The paper presents the results of study about the influence of the initial weights choice on the long-term forecast accuracy in the problem of multi-step forecast with a neural network based on long short-term memory (LSTM-net) for time series, composed of time-ordered samples of a harmonic, an amplitude-modulated signal and a frequency-modulated signal. The recursive forecast has been estimated on model time series data providing the means to measure the actual accuracy of the forecast while controlling influence of different characteristics. The analysis of the results show that a necessary condition for obtaining a high-quality long-term forecast is the correct choice of the LSTM-net parameters, especially the initialization of weights for neural network layers. At the same time the use of LSTM-net parameters, which provide high accuracy of short-term forecast, does not guarantee the accuracy of the long-term forecast, and vice-versa. In this regard it is concluded that the usage of other forecast methods and /or algorithms for correcting predicted values for mentioned types of time series is preferable.