This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series. Using an experimental design of the low-and high-fidelity code levels, an original Gaussian process regression method is proposed. The code output is expanded on a basis built from the experimental design. The first coefficients of the expansion of the code output are processed by a co-kriging approach. The last coefficients are collectively processed by a kriging approach with covariance tensorization. The resulting surrogate model taking into account the uncertainty in the basis construction is shown to have better performance in terms of prediction errors and uncertainty quantification than standard dimension reduction techniques.