INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNO V A T ION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |V o lume XII Issue XI November 2025

Multivariate Monitoring of Gross Domestic Product and Inflation

Rate in Ghana

Mutala Mohammed, Wahab Mashud, Abu Ibrahim Azebre

Department of Statistics and Actuarial Science, C.K. Tedam University of Technology and Applied

Sciences

DOI: https://dx.doi.org/10.51244/IJRSI.2025.12110089

Received: 07 October 2025; Accepted: 12 October 2025; Published: 09 December 2025

ABSTRACT

Multivariate control charts are statistical tools increasingly used for the simultaneous monitoring of multiple

interrelated variables. This study applied Hotelling T², multivariate cumulative sum (MCUSUM), and

multivariate exponentially weighted moving average (MEWMA) control charts to jointly monitor Gross

Domestic Product (GDP) and inflation rate in Ghana, aiming to detect both small and large shifts in the mean

vector of these variables. Annual data for the period 1973–2022 were obtained from the Bank of Ghana. Results

indicate that the Hotelling T² chart flagged out-of-control points in 1976, 1980, 1982, 2012, and 2013, primarily

reflecting moderate-to-large shifts in GDP and inflation. The MCUSUM chart detected a deviation in 1982,

while the MEWMAchart identified out-of-control points in 1980, 1982, and 2013, capturing subtle but persistent

changes. Comparative analysis suggests that Hotelling T² is most effective for detecting moderate-to-large shifts,

whereas MCUSUM and MEWMAprovide complementary sensitivity to smaller or time-weighted changes. This

study is novel in applying multivariate SPC techniques to Ghana’s macroeconomic indicators, offering a

proactive framework for monitoring GDP and inflation jointly. Integrating such charts into the Bank of Ghana’s

economic monitoring tools could facilitate earlier detection of macroeconomic deviations and support more

informed policy responses.

BACKGROUND

Macroeconomic and financial statistics are fundamental to shaping national economic policies, as they provide

insights into a country’s wealth, economic performance, and financial health through indicators such as gross

domestic product (GDP) and inflation. GDP, defined under the System of National Accounts 2008 as the total

market value of goods and services produced within a specific period, remains central to budget planning and

economic forecasting (United Nations et al., 2009; Bade, 2016). It is widely regarded as the most reliable

measure of a nation’s economic health because it captures both the scale and dynamics of production.

Inflation, understood as a sustained rise in the general price level, reduces purchasing power and distorts

decision-making by households, firms, and policymakers. It may be driven by factors such as fiscal imbalances,

monetary expansion, or surges in external demand. According to the International Monetary Fund, low, stable,

and predictable inflation is critical for fostering long-term growth and macroeconomic stability (Oner, 2010).

Economists typically distinguish among creeping, walking, galloping, and hyperinflation, each reflecting

different magnitudes of price acceleration and distinct policy challenges.

In Ghana, monetary policy is entrusted to the Bank of Ghana, which operates an inflation-targeting framework

with the objective of ensuring price stability as a foundation for sustainable growth (Abradu-Otoo et al., 2024).

Although maintaining stable inflation is a critical goal (Alhassan & Fiador, 2014), it does not by itself provide a

full picture of overall economic health, highlighting the need for complementary indicators such as GDP to

capture broader macroeconomic performance. This policy orientation underscores the centrality of inflation

control in Ghana’s macroeconomic management, yet it also raises the question of how price dynamics interact

with output performance, suggesting the importance of studying GDP and inflation together rather than in

isolation.

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INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNO V A T ION (IJRSI)

ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |V o lume XII Issue XI November 2025

Previous studies have mainly analyzed inflation and GDP separately, often using univariate models, despite calls

for joint monitoring approaches (Mbeah-Baiden, 2013; SACU, 2013). While various statistical models such as

regression, time series, Vector Auto-regressive (VAR), and Auto-regressive Integrated Moving Average

(ARIMA) have been applied to Ghana’s macroeconomic variables (Agalega & Antwi, 2013; Asenso et al., 2017),

these models are primarily designed for forecasting or understanding dynamic relationships rather than for

ongoing, real-time surveillance of macroeconomic health.

In contrast, methods drawn from Statistical Process Control (SPC), in particular multivariate control charts offer

a complementary approach better suited for continuous monitoring and early anomaly detection. SPC originated

in industrial quality control, but recent applications have demonstrated its utility beyond manufacturing.

Multivariate control charts such as Hotelling’s T2 chart, Multivariate CUSUM (MCUSUM), and Multivariate

Exponentially Weighted Moving Average (MEWMA) are especially powerful when two or more correlated

variables must be watched simultaneously (Quality Magazine, 2024).

The advantages of multivariate control charts over univariate monitoring approaches are well established in the

quality-control and process-monitoring literature. First, multivariate charts enable the simultaneous monitoring

of multiple interrelated indicators while incorporating the covariance structure between them, thereby providing

a more holistic and statistically coherent view of system behaviour than separate univariate charts (Montgomery,

2019; Fuchs & Runger, 2010). Second, because they define a single joint control region, multivariate charts

preserve the intended overall Type I error rate, whereas applying separate univariate charts to correlated variables

can inflate false-alarm probabilities and distort control behaviour (Durfee, 1994; Phaladiganon et al., 2010).

Third, cumulative-based schemes such as the Multivariate Cumulative Sum (MCUSUM) and the Multivariate

Exponentially Weighted Moving Average (MEWMA) are particularly sensitive to small and persistent shifts in

the process mean vector—subtle drifts that may remain undetected by Shewhart-type charts or by traditional

econometric forecasting models designed primarily for prediction rather than continuous structural supervision

(Lowry et al., 1992; Fallahnezhad & Ghalichehbaf, 2023).

Moreover, Statistical Process Control (SPC) techniques are widely recognized for supporting rapid or near real-

time monitoring because they produce immediate visual signals that allow for prompt corrective action—an

attribute increasingly relevant for macroeconomic surveillance and early-warning systems (Singh et al., 2002;

SPC Software, 2023). Given the complexity and interdependence of macroeconomic variables such as GDP and

inflation, multivariate control charts offer a proactive analytical tool for detecting emerging structural changes

or early signs of instability rather than relying solely on periodic forecasts or ex post statistical evaluations

(Yeganeh et al., 2023; Arciszewski, 2023).

