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American Journal of  Applied 
Statistics and Economics (AJASE)

Forecasting Key Macroeconomic Indicators in Ghana Using a Time-Varying VECM 
with Conformal Prediction Intervals

Chinton Emmanuel1*, Donkoh Kojo Isaac2, Acquah Oware Nana Emmanuel3

Volume 4 Issue 1, Year 2025
ISSN: 2992-927X (Online)

DOI: https://doi.org/10.54536/ajase.v4i1.5752
https://journals.e-palli.com/home/index.php/ajase

Article Information ABSTRACT

Received: July 20, 2025

Accepted: August 22, 2025

Published: September 29, 2025

This paper presents a six-month-ahead forecast of  three key Ghanaian macroeconomic 
indicators: the USD/GHS exchange rate, the Consumer Price Index (CPI) and the Monetary 
Policy Rate (MPR). A Time-Varying Vector Error Correction Model (TV-VECM) is utilized 
to capture dynamic interrelationships among the variables. Conformal prediction intervals 
are incorporated to quantify uncertainty under minimal distributional assumptions. The 
results suggest moderate currency depreciation, persistent inflationary trends and stability in 
nominal interest rates over the forecast horizon.

Keywords

Conformal Prediction, Exchange 
Rate Forecasting, Ghana, Inflation, 
Monetary Policy, Time-Varying 
VECM

1 Department of  Statistics, University of  Cape Coast, Ghana
2 Financial Engineering, WorldQuant University,, USA
3 Department of  Economics and Finance, Youngstown State University, USA
* Corresponding author’s e-mail: emmanuelchinton7@gmail.com

INTRODUCTION
Forecasting macroeconomic indicators is essential for 
effective policy design and economic planning. This study 
employs a Time-Varying Vector Error Correction Model 
(TV-VECM) to analyze short-term movements in three 
critical Ghanaian macroeconomic variables: the USD/
GHS exchange rate, the Consumer Price Index (CPI) 
and the Monetary Policy Rate (MPR). The TV-VECM 
framework captures both long-run equilibrium and 
evolving short-term dynamics. To account for forecast 
uncertainty, conformal prediction intervals are utilized 
which offer valid coverage without assuming specific 
error distributions.

LITERATURE REVIEW
Time-varying VECM (TV-VECM) for Ghana
Macroeconomic relationships in Ghana among inflation, 
the cedi/US$ rate, policy rates, money, output, and 
commodity prices are well known to be non-stationary 
with evolving long-run equilibria and shifting short-run 
dynamics (policy regime shifts, commodity price cycles, 
IMF programs, and disinflation episodes). Standard 
(time-invariant) VAR/VECM studies on Ghana capture 
cointegration and error-correction but assume fixed 
parameters, which can miss structural drifts that matter 
for forecasting and policy analysis. Using a time-varying 
cointegration framework lets the data accommodate 
gradual changes in adjustment speeds or even the 
cointegration vector itself  exactly the type of  flexibility 
needed in an economy that has seen alternating easing 
cycles and large disinflation in 2024–2025. 

Core Advances on Time-Varying Cointegration and 
VECM
Early contributions showed how cointegration can 
evolve smoothly and proposed tests for time-invariance 
of  the long-run vector (and rank). Bierens & Martins 
(2009/2010) formalize a time-varying cointegration setup 
where the cointegrating relationship changes smoothly; 
they derive a likelihood-ratio test against time-variation. 
This line of  work motivates allowing βt and even αt to 
drift in a VECM.
A cautionary strand highlights pitfalls with state-space/
Kalman estimation of  time-varying cointegration: if  not 
handled carefully, the Kalman filter can absorb unit-root 
behavior into the time-varying state and spuriously “find” 
time-varying cointegration between unrelated I(1) series. 
Robust procedures and bootstrap testing frameworks 
are proposed to distinguish no cointegration vs. fixed vs. 
time-varying cointegration. This is highly relevant if  one 
estimates TV-VECMs for Ghana with state-space methods.
Recent econometric theory pushes further with smoothly 
time-varying VECMs: Gao, Peng & Yan (2023, 2025) 
develop a time-varying Granger Representation Theorem, 
estimation/inference for both short-run and long-run 
coefficients, a singular-value-ratio rank test, and stability 
tests providing a principled toolkit to build and validate 
TV-VECMs without resorting solely to ad-hoc filters.
Related strands include threshold/smooth-transition 
VECMs (to handle nonlinear adjustment) and applications 
showing that allowing for time-variation materially changes 
conclusions about long-run relations. These reinforce the 
empirical gains from flexible cointegration structures.



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Estimation Strategies for TV-VECMs
Three broad routes appear in the literature:

State-space / Kalman TVP-VECMs (or TVP-VARs 
with Cointegration)
Flexible but require care to avoid spurious cointegration; 
bootstrap or robust testing is recommended. 

Nonparametric/Smoothly-Varying Coefficients
Treat α(τ), Π(τ) as smooth functions of  rescaled time τ 
with associated theory for rank, stability, and inference; 
this avoids some Kalman pitfalls and aligns with gradual 
Ghanaian regime shifts. 

