This paper introduces a diluted prediction method for bitcoin and gold based on cycle prediction. This method does not need to quantify the external parameters like robot learning and neural network autoregressive model, but mainly uses ARIMA to feedback the parameter values into risk coefficients under the condition of obtaining the optimal solution circularly, and the price prediction of a single period in the future is carried out with a fixed number of samples, thus realizing the high-precision prediction of bitcoin and gold prices. In the application simulation, the real data of bitcoin and gold from 2016 to 2021 are selected. After 1000 times of Monte Carlo simulations, 919 times of the yield is more than 3 times, 157 times of the yield is more than 8 times, and the minimum yield is about 2 times. At the same time, this paper puts forward an investment strategy for this prediction method, which realizes a very safe profit with a final return rate of 6.2 times under the condition of making full use of the prediction risk coefficient. The prediction method and investment scheme bring a brand-new high-precision prediction method and targeted investment strategy with high safety coefficient to all the investors, which has great economic value.INDEX TERMS ARIMA, Periodic method, Monte carlo, Circulation, White noise, ADF.