This study addresses this gap by applying Hotelling’s ², Multivariate Cumulative Sum (MCUSUM), and

Multivariate Exponentially Weighted Moving Average (MEWMA) control charts to jointly monitor Ghana’s

GDP and inflation from 1973 to 2022. The objectives are to apply each method individually, compare their

performance, and identify the most effective technique for macroeconomic monitoring. The paper seeks to

achieve two specific objectives;

i.

To jointly monitor Ghana’s GDP and inflation rate using Hotelling’s ², MCUSUM, and MEWMA

control charts.

ii.

To compare the performance of these methods and identify the most effective approach for monitoring

GDP and inflation.

REVIEW OF LITERATURE

Empirical Studies

Recent empirical studies on Ghana’s macroeconomic dynamics highlight persistent challenges related to

inflation volatility, exchange rate depreciation, fiscal imbalances, and their combined effects on economic

growth. These studies provide important context for jointly monitoring GDP and inflation using multivariate

control charts.

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ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |V o lume XII Issue XI November 2025

Ghana has experienced episodes of prolonged high inflation particularly during 2014–2016 and again after 2020

which was driven by exchange-rate depreciation, supply constraints, and fiscal pressures (Ackah & Opoku, 2023;

Osei-Assibey & Adu, 2022). Several studies show that inflation in Ghana is often cost-push in nature, originating

from imported inflation and energy price shocks rather than excess demand (Bawumia & Abradu-Otoo, 2021).

This supports the need for real-time monitoring frameworks that can capture abrupt or structural shifts in

inflation behaviour.

The relationship between inflation and economic growth has also been widely examined. Empirical findings

generally suggest that moderate inflation may be compatible with growth, but high or unstable inflation

significantly undermines economic performance in Ghana (Frimpong & Oteng-Abayie, 2010; Aboagye &

Oteng-Abayie, 2020). For instance, Frimpong and Oteng-Abayie (2010) identified a threshold effect, where

inflation above approximately 11% exerts a negative impact on growth. More recent analyses confirm that

inflation’s influence on GDP is asymmetric: inflation spikes have stronger negative effects on growth than

disinflation episodes have positive effects (Ocran & Wiafe, 2021).

Studies focusing on macroeconomic stability indicators further show that GDP growth in Ghana is sensitive to

combined shocks involving inflation, exchange rate movements, and fiscal deficits (Adom & Fiador, 2022;

Boakye & Ackah, 2023). Importantly, these studies mostly rely on VAR, ARDL, or regression-based

frameworks, which, while useful for forecasting and long-run relationships, are not designed for continuous

process monitoring or early detection of abnormal behaviour. This methodological gap underscores the potential

value of applying Statistical Process Control (SPC) techniques to Ghana’s macroeconomic variables.

Integrating SPC methods, particularly multivariate control charts, offers a novel way to monitor the joint

behaviour of GDP and inflation; variables that have demonstrated significant co-movement during periods of

macroeconomic stress. Given the documented instability in Ghana’s inflation dynamics and its measurable

impact on economic activity, multivariate monitoring tools may help detect unusual shifts more rapidly than

traditional econometric models, thereby supporting proactive policy responses.

Theoretical Framework

Multivariate control charts, extensions of univariate charts, are used to simultaneously monitor multiple related

process variables, especially when they exhibit high cross-correlation (Mohmoud & Maravelakis, 2013;

Montgomery, 2005). Widely applied in sectors like manufacturing and pharmaceuticals, these charts help detect

small to moderate shifts in the process mean vector more effectively than separate univariate charts, particularly

when variables are dependent (Alt, 1988; Montgomery, 1991). They operate by plotting each sample’s test

statistic against an upper control limit (UCL), with points above the UCL indicating potential process issues.

The MCUSUM chart, a multivariate extension of the univariate CUSUM, is designed to improve the sensitivity

of the Hotelling’s ²chart in detecting small to moderate shifts in the process mean vector by using accumulated

data from previous observations (Crosier, 1988; Busaba et al., 2012a, 2012b). Various methods for constructing

MCUSUM charts have been proposed, including approaches by Healy (1987), Woodall and Ncube (1985),

Crosier (1988), and Pignatiello and Runger (1990). The MEWMA chart, proposed by Roberts et al. (1959) as

the multivariate version of EWMA, monitors shifts using weighted averages of past observations and is highly

sensitive to small and moderate process changes (Montgomery, 2005). Enhancements and applications have been

studied in various contexts, such as clinical trials and VAR (1) processes (Khoo et al., 2006; Joner et al., 2008;

Mahmoud & Zahran, 2010; Patel & Divecha, 2013), with modifications like the BMEWMA percentile approach

addressing control limit selection issues (Fricker, 2007).

Multivariate Shewhart control charts, though widely used for detecting large process changes over 1.5σ

(Mahmoud et al., 2015), are less effective for small to moderate changes and can produce more false alarms

when normality assumptions are violated (Montgomery, 2009; Phaladiganon et al., 2011). In contrast, CUSUM

and EWMA-type charts are more suited for detecting smaller shifts (Yeh et al., 2006). Average Run Length

(ARL) measures the performance of these charts, with high in-control ARL minimizing false alarms and low

out-of-control ARL enabling quicker detection of process changes (Montgomery, 2005; Pham, 2006).

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ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |V o lume XII Issue XI November 2025

Related Works

Research comparing multivariate and univariate models shows that multivariate approaches often perform better

for forecasting and risk management, especially with sufficiently large sample sizes (Siaw, 2014; Santos et al.,

2009, 2013; Christoffersen, 2009). For example, multivariate GARCH models improve portfolio value-at-risk

predictions, and bi-variate CUSUM methods detect small and moderate mean shifts faster than Shewhart charts

(Woodall & Ncube, 1985). Variations of multivariate CUSUM by Crosier (1988), Healy (1987), and Pignatiello

& Runger (1990) have comparable performance, though each has strengths in detecting specific types of shifts.

In practice, MEWMAand MCUSUM charts have been effective for detecting modest changes even when quality

indicators are uncorrelated (Fricker, 2007). Methodological advances include bootstrap-based control limits,

generalized variance approaches, and boosting methods for identifying out-of-control variables (Phaladiganon

et al., 2011; Yeh et al., 2006; Alfaro et al., 2009), as well as innovations in handling auto-correlated processes

(Kalgonda, 2013, 2015; Gandy & Kvaløy, 2013).

Inflation is the sustained rise in prices, which erodes purchasing power and can signal poor economic

management when rates are high, as it often leads to low growth and higher borrowing costs (McConnel & Brue,

2008; Asiedu & Lien, 2004). GDP, defined as the total market value of goods and services produced in a given

period, is a central measure of economic performance, used for budgeting, forecasting, and assessing the overall

health of an economy (Bade, 2016; Mankiw & Taylor, 2007). Both variables are key macroeconomic indicators,

essential for understanding and managing a nation’s economic trajectory.

