Computation of Periodogram Using A Jackknife Procedure And Its Applications ABSTRACT: Some points concerning computation of periodogram and its applications are presented. Using an idea similar to jackknifing a numerical procedure is presented for identification of hidden periodicities and is illustrated using both real and simulated data. Applications of the procedure to the Fisher's test for detection of hidden periodicities is discussed in detail. To demonstrate the advantages of the new procedure some equivalent expressions are obtained for periodogram and are compared with each other from computational viewpoints. Part of the comparison is based on the finding that the periodogram is a function of a circulant matrix. An application of this procedure to the detection of periodicities for Wolfer Sunspot numbers is also presented.