This study investigates possible alternative modeling of Naira-Dollar exchange rate volatility in Nigeria. The paper makes use of the monthly data on Naira-Dollar exchange rates from 1991 to 2016 which was sourced from the Central Bank of Nigeria statistical bulletin. In order to realize the aim of this study, a newly proposed Quadratic Moving Average Conditional Heteroscedasticity (QMACH) model was employed to investigate the volatility of Naira-Dollar exchange rate. The ADF unit root test reveals that the Naira-Dollar exchange rate return is stationary and this permits the usage of Quadratic Moving Average Conditional Heteroscedasticity (QMACH) methodology. The empirical analysis indicates that Naira-Dollar exchange rate volatility indeed follows the QMACH movement just like it follows both ARCH and GARCH movement .In comparison with ARCH and GARCH modeling, QMACH outperforms both as shown through the log likelihood statistics and the information criteria