This study applies Statistical Process Control (SPC) techniques, Hotelling’s ², Multivariate Cumulative Sum

(MCUSUM), and Multivariate Exponentially Weighted Moving Average (MEWMA) control charts to jointly

monitor Ghana’s Gross Domestic Product (GDP) and inflation rate, a method rarely used in macroeconomic

analysis. In contrast to prior research that primarily relied on regression, univariate time series, or Vector Auto-

regressive (VAR) models examining each variable separately, this approach employs multivariate SPC tools,

widely used in industrial quality control, to capture the interdependence between GDP and inflation and detect

both significant and subtle shifts in their joint mean vector. The comparative performance assessment shows

Hotelling’s ²as the most effective for early shift detection, with MCUSUM and MEWMA offering additional

sensitivity to smaller changes, providing policymakers with a more robust framework for timely and accurate

economic monitoring in Ghana.

METHODS

Data and Source

This study utilized annual secondary data covering the period 1973–2022. Data on Gross Domestic Product

(GDP) and inflation rate were obtained from official publications of the Bank of Ghana (BOG). Specifically,

GDP data were extracted from the National Accounts Statistical Series, and inflation data from the Consumer

Price Index (CPI) Statistical Reports. The datasets are publicly accessible through the Bank of Ghana’s Statistical

Database (https://www.bog.gov.gh/) (Bank of Ghana, 2023). The data provide consistent, official

macroeconomic indicators suitable for applying multivariate control charts over the 50-year period.

Basic Time Series Model

The basic time series model is denoted as (AR (1)), being the first order Auto-regression model were considered.

The purpose of the AR(1) model is to remove the effects of auto-correlation that may affect the chart. The de-

trended data from the AR (1) model were used for the control chart. The value of y at time is a linear function

t

t - 1_{. Since the data was collected over time, we consider a basic time series model}

of the value of y at time

(AR (1)) of the form;

y_t y_t1_t

(3.1),

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For GDP, we have

y_1t₁

₁y_1t_1t

(3.2),

(3.3),

For inflation, we have

y_2t₂

₂y_2t_2t

where = 1, 2, …, 50, Y_1tis the GDP, δ₁is the intercept for GDP, Ф₁is the coefficient of the auto-regressive

t

term, ε_1tis the error (residuals) for GDP, Y_2tis the inflation rate, δ₂is the intercept for inflation rate, Ф₂is the

coefficient of the auto-regressive term and ε_2tis the error (residuals) for inflation rate. The errors were then used

for monitoring.

Testing the Stationarity of Time Series

In order to appropriately build a model, all series that are used in the analysis must be stationary. Since non-

stationarity levels leads to spurious results, there is the need to make them stationary. The non-stationarity and

the stationarity process can be distinguished by employing the Augmented Dickey – Fuller (ADF) unit-root test

to check the Stationarity of the time series (Sim et al., 1990).

Model Specification

The models applied in this study were Hoteling T ², MCUSUM and MEWMA control charts. These joint models

were used to monitor GDP and inflation rate growth of Ghana.

The Estimation of Parameters

The AR (1) model although, is fundamental to time series data, and is easy to estimate the parameters. Also, the

number of lags when determine, the one with the minimum AIC value is chosen. The AIC value if not minimised

with the same model, the likelihood ratio (LR) test method is applied (Johansen, 1995).

_HotelingT ²

Control Chart

T ²

The Hoteling

control chart is the most well-known multivariate chart presently in use in the literature.

T ²

(Montgomery, 2009) observed that the Hoteling

control research. Hotelling used multivariate control approach with data that included bomber location

information during World War II.

chart was a trailblazer in the field of multivariate quality

The first assumption made by Hotelling was that the quality characteristics belonged to a normal multivariate

p

n

distribution, with a covariance matrix S and a mean vector . As a result, samples of size for each of the

variables to be tracked and the estimates of the parameters are used to create the equation for calculating the

_{estimates of the statistic}T ²

'

T² X  X S^1X  X









(3.4),

where s^{- 1}and

stand for the inverse of the covariance matrix and the estimates for the vector of means,

T ²

respectively. The Hoteling

chart for individual observations is built using expression (3.4) as a foundation

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(Lowry et al., 1995). On the other hand, the statisticsT ²in phase (I) validate the control and are stated by

p

F

following, the

distribution with

and (mn- m- p+ 1) degrees of freedom.

The phase (I) monitoring of the process involve collecting information that is sufficient to determine whether or

not the process reveals an in-control situation based on historical data. The upper control limit of the phase (I)

monitoring scheme is expressed below;

p(m 1)(n 1)

mn  m  p 1

UCL 

F



, p,mnm p1

(3.5),

Also, based on the control limits calculated from Phase (I), Phase (II) which is the future observations are

monitored to determine if the process continues to be stable or not. The upper control limit of the phase (II)

monitoring scheme is expressed below;

p(m 1)(n 1)

mn  m  p 1

UCL 

F

(3.6),



, p,mnm p1

p_,

F

F _,

where the superior percentage point of α to a distribution is denoted by

.

m

, and

n

a , p,mn- m- p+1.

denote the number of samples, sample size, and number of quality characteristic (variables). The process is

considered to be out of statistical control if the value of T ²is greater than the upper control limit (UCL). For

both stages, the lower control limit (LCL) is zero.

However, it is worth mentioning that the use of the cumulative sum of difference in terms of their mean was

examined by (Sullivan and Woodall, 1996), while the difference among consecutive observations instead of the

difference respecting the mean was proposed by (Holmes and Mergen, 1993).

