Because of the non-linearity and strong stochastic volatility of financial time series, the interval forecasting method which combines Fourier transform with ARMA model is proposed. Through the distribution of spectral density, signal-noise ratio (SNR) and variance, the multi-cycle trend of time series is achieved. The research indicates that the residual series of this kind trend is suitable for ARMA model. The forecasting method is applied to the daily close data of NASDAQ Composite Index during from 28th November, 2012 to 21th July, 2015, and the result shows that the best trend of the series is added by two periodic series. The ideal result of interval forecast is achieved by applying ARMA model to the residual series.