Andreas M Brandmaier
I assume by tau you refer to the time lag between two observations of the process, and thus r(tau) is the auto covariance function of a stochastic process. In that case, you need to make sure that the resulting covariance matrix is positive semi-definite, e.g., by checking whether all eigenvalues are positive.
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Qihong Duan
Andreas Brandmaier is right. I prefer to compute the Fourier transform of a function. A non negative result implies that the function is a covariance function. Here is a Proposition from E Wong, Stochastic Processes in Information and Dynamical Systems, McGRAW-HILL, 1971.
(Proposition 5.1 on p94) A function R(τ), -∞
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