MCUSUM Control Chart

One of the test statistics for the MCUSUM techniques that (Crosier, 1988) gave, with the version that performs

better in the ARL is;

1



^1/2



n

 

 

p² s^'

s

 h ,

(3.7),



_k

k

 

1









where k = 1, 2, 3, … an out-of-control alarm is signal if p²> h₁, where the control limit is h₁. The value of h₁

can be obtained by simulation (Alves et al., 2010) and (Fricker et al., 2008)). The proposed MCUSUM by

(Crosier, 1988) is derived by replacing the scalar quantities of a uni-variate CUSUM by vectors. The control

chart may be expressed as follows:

^1/2



1



'



n

 

 

C  S  X _k

S

k1

 X _k

(3.8),





₀



₀

k

k1

 









k = 1, 2, 3, … where covariance matrix is Σ and

are the cumulative sums as determined by:

s_k

0

≤

= {

(3.9),

(

)

+

−

(1 −

)

>

−1

0

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where

m

> 0, is the reference value, the target value for the mean vector is µ and

= 0 (Khoo et al., 2009).

s_k

0

The selection of m given by (Crosier, 1988) is

to minimize the ARL at θ for a given in-control ARL.

m

= θ/2, where θ is defined in equation (3.14), and this appears

MEWMA Control Chart

(Lowry et al., 1992) developed a MEWMA control chart. The MEWMA control chart employs weighted

averages of previously observed random vectors to monitor the mean vector of the process. Consider that a p-

dimensional random vector X_k= (X_l, X_{2, …,}Xp)' has random variables as its components at time , then the

MEWMA control chart is defined as;

Z_k



X_k(1)X_k1

(3.10),

where k = 1, 2, 3 … and

is the weighted average of the time k. Consider that ₀= 0 where λ is the diagonal

p x p matrix of the smoothing constant with (0 < λ ≤ 1) being the weighting constant and Z_0,which is the mean

vector in-control of the process. Thus, the MEWMA control chart has a test statistic;

P² Z_k^'^_Z¹Z_k h₂

(3.11),

k

where a defined control limit is denoted by h_2.Every time P²surpasses a predetermined control limit, which is

calibrated to produce a desired average time between false signals (ATFS), the MEWMA sounds an alarm. If P²

does not exceed h₂then the MEWMA move a new observation vector, and iterates through the next time step,

2

recalculating the test statistic. The process continues until when

> ℎ₂. Since the test statistic is always non-

negative as a result, only the upper control limit (UCL) is needed to monitor. The covariance of (∑ ) is

dependent upon the number of samples taken, the UCL will also depend on k. More so, the lower control limit

(LCL) for the two phases is equal to zero in multivariate setting.

The two approaches provided by (Lowry et al., 1992), for estimating the Σ_z, is shown below; with the exact

covariance matrix given as;

2k



















1 1











(3.12),

_Z







_x

k

(2 

)









Also, the asymptotic covariance matrix is given as;



2 





_Z





_x

(3.13),









k



It is shown in literature that equation (3.9) performed better. Furthermore, (Lowry et al., 1992) again suggested

that, the efficiency of the MEWMA chart in terms of the ARL relies on the mean vector µ and covariance matrix

Σ_z, solely through the value of the non-centrality parameter θ, and

^1/2



'



        



₀ 

₀

(3.14),

1



Large values of θ corresponded, in general, to larger mean changes. The statistical process control situation that

is under control is represented by θ = 0. Keep in mind that, with the exception of very large values of θ or big

shifts, ARLs typically tend to grow as λ increases for a given shift size. However, a special case of the MEWMA

control chart is transformed on P²chart when λ = 1, it leads to

=

_Kand

. This is simply

Z_K

X

p² X '

^1X_k

_k_x

known as the χ²chart or multivariate Shewhart control chart. Also, MEWMA with λ < 1 is more sensitive to

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minor alterations in the mean vector. From Equation (3.10) it is obvious that, when Z_kis expanded recursively

the expression below is obtained;

Z_k X_k (1)X_k1 (1)²X_k2... (1)^k1X₁ (1)^kz₀

(3.15),

Thus, Z_ktakes on a geometric form and is the weighted average of the time k quality measurements that are

provided with weights. The chart is known as multivariate exponentially weighted moving average in the

literature.

Limitations

Although the dataset spans 50 years, the annual frequency may limit the sensitivity of multivariate control charts,

particularly for detecting short-term fluctuations or seasonal effects. Control chart parameters estimated from a

single annual time series may not fully capture intra-year variability (Montgomery, 2019).

Using only BOG-reported data may introduce source-specific biases or reporting inconsistencies. Cross-

validation with other databases (e.g., Ghana Statistical Service) was not performed, which may affect robustness.

Ghana experienced major economic events, including high inflation periods, currency devaluations, and fiscal

adjustments. These structural breaks may affect the assumption of process stability and the estimation of control

limits (Pham, 2006; Montgomery, 2019).

To mitigate potential bias, control limits for Hotelling’s T², MCUSUM, and MEWMA charts were estimated

using standard procedures from multivariate SPC literature, with in-control process assumptions checked via

historical baseline periods (Lowry et al., 1992; Fallahnezhad & Ghalichehbaf, 2023).

By acknowledging these limitations, the study ensures transparency and guides interpretation of the findings,

emphasizing that multivariate control charts are applied as complementary monitoring tools rather than definitive

predictive models.

RESULTS AND DISCUSSIONS

Descriptive Statistics

The descriptive statistics is shown below in Table 4.1. The statistics include mean, standard deviation, skewness,

and excess Kurtosis of Gross Domestic Product (GDP) and inflation rate. The Gross Domestic Product (GDP)

and inflation rate have positive average values (means) of about 20.67 and 28.99, respectively, with standard

deviations of 24.09 and 26.45, respectively.

The results from the descriptive statistics also showed that the Gross Domestic Product (GDP) is positively

skewed (skewness value of 1.238), which further demonstrates that the majority of Gross Domestic Product

(GDP) values are less than their means. The excess kurtosis for Gross Domestic Product (GDP) is negative

making it platykurtic (-0.008). Hence, its peak is flatter than the typical normal distribution. Table 4.1 also

showed that Ghana's inflation rate is positively skewed (skewness value of 2.200), indicating that the majority

of inflation rate values are less than their means. The excess kurtosis for inflation rate is positive making it

leptokurtic (4.814), hence exhibiting more peaked values than the normal distribution. Table 4.1 presents

summary of the results.

Table 4.1: Summary of Descriptive Statistics of the Variables for Ghana

Variable

GDP

N

Min

Max

Mean

Std. Dev.

24.0885

26.4488

Skewness

1.2380

Excess kurtosis

-0.0080

50

2.7700

8.6800

79.1600

121.3500

20.6666

26.4480

Inflation

2.2000

4.8140

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Testing the Stationarity of Time Series

Table 4.2 showed the results for the stationarity test of the original data on both GDP and inflation for the ADF

test. The output shows non-stationarity on GDP since the p-values is greater than 0.05 as shown below.

Table 4.2: Stationarity Test of the Original Variables

Gross Domestic Product

Inflation Rate

Statistic

ADF Test

Statistic

P-value.

