA Forecast (dotted line)
represent the forecasted values using the ARIMA (Auto Regressive Integrated Moving Average) model. ARIMA
is a widely used statistical method for time-series forecasting, particularly for data that shows trends and
seasonality. The model predicts future data points based on past observations.
Explanation of ARIMA Forecasting for Health Expenditure in Italy:
From the above ARIMA forecasting model, we observed that
1. Actual Values indicated by a solid line, showing the real health expenditure over time.
2. Forecasted Values represented by a dashed or dotted line, showing the predicted health expenditure based
on the model.
3. Trend Compared the overall trend of the actual values with the forecasted values. They should follow a
similar path, indicating that the model has captured the trend well.
4. The ARIMA forecasts (red stars) generally follow the blue line representing actual expenditure. This
suggests that the model captures the overall trends and cyclical patterns present in the data.
5. The ARIMA model does a good job of tracking the health expenditure, there are periods where the
forecast slightly deviates from the actual data and from the above figure-4, we observed that the forecast
data almost coincide with actual data of health expenditure for the period from 2012 to 2022 in Italy.
6. The expenditure data shows significant volatility, with sharp rises and falls. The ARIMA model attempts
to capture these changes but is limited in fully predicting extreme fluctuations, such as sudden spikes or
drops around 2018 and 2020.
7. Both the actual data and ARIMA forecast stabilize, with fewer pronounced fluctuations, indicating a
more consistent trend in health expenditure within the period from period 2021 to 2022.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 923
Section: III
The ARCH Model:
ARCH (Autoregressive Conditional Heteroskedasticity) is used to model time series data with changing variance
(heteroskedasticity), where periods of high volatility are followed by high volatility and periods of low volatility
are followed by low volatility.
We know ARCH equations are
The Mean equation is
y
t
= μ + εt……………………………………….….…………(9)
Where is the y
t
is observed time series, μ is the mean εt is the error term
The Variance equation is
εt = σ������……………………………………………………….(10)
where ���� is white noise with zero mean and σ�� ���� unit variance.
Conditional variance
����
2 = ��0 + ��1����−1
2 + ��2����−2
2 +. … … … … + ��������−��
2 …………….……..(11)
Where ��0 > 0 ������ ���� ≥ 0 ������ �� = 1,2,3, … … … … … … . ,��
The Estimated equation of ARCH model is
����
2 = 0.005 + 0.264 ����−5
2 ………………………………(12)
t-Stat. 3.496 2.833
S.E. 0.001 0.093
P-Value 0.001 0.005
R2 = 0.070 Adj. R2 = 0.062
F-Stat. = 8.028 D.W. Stat. = 1.995
The coefficient of residual lag 5 of health expenditure indicates that a one-unit increase in the residual of health
expenditure lagged by 5 periods is associated with a 0.264 increase in the current residual. The coefficient is
statistically significant (p-value = 0.005), indicating that past residuals have a meaningful impact on current
residuals. The value of R2 suggested that there is only about 7.04% of the variation in the residual of health
expenditure is explained by the lagged residual of health expenditure in the model and values of R2 is relatively
low which suggesting that the other factors not included in the model may explain most of the variation and
Adj. R2 value indicated that there is slightly lower than R2, reflecting the inclusion of lagged variables and their
limited explanatory power. Similarly, F-stat value is significant (p-value = 0.005), indicating that the model as
a whole is statistically significant and D.W Stat value is close to 2, suggesting that there is no significant
autocorrelation in the residuals.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 924
Figure: 4 Correlogram of Residual in ARCH Model
It is observed from the figure - 4 that
the ACF is marked by the absence of any dying out pattern of spikes.
no singularly significant large spike appears at the first lag of the corresponding PACF.
So, we observed that these features of the correlogram, as given in the Figure - 4, confirm that the first differenced
series of residual value of health expenditure is stationary.
This suggests that health expenditure residuals exhibit a persistent trend or integrated behavior (I(1)), meaning
shocks or changes in expenditure levels tend to have lasting effects rather than reverting quickly to a mean. The
significant coefficient at lag 5 (0.264, p=0.005) in what appears to be an autoregressive (AR) model implies a
cyclical or periodic dependence every five periods.
Section: IV
GARCH Model:
GARCH (Generalized Autoregressive Conditional Heteroskedasticity) extends the ARCH model by including
lagged conditional variances in the variance equation, allowing for a more flexible representation of time-varying
volatility.
