Assessment of the Relative Efficiency of Bootstrap Resampling Methods for Forecast Uncertainty Quantification in Nigerian Macroeconomic Time Series: Evidence from Inflation and Exchange Rate Data (1960-2025)

Abstract

Quantifying forecast uncertainty is a prerequisite for responsible use of time series models in Nigerian macroeconomic analysis, yet researchers rarely benchmark resampling schemes used to estimate that uncertainty against alternatives on long-run Nigerian data. This study compares three bootstrap procedures for response time series the stationary bootstrap, the moving block bootstrap, and the sieve bootstrap across five ARIMA data-generating processes of increasing complexity: ARIMA(1,0,0), ARIMA(1,1,0), ARIMA(1,1,1), ARIMA(2,1,1), and ARIMA(1,1,3). The simulation design follows a Monte Carlo framework comparable to earlier benchmarking studies. The same three methods are then applied to two real Nigerian macroeconomic series: annual headline inflation (World Bank/FRED, 1960-2025, 66 observations) and the log of the annual NGN/USD exchange rate (Penn World Table/FRED, 1960-2023, 64 observations), both considerably longer than the short annual series used in prior comparative work of this kind. Across all five simulated data-generating processes and both empirical series, the stationary bootstrap yielded the lowest mean squared error (MSE) of one-step-ahead forecasts; the moving block bootstrap was a close second throughout; the sieve bootstrap was markedly less accurate, particularly for integrated I(1) processes. These results diverge from prior work suggesting block-based methods are dominated by ARMA processes with genuine moving-average components, and from work favouring the sieve bootstrap for autoregressive-dominated series. Possible explanations are discussed, including the sensitivity of the sieve reconstruction step to compounding during re-integration of a differenced series. The scope limitations of a reduced-scale Monte Carlo design are noted, and further replication is identified as necessary before firm practical guidance can be issued to Nigerian forecasting practitioners.