The hyper H_∞ filter derived in our previous work provides excellent convergence, tracking, and robust performances for linear time-varying system identification. Additionally, a fast algorithm of the hyper H_∞ filter, called the fast H_∞ filter, is successfully developed so that identification of linear system with impulse response of length N is performed at a computational complexity of O(N). The gain matrix of the fast filter is recursively calculated through estimating the forward and backward linear prediction coefficients of an input signal. This suggests that the fast H_∞ filter may be applicable to linear prediction of the signal. On the other hand, an alternative fast version of the hyper H_∞ filter, called the J-fast H_∞ filter, is derived using a J-unitary array form, which is amenable to parallel processing. However, the J-fast H_∞ filter explicitly includes no linear prediction of input signals in the algorithm. This work reveals that the forward and backward linear prediction coefficients and error powers of the input signal are indeed included in the recursive variables of the J-fast H_∞ filter. These findings are verified by computer simulations.