In GARCH model also there are three equations the mean and variance equation are same as in ARCH that have
mentioned in equations no 9 and 10 but the conditional equation is different,
conditional equation
����
2 = ��0 + ��1����−1
2 + ⋯ … … … + ��������−��
2 + ��1����−1
2 + ⋯ … … … + ��������−��
2 ……………….(13)
Where ��0 > 0 ������ ���� ≥ 0 ������ �� = 1,2,3, … … … … … … . ,��, ���� ≥ 0 ������ �� = 1,2,3, … … … …��
These ARIMA, ARCH and GARCH models are the fundamental in time series analysis and forecasting,
particularly in finance, economics we so try to understanding and predicting time-dependent data of health
expenditure in the economy of Italy.
The Estimated Mean equation of GARCH (1,1) model is
Et = 0.042 + 0.283 ARIMA(F) t−12 + 0.169����������(��)��−5………..(14)
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 925
P-Value 0.000 0.002 0.055
Where ARIMA(F) stands for Autoregressive Integrated Moving Average Forecasting and GARCH(F) means
Generalized Autoregressive Conditional Heteroskedasticity Forecasting and
���� = ��1√ℎ�� means error term with zt~N(0,1) .
Here we see that coefficient of constant term is highly significant with p-value is 0.000 . Similarly, coefficient
of ARIMA(F) and GARCH(F) are also significant.
The Variance equation is
ℎ�� = ��0 + ∑ ��������−��
2��
��=1 + ∑ ����ℎ��−��
��
��=1 ………………………….(15)
ht = conditional variance at time t
α0 > 0: Constant term, αi ≥ 0: coefficient of lag squared error (ARCH terms)
β
j
≥ 0: coefficient of lag conditional variances (GARCH terms)
The sum ∑ αi + ∑ β
j
< 1 ensure stationarity of the variance process.
The estimated Variance Equation of GARCH(1,1) of equation (15) is
ht = 0.002 − 0.0104 ��2
t−1 + 1.034ℎ��−1 − 0.043���� + 0.041����������(��)�� − 0.002����������(��)��..(16)
P-value 0.001 0.034 0.000 0.259 0.001 0.946
R2 = 0.069 Adj R2 = -0.008 D.W. stat.= 1.888 AIC = -2.185 Mean = 0.040 S.D. = 0.086
Where ht: Conditional variance of ϵt, capturing volatility in health expenditure growth.
��2
t−1 : Squared residual from the previous period (ARCH term).
ℎ��−1: Lagged conditional variance (GARCH term).
So, we see that the coefficient of constant term is significant. Similarly, coefficient of ARCH(1), GARCH(1,1)
ARIMA forecasting value are also significant. The low value of R2 indicated that the mean equation explains
little variation in health expenditure in the economy of Italy and negative value of Adj R2 suggested that the poor
fit after adjusting for degrees of freedom. Similerly, the value of D.W stat. is close to 2 which implies that no
significant residual autocorrelation. Mean and Standard Deviation explained that the health expenditure has a
4.06% average monthly growth and high volatility (8.59%).
Figure:6 GARCH Forecasting about Health Expenditure
In the above figure -6 we examined that a time series plot comparing the actual health expenditure in Italy with
the forecasts generated by two models: ARIMA (Auto Regressive Integrated Moving Average) and GARCH
(Generalized Autoregressive Conditional Heteroskedasticity).We explained brief explanation of these models
and their relevance to health expenditure forecasting:
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 926
In the Figure - 6 indicated that the ARIMA forecast line shows red with star markers attempts to predict the
health expenditure based on its past values. ARIMA models are useful when the time series has patterns or
trends, but not necessarily large, sudden fluctuations. Similarly, GARCH forecasting was typically used for
financial time series, especially when there is volatility clustering periods of swings followed by relative calm.
Both the forecasts model we see that there have been mean and variance series, which helps capture sudden
spikes or drops.
GARCH forecasting (shown in green with triangle markers) captures the volatility or variability in health
expenditure over time. It might be useful if health expenditure has periods of high volatility, possibly due to
sudden policy changes, pandemics, or economic shifts and the blue line represents the actual health expenditure
data. The fluctuations seen may reflect various factors such as government spending, changes in healthcare
needs, or economic conditions. So, we see that both ARCH and GARCH forecasting represent the general trend
but doesn’t capture the volatility as effectively. The GARCH forecast (green triangles) better aligns with periods
of high volatility, indicating it might be more effective in capturing sudden spikes and dips.
