Linear tests and nonlinear tests for ARCH are applied to monthly real effective exchange rate of HK between 1964.1-2009.6, GJR-GARCH model parameter is specified and estimated, tests of standardized residuals for remaining ARCH, tests for higher-order GARCH and tests of parameter constancy are adopted to determine the results of model specification. According to the described information response curve, under the conditions of good news and bad news, HK exchange rate volatility shows significantly asymmetric characteristics.