The error correction model (ECM) is used to estimate the money demand function. Our technique is less dependent on Johansen's maximum likelihood estimation of cointegration but more dependent on the ordinary least squares (OLS) estimation of the equations included in the ECM. The dynamic OLS estimation proposed by Phillips and Loretan (1991) is also used to estimate the cointegration. Significance of each coefficient is tested using the t-ratios of the coefficient. Stationarity of the residual series is tested which is not necessary in the maximum likelihood approach. Since it is desirable to include current values of income and yen-dollar exchange rate as regressors in the money demand function, weak exogeneity of these variables is tested by using the standard OLS technique. Then Hendry-type autoregressive distributed lag (ADL) regressions are used to estimate the money demand function using previously estimated cointegration in the regression. It is also aimed to review the modern non-stationary time series techniques for the readers who may work in empirical studies.