Econometrics

This paper considers the problem of constructing confidence intervals (CIs) for nonlinear functions of parameters, particularly ratios of parameters a common issue in econometrics and statistics. Classical CIs (such as the Delta method and the Fieller method) often fail in small samples due to biased parameter estimators and skewed distributions. We extended the Delta method using the Edgeworth expansion to correct for skewness due to estimated parameters having non-normal and asymmetric distributions. The resulting bias-corrected confidence intervals are easy to compute and have a good coverage probability that converges to the nominal level at a rate of $O(n^{-1/2})$ where n is the sample size. We also propose bias-corrected estimators based on second-order Taylor expansions, aligning with the “almost unbiased ratio estimator” . We then correct the CIs according to the Delta method and the Edgeworth expansion. Thus, our new methods for constructing confidence intervals account for both the bias and the skewness of the distribution of the nonlinear functions of parameters. We conduct a simulation study to compare the confidence intervals of our new methods with the two classical methods. The methods evaluated include Fieller’s interval, Delta with and without the bias correction interval, and Edgeworth expansion with and without the bias correction interval. The results show that our new methods with bias correction generally have good performance in terms of controlling the coverage probabilities and average length intervals. They should be recommended for constructing confidence intervals for nonlinear functions of estimated parameters.

This study explores the new insights into the integration and dynamic asymmetric volatility risk spillovers between Bitcoin, currency pairs (USD/ZAR, GBP/ZAR and EUR/ZAR), and traditional financial assets (ALSI, Bond, and Gold) in South Africa using daily data spanning the period from 2010 to 2024 and employing Time-Varying Parameter Vector Autoregression (TVP-VAR) and wavelet coherence. The findings revealed strengthened integration between traditional financial assets and currency pairs, as well as weak integration with BTC/ZAR. Furthermore, BTC/ZAR and traditional financial assets were receivers of shocks, while the currency pairs were transmitters of spillovers. Gold emerged as an attractive investment during periods of inflation or currency devaluation. However, the assets have a total connectedness index of 28.37%, offering a reduced systemic risk. Distinct patterns were observed in the short, medium, and long term in time scales and frequency. There is a diversification benefit and potential hedging strategies due to gold’s negative influence on BTC/ZAR. Bitcoin’s high volatility and lack of regulatory oversight continue to be deterrents for institutional investors. This study lays a solid foundation for understanding the financial dynamics in South Africa, offering valuable insights for investors and policymakers interested in the intricate linkages between BTC/ZAR, currency pairs, and traditional financial assets, allowing for more targeted policy measures.

This study aimed to forecast the gross domestic product (GDP) of the South Caucasian nations (Armenia, Azerbaijan, and Georgia) by scrutinizing the accuracy of various econometric methodologies. This topic is noteworthy considering the significant economic development exhibited by these countries in the context of recovery post COVID-19. The seasonal autoregressive integrated moving average (SARIMA), exponential smoothing state space (ETS) model, neural network autoregressive (NNAR) model, and trigonometric exponential smoothing state space model with Box–Cox transformation, ARMA errors, and trend and seasonal components (TBATS), together with their feasible hybrid combinations, were employed. The empirical investigation utilized quarterly GDP data at market prices from 1Q-2010 to 2Q-2024. According to the results, the hybrid models significantly outperformed the corresponding single models, handling the linear and nonlinear components of the GDP time series more effectively. Rolling-window cross-validation showed that hybrid ETS-NNAR-TBATS for Armenia, hybrid ETS-NNAR-SARIMA for Azerbaijan, and hybrid ETS-SARIMA for Georgia were the best-performing models. The forecasts also suggest that Georgia is likely to record the strongest GDP growth over the projection horizon, followed by Armenia and Azerbaijan. These findings confirm that hybrid models constitute a reliable technique for forecasting GDP in the South Caucasian countries. This region is not only economically dynamic but also strategically important, with direct implications for policy and regional planning.