Bayesian TVP-VAR/Cointegration Frameworks 
(And Sparsity Priors)
Common in macro; while much of  this work is in TVP-
VARs, ideas translate to VECMs (shrinkage on time-
variation, stochastic volatility), though dedicated Bayesian 
TV-VECM software remains less standard.

Forecast Uncertainty
Classical VECM forecast intervals rely on parametric 
assumptions (Gaussian errors, correct specification). In 
volatile, shifting environments like Ghana’s, distribution-
free uncertainty quantification is attractive. Conformal 
prediction (CP) provides finite-sample, model-agnostic 
prediction sets with marginal coverage guarantees. 
For time series, Adaptive Conformal Inference (ACI) 
and related online methods adjust interval widths to 
distribution shift and non-exchangeability, which are 
precisely the challenges in macro data with evolving 
regimes. 
Key extensions handle multi-step and multivariate time-
series forecasting crucial when producing joint paths 
for inflation, FX, and policy rates or when reporting 
horizon-h TV-VECM forecasts. Recent work develops 
online/multi-step CP with provable properties, and 
multivariate CP to form valid prediction regions across 
series. 
An alternative, EnbPI (Ensemble Batch Prediction 
Intervals), uses ensemble residuals to deliver approximately 
valid intervals under dependence and shift; while often 
paired with ML forecasters, it is model-agnostic and can 
calibrate VECM residuals too. 

TV-VECM and Conformal Pipeline for Ghana
The literature jointly suggests:

Specify a Ghana macro system [ Pt,  et,  it,  yt, mt]
Inflation, exchange rate, policy rate, output proxy, money; 
optionally commodity/terms-of-trade).

Estimate Cointegration And Time-Variation
Using a smoothly time-varying VECM (Gao–Peng–Yan 
framework) or carefully designed state-space TV-VECM 
with robust cointegration testing/bootstrapping to guard 
against spurious time-variation (Eroğlu et al., 2022).

Forecast 
Multi-step paths from the TV-VEC

Wrap Forecasts with CP
use online ACI (or variants) for one- and multi-step 
horizons; for multiple variables/horizons, apply recent 
multivariate/multistep conformal methods to obtain 
valid joint or per-horizon intervals that adapt to regime 
changes particularly important around policy turning 
points documented for Ghana in 2025. 

Empirical Expectations And Gaps
Relative to fixed-parameter VECMs used in many 

country studies, a TV-VECM should improve calibration 
during regime shifts and commodity shocks, and better 
capture changing error-correction speeds.

Conformal layers are complementary to econometric 
inference: they provide finite-sample predictive coverage 
without re-specifying the TV-VECM and remain robust 
to mild misspecification.

Gap: Few (if  any) studies combine TV-VECM with 
conformal intervals in macroeconomic practice especially 
for Ghana. The emerging multi-step/multivariate CP 
literature now makes this feasible and methodologically 
justified.

MATERIALS AND METHODS
Data Description
Monthly data from January 2014 to June 2025 were 
compiled. CPI data were obtained from the Ghana 
Statistical Service, while exchange rate and MPR data 
were sourced from the Bank of  Ghana. All series were 
tested for unit roots using the Augmented Dickey-Fuller 
(ADF) test and found to be integrated of  order one, 
I(1). Cointegration was verified using Johansen’s method, 
confirming at least one cointegrating relationship among 
the variables.
The ADF test is based on the following regression:

                                                                                     (1)

The Johansen cointegration test is derived from the 
Vector Autoregression (VAR) representation:
                                                                   
                                                                                    (2)
where the rank of  the matrix Π determines the number 
of  cointegrating relationships.

Model Specification
A Time-Varying VECM was implemented using a 
rolling window approach. This technique allows model 
parameters to evolve, accommodating structural breaks 
and time-varying relationships. The model captures 
both equilibrium correction mechanisms and short-term 
adjustments.

Forecasting and Conformal Prediction
A six-month forecast horizon was selected. To quantify 



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forecast uncertainty, conformal prediction intervals were 
constructed using residual-based nonconformity scores. 
These intervals maintain valid coverage under mild 
assumptions and are robust to model misspecification.
Gradient Boosting Regression was employed to generate 
point forecasts. This method builds an ensemble of  
decision trees in a forward stage-wise fashion, minimizing 
a loss function by iteratively fitting residuals:

(3)

(4)

(5)

RESULTS AND DISCUSSION

Table 1: Forecast and 90% Conformal Prediction Intervals
Date USD/GHS [PI] CPI [PI] MPR [PI]
2025-07-31 10.4600 [10.12, 10.90] 258.87 [254.09, 261.07] 28.00 [28.00, 28.05]
2025-08-31 10.5900 [10.19, 10.93] 261.36 [260.11, 262.67] 28.00 [28.00, 28.01]
2025-09-30 10.7100 [10.42, 11.07] 264.56 [262.61, 265.19] 28.00 [28.00, 28.01]
2025-10-31 10.8400 [10.55, 11.21] 268.25 [265.82, 268.43] 28.00 [28.00, 28.01]
2025-11-30 10.9700 [10.67, 11.35] 272.09 [269.53, 272.18] 28.00 [28.00, 28.01]
2025-12-31 11.1000 [10.80, 11.48] 275.99 [273.39, 276.08] 28.00 [28.00, 28.01]

