A Multivariate GARCH Model with Time-Varying Correlations: What Do Inflation Data Show in Ethiopia?

Abstract Inflation is a critical global issue and also a significant challenge in Ethiopia. Despite its profound impact on the economy, research on inflation volatility in Ethiopia remains limited and insufficient. This paper aims to address these gaps by employing BEKK (Baba, Engle, Kraft, and Kroner) and DCC (Dynamic Conditional Correlation) - GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models and analyze the characteristics of inflation trends, which supports informed economic decision making. We focus on four key inflation indicators: the Consumer Price Index (CPI), the Non-Food Price Index (NFPI), the Food Price Index (FPI), and the Exchange Rate (ER), which were compiled from the National Bank of Ethiopia (NBE) from January 2010 to December 2020. The study confirms inflation volatility, supported by the ARCH effect and Ljung-Box Q ( m ) statistics, along with conditional heteroscedasticity tests. This study demonstrates that, unlike previous approaches that neglected dynamic correlations in inflation volatility, the DCC-GARCH model decisively outperforms the BEKK-GARCH model in both parameter estimation and forecasting accuracy, as evidenced by significantly better Akaike Information Criterion (AIC), Schwarz Bayesian Information Criterion (SBIC), and Hannan-Quinn Information Criterion (HQIC) metrics. Our findings revealed that the DCC (1,1) model effectively captured volatility clustering without being persistent or explosive, as the sum of coefficients $$(\theta = 0.1794, \beta = 0.7023)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.1794</mml:mn> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.7023</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is less than 1, confirming mean reversion. In contrast to previous studies, our approach provided a more robust understanding of inflation dynamics, identifying CPI and FPI as the most volatile indicators. The study reveals significant correlations among inflation indicators-CPI, FPI, NFPI, and ER indicating a cohesive inflationary pattern. The coefficients show that past volatility and shocks persistently influence current volatility, underscoring their interdependence. The forecast from the best model reveals substantial instability is observed in CPI and FPI returns. It suggests a sharp increase in FPI and a rise in ER. The better method captured inflation volatility more effectively than other competent models. The DCC-GARCH model offered deeper insights into volatility dynamics, revealing the shortcomings of earlier time series models in addressing inflation volatility.