Parametric tests of serial correlation require specification of a maximum lag length L, and in some manner combine serial correlation coefficients of equal or lesser order than this maximum horizon. If L is chosen to be too high, test power against a range of alternate hypotheses may be lost because of the inclusion of insignificant correlations while if it is chosen too low, the longer range features of some alternates may be missed. This paper presents a spectral test that is based in the frequency domain that does not require specification of a maximum lag length. Implicitly it considers all possible lagged correlations by examining the distribution of all frequencies present in the time series counterpart. To compare this new test to the Ljung-Box test with horizon length L, (LB(L)), the finite sample, size and power characteristics are simulated for a range of degrees of significance for two alternate hypotheses. The performance of the spectral test is comparable to or better than the time series test LB(L) when L is chosen with the advance knowledge that it exceeds the maximum lag structure in the alternate and is vastly superior to the LB(L) test when L does not encompass the maximum lag length.