An ARCH volatility analysis of real GDP, real gross capital formation, and foreign direct investment in Bangladesh

This paper aims to investigate the volatility of the growth rates of Bangladesh's real GDP, real gross capital formation, and net inflows of foreign direct investment. The study used data on these indicators from the World Bank for the period between 1972 and 2020. Autoregressive integrated moving average (ARIMA) and the autoregressive conditional heteroscedastic (ARCH) methods were applied to model the conditional mean and conditional variance components for each growth rate. The validity of the selected volatility models was evaluated using a variety of diagnostic techniques, such as the time series graph of estimated residuals, cumulative periodogram, and the portmanteau test for white noise. The overall performance of the selected models is evaluated using the mean squared error (MSE) and the root mean squared error (RMSE). For all three indicators, the conditional means depend on the growth rates of the previous year or two years, whereas conditional variances depend on the previous year’s rates. The outcomes of the study also indicate the existence of time-varying volatility in Bangladesh's economy. This study may be helpful in understanding the potential risks related to the volatile nature of macroeconomic growth rates.