0.9741

P-value

-0.5876

-3.5670

0.0448

Table 4.3 showed the results for the stationarity test of the residual on both GDP and inflation for the ADF test.

The output shows stationarity on both GDP and inflation rate since the p-values are all less than 0.05 as shown

below.

Table 4.3: Stationarity Test of the Residual Variables

GROSS DOMESTIC PRODUCT

INFLATION RATE

Statistic P-value

ADF Test

Statistic

P-value.

0.0100

-4.3578

-3.2722

0.0400

Results for AR (1) Model

Table 4.4 showed the parameters estimate of the AR (1) model for GDP. The AR (1) for GDP had an intercept

of 2.6463 and a slope of 0.9936 which indicates stationarity (since

< 1).

Table 4.4: AR (1) Model Parameter Estimate for GDP

Parameter

Coefficient

2.6463

se

Log-likelihood

AIC

1.3869

0.0085

Intercept( )

1

0.9936

15.71

-25.42

1

Table 4.5 showed the parameters estimate of the AR (1) model for inflation rate. The AR(1) for inflation rate

had an intercept of 3.0850 and a slope value of 0.5940 which indicates a stationarity (since

< 1)

2

Table 4.5: AR (1) Model Parameter Estimate for Inflation Rate

Parameter

coefficient

3.0850

se

Log-likelihood

AIC

0.1898

0.1111

Intercept( )

2

0.5940

-42.25

90.49

2

Table 4.6 showed the output for Ljung Box test Statistic for the original data on both GDP and inflation. The

output indicates that, there exist serial correlation on both GDP and inflation rate since the corresponding p-

values are all less than 0.05 as shown below.

Variable

Chi-Square

P-value

GDP

220.7500

0.0000

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Inflation

42.4400

0.0100

Table 4.6: Test of Serial Correlation of the Original Variables

Variable

GDP

Chi-Square P-value

220.75

42.44

0.0000

0.0100

Inflation

Table 4.7 also showed that, there is no serial correlation on both GDP and inflation rate owing to the fact that,

the corresponding p-values are greater than 0.05 as shown below.

Table 4.7: Serial Correlation of the Residuals

Variable

GDP

Chi-Square

16.7460

p-value

0.0802

0.2661

Inflation

12.2400

Hoteling T ²Control Chart Based on Sullivan and Woodall (SW) Method

Figure 4.1 showed the output of the Hoteling T ²control chart based on Sullivan and Woodall (SW) method.

The control chart based on the macroeconomic variables such as Gross Domestic Product (GDP) and inflation

rate given as, variable X₁(GDP) and variable X₂(inflation). It can be observed that, five samples (4, 8, 10, 40,

and 41) which corresponding to the years 1976, 1980, 1982, 2012, and 2013 respectively, fall outside the control

limit of 5.74 (Threshold), similar results can be seen in Table 4.6.

.

_{Figure 4.1: Hoteling}T ²

control chart by SW for GDP and inflation rate.

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Table 4.8: Sullivan Woodall method for GDP and inflation rate

Sample

1

error_GDP

-1.05727

-1.01375

-0.97139

-0.51022

-0.47257

-0.59638

-0.53697

-1.20961

-1.15285

-0.94756

-0.61815

-0.88844

0.258918

-1.68754

-0.86784

-0.95166

-0.36313

-0.31195

-1.22283

-1.48753

-1.5443

error_inflation

-4.39226

2.446733

27.09586

62.29025

4.782753

14.40802

8.626386

77.57967

-43.4044

94.00721

-21.1859

-27.2678

1.197595

-14.4143

9.664322

-5.14798

9.537973

-14.4463

-15.324

T²Chart(SW)

0.11

2

0.06

3

1.29

4

6.84

5

0.05

6

0.37

7

0.14

8

10.55

3.56

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

15.55

0.85

1.43

0.01

0.58

0.18

0.11

0.16

0.39

0.55

4.259274

-4.43241

31.8673

0.13

0.18

0.000986

-0.56871

-1.09253

-0.46135

-0.8287

1.81

6.319687

-9.88055

-9.60859

-12.5049

0.08

0.26

0.19

0.34

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28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

-3.81576

-0.66519

-0.1449

1.169894

6.841288

-16.3965

0.399357

-9.00633

-8.98881

-12.6163

-10.5136

-4.95681

-4.44792

-14.2105

-12.5376

-11.2455

-9.03712

-6.17445

-6.30507

-6.50476

-11.8648

-12.9629

-11.8243

-10.4247

-11.0048

10.53844

0.76

0.09

0.49

0.01

0.14

0.16

4.24

0.45

0.29

1.07

1.27

1.61

0.23

19.68

6.31

3.43

1.04

0.36

1.11

0.47

0.3

0.429817

0.176891

0.750139

8.985451

2.477024

2.271181

-4.32202

4.535311

5.34449

-0.07544

19.48782

-10.7358

-7.8294

4.448486

1.750025

4.265067

-1.78751

-1.15809

6.211929

-9.49622

2.07

4.68

* The bolden shows out-of-control points

_HotelingT ²

Control Chart Based on Holm and Mergen (HM) Method

_{Figure 4.2 showed the output of the Hotelling}T ²

control chart based on Holm and Mergen method. The control

chart based on the macroeconomic variables such as Gross Domestic Product (GDP) and inflation rate were

monitored given as, variable X₁(GDP) and variable X₂(inflation). It can be observed that, four samples (4, 8,

10, and 40) which correspond to the years 1976, 1980, 1982, and 2012, respectively, fall outside the control limit

of 5.74 (Threshold), similar results can be seen in Table 4.7.

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_{Figure 4.2: Hoteling}T ²

control chart by HM for the GDP and inflation rate.