Source: Authors Computation and Projections

Figure 1: Residual plot for ln CPI, MPR, and ln USDGHS (July–December 2025)

Figure 2: Autocorrelation Function (ACF) plot for residuals



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Am. J. Appl. Stat. Econ. 4(1) 108-111, 2025

Residual Plot Observations
• ln_CPI: Residuals are centered around zero with low 

variance but show a slight increase in variance from 2022 
onward.

• MPR: High residual variance with frequent spikes, 
suggesting potential outliers or structural breaks.

• ln_USDGHS: Residuals are mostly stable over time, 
with a few sharp spikes between 2022 and 2023 likely 
reflecting volatility during that period.

Autocorrelation Function (ACF) Observations
• ln_CPI Residuals: All spikes are within the 95% 

confidence bands across lags 0 to 10, confirming the 
absence of  significant autocorrelation.

• MPR Residuals: A visible spike at lag 2 exceeds the 
confidence bounds, indicating residual autocorrelation.

• ln_USDGHS Residuals: All spikes remain within the 
confidence bounds, confirming white noise residuals.

Discussion
USD/GHS Exchange Rate
The forecasted exchange rate path indicates a gradual 
depreciation of  the Ghanaian Cedi, rising from 10.46 to 
11.10 over the six-month period. The widening prediction 
intervals over time reflect increasing uncertainty as the 
forecast horizon extends.

Consumer Price Index
CPI is projected to increase gradually from 258.87 to 
275.99, suggesting continued inflationary pressure. The 
forecast intervals remain tight, indicating strong model 
confidence in the inflation trajectory over the horizon.

Monetary Policy Rate
The MPR remains effectively stable at around 28.00% 
across the entire forecast window. The extremely narrow 
interval bounds suggest little model uncertainty and high 
temporal persistence in this rate.

Model Pitfalls and Deployment
From the estimated parameters value and diagnostic plots, 
we observed that Monetary Policy Rate residuals show 
strong autocorrelation and large spikes especially after 
2022, confirming that the model does not capture MPR 
dynamics well. This suggests the presence of  possible 
outliers, structural breaks after 2022, and insufficient lags. 
Therefore, the model can be deployed to forecast only 

the Consumer Price Index (CPI) and USD/GHS. The 
long-run links look usable, but MPR short-term forecasts 
may not be reliable unless the MPR pitfalls are fixed and 
improved.

CONCLUSION
This study utilizes a Time-Varying VECM with conformal 
prediction to forecast Ghana’s key macroeconomic 
indicators over a six-month horizon. Results suggest 
moderate exchange rate depreciation, persistent inflation, 
and stability in nominal interest rates. These forecasts 
are grounded in historical data patterns and subject to 
limitations arising from policy shocks or structural 
changes outside the model’s framework.

REFERENCES
Angelopoulos, A. N., Candès, E., & Tibshirani, R. J. (2023). 

Conformal PID Control for Time Series Prediction. 
(Online CP that adapts to trend/seasonality). 

Bierens, H. J., & Martins, L. F. (2010). Time-Varying 
Cointegration. Cambridge/ET. (Smoothly time-
varying cointegration, LR test). 

Eroğlu, B. A., Miller, J. I., & Yiğit, T. (2022). Time-varying 
cointegration and the Kalman filter. Econometric reviews, 
41(1), 1-21.

Gao, J., Peng, B., & Yan, Y. (2023/2025). Time-Varying 
Vector Error-Correction Models: Estimation and 
Inference. (TV-VECM theory and methods). 

Gibbs, I. & Candès, E. (2021/2024). Adaptive Conformal 
Inference under Distribution Shift. (Online CP with 
distribution shift). Journal of  Machine Learning Research

Hallberg-Szabadváry, J. (2024). Adaptive CI for Multi-Step 
TS (Online). (H-step CP with guarantees). 

Hansen & Seo; Smooth/Threshold VECM (overview). 
KDI Journal (2021). Time-varying Cointegration Models and 

Exchange Rate (PPP and monetary models pass when 
allowing time-variation). KDI Journal of  Economic Policy

Kopetzki, S. (2025). Conformal multistep-ahead multivariate 
TS forecasting. (Joint multivariate intervals). 

Reuters (2025). Ghana policy rate moves (hike; record cut) in 
2025. (Motivation for time-variation)

Stankevičiūtė, G. (2021). Conformal Time-Series Forecasting. 
(Multi-horizon CP for TS). 

Xu, C., & Xie, Y. (2021). Conformal Prediction Interval for 
Dynamic Time-Series (EnbPI). (Ensemble CP under 
dependence). 


