In this article, we consider a real second-order discrete-time stationary process and use the corresponding finite Fourier transforms to construct an embedded Hilbertian stationary process. We provide the moving average representation for the embedded process on a certain Hilbert function space and use it for estimation of the moving average coefficients. The construction of the embedded process has two advantages. Firstly, more observations are employed in modeling and parameters estimation of finite-order moving average or autoregressive models. Secondly, it naturally and easily transforms time series data into functional data without using auxiliary functions.