Table 4.9: Holm Mergen method for GDP and inflation rate

Sample

error_GDP

-1.05727

-1.01375

-0.97139

-0.51022

-0.47257

-0.59638

-0.53697

-1.20961

-1.15285

-0.94756

-0.61815

-0.88844

0.258918

-1.68754

-0.86784

-0.95166

error_inflation

-4.39226

T²Chart(HM)

0.08

1

2

2.446733

27.09586

62.29025

4.782753

14.40802

8.626386

77.57967

-43.4044

94.00721

-21.1859

-27.2678

1.197595

-14.4143

9.664322

-5.14798

0.05

3

1.13

4

5.82

5

0.04

6

0.32

7

0.12

8

9.04

9

2.92

10

11

12

13

14

15

16

13.23

0.70

1.17

0.01

0.46

0.17

0.08

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18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

-0.36313

-0.31195

-1.22283

-1.48753

-1.5443

9.537973

-14.4463

-15.324

0.14

0.32

0.43

0.12

0.14

1.52

0.07

0.21

0.15

0.27

0.67

0.09

0.41

0.01

0.12

0.14

3.86

0.43

0.27

0.90

1.21

1.50

0.19

17.40

5.37

2.90

0.95

0.34

4.259274

-4.43241

31.8673

0.000986

-0.56871

-1.09253

-0.46135

-0.8287

6.319687

-9.88055

-9.60859

-12.5049

1.169894

6.841288

-16.3965

0.399357

-9.00633

-8.98881

-12.6163

-10.5136

-4.95681

-4.44792

-14.2105

-12.5376

-11.2455

-9.03712

-6.17445

-6.30507

-6.50476

-11.8648

-3.81576

-0.66519

-0.1449

0.429817

0.176891

0.750139

8.985451

2.477024

2.271181

-4.32202

4.535311

5.34449

-0.07544

19.48782

-10.7358

-7.8294

4.448486

1.750025

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46

47

48

49

4.265067

-1.78751

-1.15809

6.211929

-9.49622

-12.9629

-11.8243

-10.4247

-11.0048

10.53844

1.05

0.37

0.23

1.91

4.23

* The bolden shows out-of-control points

_{Decomposition of the}T ²

Chart

The decomposition issue was utilized to identify which quality features (variables) were in charge for the

variation when an out-of-control signal occurred. Nonetheless, (Mason et al., 1995) approach is the one that is

most commonly accepted to address the decomposition problem. Table 4.8 and 4.9 showed results of

decomposition analysis for Sullivan and Woodall (SW) method and Holm and Mergen (HM) method. From

Table 4.8 and 4.9, it revealed that the combined influence variable is represented by the third decomposed row,

with the first two decomposed rows representing each of the variables investigated. The variable X₂(inflation)

indicates the source of variability for the out-of-control situation at time point 4, which correspond to the year

1976. It follows that, variable X₂(inflation) went out-of-control situation since it is significant (p-value < 0.05)

for the period 1976.

The variable X₂(inflation) indicate the source of variability for the out-of-control situation at time point 8, which

correspond to the years 1980. This means that, variable X₂(inflation) went out-of-control situation since it is

significant (p-value < 0.05) for the period 1980. Again, the variable X₂(inflation) indicate the source of

variability for the out-of-control situation at time point 10, which correspond to the years 1982. This means that,

variable X₂(inflation) went out-of-control situation since it is significant (p-value < 0.05) for the period 1982.

In addition, the variable X₁(GDP) reveals the source of variability for the out-of-control situation at time point

40, which correspond to the years 2012. It follows that, variable X₁(GDP) went out-of-control situation since it

is significant (p-value < 0.05) for the period 2012. The variable X₁(GDP) again, reveals the source of variability

for the out-of-control scenario at time point 41, which correspond to the years 2013. This also reveals that,

variable X₁(GDP) went out-of-control situation since it is significant (p-value < 0.05) for the period 2013.

Table 4.10: Decomposition of GDP and inflation rate by SW method

Sample

t²

Decomp

0.0135

6.7848

6.8413

0.0756

10.5244

10.5513

0.0464

UCL

P-value

0.9081

0.0122

0.0024

0.7845

0.0021

0.0002

0.8304

GDP (X1) Inflation (X2)

[1,]

[2,]

[3,]

[1,]

[2,]

[3,]

[1,]

6.6988

5.6988

8.7161

5.6988

8.7161

5.6988

1

2

1

2

1

0

2

0

2

0

4

8

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10

40

41

[2,]

15.4533

15.5543

19.6283

0.1428

19.6775

5.9570

0.0667

6/3084

5.6988

8.7161

5.6988

8.7161

5.6988

8.7161

0.0003

0.0000

0.0001

0.7072

0.0000

0.0184

0.7974

0.0037

2

1

2

1

2

0

2

0

2

0

[3,]

[1,]

[2,]

[3,]

[1,]

[2,]

[3,]

1

2

Table 4.11: Decomposition of GDP and inflation rate by HM method

Sample

t²

Decomp

0.0119

UCL

P-value GDP (X1)

0.9136

Inflation (x2)

[1,]

[2,]

[3,]

[1,]

[2,]

[3,]

[1,]

6.6988

5.6988

8.7161

5.6988

8.7161

5.6988

8.7161

5.6988

8.7161

1

2

1

2

1

2

1

2

1

0

2

0

2

0

2

0

2

4

5.8164

0.0198

0.0055

0.7971

0.0042

0.0005

0.8403

0.0007

0.0000

0.0001

0.7279

0.0000

5.8169

0.0669

8

9.0222

9.0442

0.0410

10

40

[2,] 13.2477

13.2524

17.3564

0.1224

[3,]

[1,]

[2,]

[3,]

17.3953

MCUSUM Control Chart

Figure 4.3 showed the MCUSUM control chart based on macroeconomic variables such as Gross Domestic

Product (GDP) and inflation rate were monitored. The chart was constructed using m = 0.5 and c = 5.5. It can

be observed that, only one sample point (10) which correspond to the year 1982, falls outside the control limit

of 5.5 (Threshold).

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Figure 4.3: MCUSUM Control Chart for GDP and Inflation Rate

Table 4.12: MCUSUM Chart for GDP and inflation rate

Sample

error_GDP

-1.05727

-1.01375

-0.97139

-0.51022

-0.47257

-0.59638

-0.53697

-1.20961

-1.15285

-0.94756

-0.61815

-0.88844

0.258918

-1.68754

-0.86784

-0.95166

9-0.36313

error_inflation

-4.39226

2.446733

27.09586

62.29025

4.782753

14.40802

8.626386

77.57967

-43.4044

94.00721

-21.1859

-27.2678

1.197595

-14.4143

9.664322

-5.14798

9.537973

MCUSUM

0.00

0.64

2.75

2.45

2.55

2.41

5.16

2.87

6.28

4.91

3.31

2.85

1.88

1.81

1.23

1.10

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

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19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

