In this paper, modeling of contours by a time-varying autoregressive (TVAR) model is considered. In general, a contour function is not a stationary process, and stationary models are often unsatisfactory in representing local features. Recently, there have been advances in time-series modeling of nonstationary processes. In a typical TVAR modeling approach, autoregressive coefficients are expanded as a linear combination of deterministic functions. In this paper, a low-order discrete Fourier transform (DFT) is used to expand autoregressive coefficients. It is based on the fact that a contour is represented by a complex function, and the model coefficients need to be expanded by a set of complex functions. The parameter estimation and order selection in TVAR models are also considered. A least squares estimator of the TVAR model parameters is presented, and the maximum likelihood approach for determining the model order is also presented. The efficacy of the TVAR modeling approach in modeling a closed contour is demonstrated by estimating the time-varying spectrum of a synthetic contour by different approaches, and is tested by detecting curvature extrema points of synthesized contours. For the classification of contours of planar shapes, the estimated TVAR model parameters are used as features. A neural network is used to classify TVAR features extracted from complex contour functions. In the classification experiment with contours of various planar shapes, about 97% of samples are correctly classified.