Summary Conclusions and Policy Implication in the Economy of Italy:
The coefficient of constant term indicated that the 4.26% monthly growth rate implies strong structural increases
in Italy’s health expenditure, driven by an aging population, rising medical costs, and the universal healthcare
system (Servizio Sanitario Nazionale, SSN). This aligns with Italy’s healthcare spending (8–9% of GDP). The
value of coefficient of ARIMA forecasting indicated that a 1% increase in growth 12 months prior raises current
growth by 0.284%, indicating annual seasonality (e.g., fiscal budgets, winter health costs). This reflects
predictable cycles in healthcare spending. In case of short term, we see that the value for GARCH forecasting
implies 1% increase in growth 5 months prior raises current growth by 0.169%, marginally significant. The
high GARCH coefficient indicates persistent volatility, meaning shocks (e.g., COVID-19 costs in 2020–2021)
have long-lasting effects on expenditure variability.
The significant value for ARIMA forecasting in the variance equation suggests that forecasting signals influence
volatility. The sample period from 2012 to 2022 includes Italy’s economic recovery and the COVID-19
pandemic, which likely increased expenditure volatility.
Policy Implications: The 4.26% baseline growth and 12-month persistence suggest predictable increases, useful
for planning annual healthcare budgets. We used the lagged expenditure data (12- and 5-month lags) to forecast
spending, ensuring sufficient allocations for seasonal peaks. The high GARCH value persistence indicates
sustained volatility, especially post-COVID-19, requiring flexible budgets for unexpected shocks. There should
be create a contingency funds and use GARCH-based volatility forecasts to prepare for high-risk periods (e.g.,
pandemics, policy shifts). The negative ARCH coefficient and low value of R2 suggested that misspecification.
Missing variables (e.g., GDP, inflation) likely drive expenditure growth.
Increasing public investment in healthcare infrastructure can mitigate projected cost increases due to population
aging—potentially by allocating a larger share of GDP through targeted taxes or efficiency-enhancing reforms.
In both economic and health policy circles, differentiated budgetary responses—such as ring-fencing health
funds during recessions—can protect vulnerable populations and essential services. Furthermore, linking health
expenditure to broader macroeconomic objectives, such as GDP growth or EU recovery funds, would improve
the predictive power of models beyond simple lagged effects, thereby fostering long-term sustainable
development.
REFERENCE:
1. Barma, S. C. (July, 2025) Forecasting INR Exchange Rates Using ARIMA: A Comparative Study with
Euro, Pound, and Singapore Dollar. Journal of Emerging Technologies and Innovative Research, Vol-
12, I-7.
2. Chaabouni, S., & Abednnadher, C. (2013). Modelling and forecasting of Tunisia’s health expenditures
using artificial neural network and ARDL models. International Journal of Medical Science of Public
Health, 2, 495–503.
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025
Page 927
3. Di Matteo, L. (2010). The sustainability of public health expenditures: Evidence from the Canadian
federation. European Journal of Health Economics, 11(6), 569–584.
4. Getzen, T. (2000). Forecasting health expenditures: Short, medium, and long term. Journal of Health
Care Finance, 26, 56–72.
5. Getzen, T., & Poullier, J.-P. (1992). International health spending forecasts: Concepts and evaluation.
Social Science and Medicine, 34, 1057–1068.
6. Hannan, E. J., & Quinn, B. G. (1979). The determination of the order of an autoregression. Journal of
Royal Statistical Society, B14, 190–195.
7. John Bryant, Audrey Teasdale, Martin Tobias, Jit Cheung and Mhairi McHugh (2004), Population
Ageing and Government Health Expenditures in New Zealand, 1951-2051 . New Zealand Treasury
Working Paper, No. 04/14. www.econstor.eu.
8. Lee, R., & Miller, T. (2002). An approach to forecasting health expenditures, with application to the U.S.
medicare system. Health Services Research, 37(5), 1365–1386.
9. Paraskevi Klazoglou and Nikolaos Dritsakis (2018), Modeling and Forecasting of US Health
Expenditures Using ARIMA Models. https://www.researchgate.net/publication/324567808.
10. Peijun, C. (2016), “Predictive Analysis of Chinese Total Health Expenditure Base on ARIMA Model”,
Medicine and Society, (03).
11. Yue Z., W. Shengnan and L. Yuan (2015), “Application of ARIMA Model on Predicting Monthly
Hospital Admissions and Hospitalization Expenses for Respiratory Diseases”, Chinese Journal of Health
Statistics, (02), 197-200.
12. Zhao, J. (2015). Forecasting health expenditure: Methods and applications to international databases.
Working Paper, Centre for Health Economics and Policy Analysis.
13. Ulf-G. Gerdtham, Bengt Jönsson (2000), International Comparisons of Health Expenditure: Theory,
Data and Econometric Analysis. Handbook of Health Economics. Volume 1, Part A, 2000, Pages 11-53.