-0.31195

-1.22283

-1.48753

-1.5443

-14.4463

-15.324

0.23

0.27

0.02

0.00

0.85

0.60

0.00

0.09

0.42

0.10

0.18

0.00

1.58

1.71

1.74

0.54

1.14

1.90

1.62

5.33

2.59

1.16

1.38

1.48

2.00

4.259274

-4.43241

31.8673

0.000986

-0.56871

-1.09253

-0.46135

-0.8287

6.319687

-9.88055

-9.60859

-12.5049

1.169894

6.841288

-16.3965

0.399357

-9.00633

-8.98881

-12.6163

-10.5136

-4.95681

-4.44792

-14.2105

-12.5376

-11.2455

-9.03712

-6.17445

-6.30507

-6.50476

-11.8648

-12.9629

-3.81576

-0.66519

-0.1449

0.429817

0.176891

0.750139

8.985451

2.477024

2.271181

-4.32202

4.535311

5.34449

-0.07544

19.48782

-10.7358

-7.8294

4.448486

1.750025

4.265067

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47

48

49

-1.78751

-1.15809

6.211929

-9.49622

-11.8243

-10.4247

-11.0048

10.53844

1.60

1.39

1.98

0.78

* The bolden shows out-of-control points

MEWMA Control Chart

Figure 4.4 also showed the MEWMA control chart based on macroeconomic variables such as Gross Domestic

Product (GDP) and inflation rate were monitored. The chart was constructed such that p = 2, λ = 1, ARL₀= 200.

It can be observed that three samples points (8, 10, and 41) which correspond to the years 1980, 1982, and 2013

respectively, fall outside the control limit of 8.63 (Threshold).

Figure 4.4: MEWMA control chart with λ = 1 using the GDP and inflation rate

Table 4.13: MEWMA Chart for GDP and inflation rate

Sample

error_GDP

-1.05727

-1.01375

-0.97139

-0.51022

-0.47257

-0.59638

-0.53697

-1.20961

-1.15285

error_inflation

-4.39226

MEWMA

0.11

1

2

3

4

5

6

7

8

9

2.446733

27.09586

62.29025

4.782753

14.40802

8.626386

77.57967

-43.4044

0.12

0.56

4.27

3.42

3.60

3.35

10.00

3.81

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11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

-0.94756

-0.61815

-0.88844

0.258918

-1.68754

-0.86784

-0.95166

-0.36313

-0.31195

-1.22283

-1.48753

-1.5443

94.00721

-21.1859

-27.2678

1.197595

-14.4143

9.664322

-5.14798

9.537973

-14.4463

-15.324

12.51

7.52

3.81

3.09

1.86

2.00

1.49

1.59

0.87

0.56

0.70

0.74

1.17

1.19

0.87

0.63

0.55

1.10

1.03

0.89

0.65

0.58

0.49

0.42

0.75

0.97

0.55

1.15

4.259274

-4.43241

31.8673

0.000986

-0.56871

-1.09253

-0.46135

-0.8287

6.319687

-9.88055

-9.60859

-12.5049

1.169894

6.841288

-16.3965

0.399357

-9.00633

-8.98881

-12.6163

-10.5136

-4.95681

-4.44792

-14.2105

-3.81576

-0.66519

-0.1449

0.429817

0.176891

0.750139

8.985451

2.477024

2.271181

-4.32202

4.535311

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39

40

41

42

43

44

45

46

47

48

49

5.34449

-12.5376

-11.2455

-9.03712

-6.17445

-6.30507

-6.50476

-11.8648

-12.9629

-11.8243

-10.4247

-11.0048

10.53844

2.13

2.09

8.82

3.26

1.59

2.06

2.41

3.33

2.89

2.68

3.78

1.49

-0.07544

19.48782

-10.7358

-7.8294

4.448486

1.750025

4.265067

-1.78751

-1.15809

6.211929

-9.49622

*The bolden shows out-of-control points

Performance Comparison of Hoteling T ², MCUSUM and MEWMA Charts

The performance of the charts (Hoteling T ², MCUSUM and MEWMA chart) were compared. It can be

T ²

observed From Figure 4.1, 4.2 and Table 4.8, 4.9 show that, the Hoteling

Woodall (SW) signaled a shift in the mean vector at the time points (4, 8, 10, 40, and 41) which represents the

control chart for Sullivan and

years 1976, 1980, 1982, 2012, and 2013 respectively, whiles the Hoteling T ²control chart for Holm and

Mergen (HM) signaled a shift in the mean vector at the time points (4, 8, 10, and 40) which also represents the

years 1976, 1980, 1982, and 2012 respectively. Both Sullivan and Woodall (SW), Holm and Mergen control

charts have the same performance since the out-of-control signal (alarm) is detected earlier at the 4^thsample at

the control limit of 5.74.

On the other hand, MCUSUM control chart in Figure 4.3 and Table 4.10 detected the signal at the time point 10,

representing the year 1982. These sample point experienced the signal (alarm) earlier at the 10^thsample at the

control limit of 5.5. MEWMA chart also, signaled earlier at the 8^thsample at the control limit of 5.5, as seen in

Figure 4.4 and Table 4.11. The control charts perform better when the signal (alarm) is spotted earlier. Clearly,

the Hotelling T²control chart outperform both MCUSUM and MEWMA control chart. Meanwhile, MEWMA

chart also outperform MCUSUM chart.

Furthermore, there may be a large shift in the Gross Domestic Product (GDP) and inflation rate data since

Hotelling T²chart was faster in determining the mean shift, MCUSUM and MEWMAcharts were able to identify

small and moderate shifts in the mean vector.

DISCUSSIONS

This study applied Hotelling’s T², MCUSUM, and MEWMA control charts to jointly monitor Ghana’s GDP and

inflation rate from 1973 to 2022, evaluating their ability to detect unusual shifts in the macroeconomic

environment. The charts revealed distinct out-of-control signals, which can be interpreted in the context of

Ghana’s historical economic events.

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The Hotelling T² chart indicated out-of-control situations at sample points 4, 8, 10, 40, and 41, corresponding to

the years 1976, 1980, 1982, 2012, and 2013, respectively. The MCUSUM chart (k = 0.5, c = 5.5) flagged only

the 10th sample point (1982) as exceeding the control limit, whereas the MEWMA chart (p = 2, λ = 1, ARL₀ =

200) identified three points; 1980, 1982, and 2013 as out-of-control, exceeding the limit of 8.63.

Interpretation of Out-of-Control Signals

1976 (Inflation, Hotelling T²): Ghana faced high inflation, currency depreciation, and balance-of-payments

pressures during this period (Aryeetey & Fosu, 2005). These macroeconomic challenges likely contributed to

the observed out-of-control signal in inflation, reflecting instability in the joint GDP-inflation dynamics.

