Abstract
Abstract Estimation error has been a major problem when the simple linear regression model is used to estimate optimal hedge ratios. Herbst (1989) pointed out that Ederingtion’s (1979) method of using the OLS regression to estimate optimal hedge ratios between spot and futures rates of foreign currencies would yield biased estimators because the error terms are significantly serially correlated which violates stringent assumptions of the OLS regression. Meanwhile, time series data of spot and futures may follow the I (1) process and is not cointegrated. Thus the OLS will yield spurious estimators. Due to this problem, more recent studies estimate the optimal hedge ratios based on the change of spots and the change of futures contracts. These studies transform the nonstationary process into the stationary process in order to avoid solving the possible spurious regression problem. Thus, they only study hedge ratio problem based on either the cointegration or stationary situation, which in fact is not necessary. Even if we get stationary equations by taking first difference of dependent and independent variables, heteroscedasticity usually appears, making another estimation error. This paper provides a guideline on how to choose the estimation methods to solve the estimation error problem in different situations. We perform Monte Carlo simulations of cointegrated and spurious regressions with and without measurement errors and heteroscedasticity. Serial correlation is simulated in all the cases. Then eight estimation methods are used to estimate these regressions. Finally, we find the best estimation method in each case. In empirical study, we use CVAR (Gatarek and Johansen, 2014) model combined with our eight estimation methods to compute post-sample performances and we show that the present method produces better results than those of the VAR and EC models, which are prevalent in hedge ratio study.