Vocoders, encoding speech signals into acoustic features and allowing for speech signal reconstruction from them, have been studied for decades. Recently, the rise of deep learning has particularly driven the development of neural vocoders to generate high-quality speech signals. On the other hand, the existing end-to-end neural vocoders suffer from a black-box nature that blinds the speech production mechanism and the intrinsic structure of speech, resulting in the ambiguity of separately modeling source excitation and resonance characteristics and the loss of flexibly synthesizing or modifying speech with high quality. Moreover, their sequence-wise waveform generation usually requires complicated networks, leading to substantial time consumption. In this work, inspired by the quasi-harmonic model (QHM) that represents speech as sparse components, we combine the neural network and QHM synthesis process to propose a novel framework for the neural vocoder. Accordingly, speech signals can be encoded into autoregressive moving average (ARMA) functions to model the resonance characteristics, yielding accurate estimates of the amplitudes and phases of quasi-harmonics at any frequency. Subsequently, the speech can be resynthesized and arbitrarily modified in terms of pitch shifting and time stretching with high quality, whereas the time consumption and network size decrease. The experiments indicate that the proposed method leverages the strengths of QHM, the ARMA model, and neural networks, leading to the outperformance of our methods over other methods in terms of generation speed, synthesis quality, and modification flexibility.