1980 (Inflation, Hotelling T² and MEWMA): The 1980 out-of-control signal coincides with severe internal

and external debt pressures, exchange rate depreciation, and declining commodity prices (Antwi et al., 2014).

These factors created heightened inflationary pressures, consistent with the MEWMAand Hotelling T² detection

of abnormal joint behaviour.

1982 (Inflation, Hotelling T², MCUSUM, MEWMA): This period corresponds to ongoing economic

difficulties, including increased government borrowing and fiscal imbalances, which exacerbated inflationary

pressures (Frimpong & Oteng-Abayie, 2010). The convergence of all three charts in signaling this year

underscores the persistence of small but sustained shifts in macroeconomic variables.

2012 (GDP, Hotelling T²): The out-of-control signal in GDP aligns with the pre-election fiscal expansion for

the presidential and legislative elections. Although the economy had benefited from the discovery of offshore oil

reserves in 2007, government spending surged in anticipation of elections, temporarily accelerating GDP growth

beyond expected trends (Agyire-Tettey, 2017; Weiseke, 2019).

2013 (GDP, Hotelling T² and MEWMA): The subsequent fiscal year experienced post-election fiscal pressures,

including increased domestic and external borrowing to finance election-related expenditures and debt servicing

(Mbaye, 2019). This likely explains the observed out-of-control points for GDP, capturing the delayed effects of

expansionary policies on macroeconomic stability.

Comparative Performance of Control Charts

Consistent with Moraes et al. (2015), the Hotelling T² chart performed best in detecting moderate to large shifts

in the mean vector, capturing most major deviations in GDP and inflation. The MCUSUM chart, in contrast, was

more sensitive to small, persistent shifts, detecting the 1982 inflation deviation even when Hotelling T² and

MEWMA showed less responsiveness. The MEWMA chart effectively highlighted subtle drifts over time, such

as the 1980 inflation and 2013 GDP shifts, corroborating prior findings on its utility for early detection of

incremental changes (Custódio et al., 2013). Overall, the combined application of all three charts provides

complementary insights: Hotelling T² for broad shifts, MCUSUM for accumulated small deviations, and

MEWMA for time-weighted detection.

These findings demonstrate that multivariate SPC tools can provide a proactive monitoring framework for

macroeconomic variables, enabling policymakers to detect emerging instabilities associated with major events

such as fiscal expansions, debt accumulation, or election-related spending, well before traditional forecasts signal

potential risk.

Study Limitations and MCUSUM Performance

While the multivariate control charts provided valuable insights into the joint behaviour of GDP and inflation in

Ghana, several limitations should be acknowledged. First, the analysis relied on annual data, which may reduce

the sensitivity of the control charts to short-term fluctuations or seasonal variations. Second, structural breaks,

such as oil discoveries, fiscal expansions, and election-related spending, could violate the assumption of a stable

in-control process, potentially affecting the estimation of control limits. Third, the study uses a single data source

(Bank of Ghana), which may introduce reporting biases or limit cross-validation opportunities. Finally, the

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dataset spans 50 years, and although substantial, the sample size for multivariate SPC parameter estimation is

modest, particularly for detecting small, incremental shifts.

The observed underperformance of the MCUSUM chart in this study warrants discussion. Although MCUSUM

charts are theoretically sensitive to small and persistent shifts (Lowry et al., 1992; Crosier, 1988), the limited

number of detected out-of-control points suggests that the shifts in Ghana’s GDP and inflation during the study

period were predominantly moderate to large, rather than subtle. Additionally, the chosen MCUSUM parameters

(k = 0.5, c = 5.5) may not have been optimal for the economic context of Ghana, given the relatively high

variability in historical macroeconomic indicators. It is possible that alternative parameter settings or a finer-

grained dataset (e.g., quarterly data) would enhance the chart’s sensitivity to small changes. These considerations

highlight the importance of careful parameter selection and contextual adaptation when applying multivariate

SPC techniques to macroeconomic time series.

Despite these limitations, the combination of Hotelling T², MCUSUM, and MEWMA charts offers a

complementary framework, with Hotelling T² detecting moderate-to-large shifts, MEWMA capturing time-

weighted deviations, and MCUSUM providing potential sensitivity to smaller accumulative changes.

Collectively, these tools contribute to a proactive monitoring system for macroeconomic stability in Ghana.

CONCLUSION AND RECOMMENDATION

This study jointly monitored Gross Domestic Product (GDP) and inflation rate in Ghana using Hotelling T²,

MCUSUM, and MEWMA control charts over the period 1973–2022. The Hotelling T² chart indicated out-of-

control signals at sample points 4, 8, 10, 40, and 41 (1976, 1980, 1982, 2012, and 2013, respectively). The

MCUSUM chart flagged only the 10th sample point (1982), while the MEWMA chart detected deviations at

points 8, 10, and 41 (1980, 1982, and 2013).

Comparative analysis shows that Hotelling T² outperformed both MEWMA and MCUSUM charts in detecting

early shifts in the joint mean vector of GDP and inflation. MEWMA detected deviations earlier than MCUSUM,

demonstrating its usefulness for identifying gradual or time-weighted changes. These findings suggest that

multivariate control charts, particularly Hotelling T², can provide a proactive monitoring tool for Ghana’s

macroeconomic management.

Recommendations

The Bank of Ghana (BoG) could integrate the Hotelling T² chart into its macroeconomic monitoring dashboards,

leveraging high-frequency data (e.g., quarterly or monthly) to flag periods of potential macroeconomic

instability. This would allow policymakers to investigate early warning signals before significant economic

disruptions occur.

Several out-of-control points corresponded to election years (2012 and 2013), suggesting that pre- and post-

election fiscal expansion contributed to deviations in GDP. Policymakers should design more targeted, counter-

cyclical fiscal measures during election periods, ensuring that public spending does not disproportionately

destabilize inflation or growth.

The decomposition analysis highlighted that inflation was the primary driver of certain out-of-control signals,

particularly in the 1970s–1980s and early 2010s. While the BoG has implemented measures such as inflation-

targeting frameworks and monetary tightening, the study suggests complementing these with sector-specific

interventions, such as stabilizing energy and food prices, improving supply chain efficiency, and monitoring

imported inflation pressures.

Researchers could explore Bayesian approaches to multivariate control charts or hybrid methods combining SPC

with VAR/ARIMA models to enhance sensitivity to both small and large shifts in macroeconomic indicators.

Additionally, applying the method to higher-frequency data (monthly or quarterly) may provide more actionable

insights for real-time policy interventions.

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