Abstract: Although the instability of systemetic risk has been commonly recognized, the beta coefficient of the market model was often estimated under the hypothesis of stability （or local stability）, or was estimated by allowing beta to follow a fixed parametric model. By supposing the price or return of an asset is a random process, we give the nonparametric estimation of the mean and covariance function. And use these result, we get the nonparametric estimation of beta coefficient.