A long-term prediction coding and decoding method and apparatus are described in which an error signal sample is obtained by subtracting from a current sample of an input sample time-series signal a multiplication result obtained by multiplying a past sample which is a predetermined time lag older than the current sample of the input sample time-series signal, by a multiplier. There are four possible methods for outputting parameters of a quantized multiplier p' and time lag τ as follows: 1) To output p' and τ once in the frame; 2) to output the quantized multiplier p' in each sub-frame; 3) to output the time lag τ in each sub-frame; 4) to output p' and τ in each sub-frame. In any of the above cases, the parameters are outputted in coded form.