This paper proposes the analysis of panel data whose dynamic structure is heteroge- neous across individuals. To investigate heterogeneous dynamics, we propose estimating the cross-sectional distributions and/or some distributional features of the individual mean, autocovariances, and autocorrelations. Our proposed method is easy to implement without assuming any specific model for the dynamics. We first compute the sample mean and autocovariances for each individual and then estimate the parameter of interest based on the empirical distributions of the estimated mean and autocovariances. The asymptotic proper- ties of the proposed estimators are investigated using double asymptotics under which both the cross-sectional sample size (N) and the length of the time series (T) tend to infinity. We prove the functional central limit theorem for the empirical process of the proposed distribution estimator. When the parameter of interest can be written as the expectation of a smooth function of the individual mean and/or autocovariances, the bias can be reduced by the split-panel jackknife bias-correction. We also develop an inference procedure based on the cross-sectional bootstrap and prove its theoretical justification. We demonstrate our proposed procedures by applying earning dynamics and productivity dynamics and find that both dynamics exhibit lots of heterogeneity. The results of Monte Carlo simulations show that our asymptotic results are informative regarding the finite-sample properties of the estimators and the proposed inference procedures. Joint with Takahide Yanagi (Hitotsubashi University).