## 2 Time Series Prediction Methods of Bank Cash Flow
### The First Moving Average Predictive Method  
The moving average method is a predictive technique developed on the basis of the arithmetic average. The arithmetic average method can only reflect the average of a set of data and cannot reflect the change trend of the data. However, the basic idea of the moving average method is item by item based on time series data by taking a certain number of cycles of data to be averaged every time, successive advancing in chronological order. In each propulsion cycle, the forward cycle data is rejected, a new cycle data is added and the average value is calculated [16]. Set \(X_{t}\) is the actual value of the cycle \  
So the predictive value of the next period (\(t+1\)) is:  
\[\hat{X}_{{}_{t+1}}=M_{t}^{(1)} \tag{2}\]  
where N is the number of selected data for calculating the first moving average value and \(\hat{x}_{{}_{t+1}}\) is the predictive value of the next period (\(t+1\)).  
Based on the collected data in a commercial bank from January to April in 2011 and 2012, the first moving average method is adopted to realize the time series prediction of bank cash flow. The cycle number of the moving average in 2011 is 2-15 and the continuous sample points are 100. The optimal moving average value for the selected data is N = 6 and the simulation results are shown in Figure 2. The cycle number of the moving average in 2012 is 2-15 and the continuous sample points are 100. The optimal moving average value for the selected data is N = 2 and the simulation results are shown in Figure 3.  
It can be seen from Figures 2 and 3 that the random fluctuations of bank actual cash flow values is larger, but the random fluctuations are reduced significantly after the first moving average calculations. The more used months by calculating the average, that is to say the greater N, the stronger of the smoothing degree and the more small fluctuation. However, in this case, the reaction velocity on this change trend for the actual data is slower. Conversely, if N is set lower, the reaction velocity on this change trend for the actual data is more sensitive, but the smoothing degree is less and it is easy to reflect the random interference as the trend. Therefore, the choice of N is very important, which should be selected according to the specific situation.  
When N is equal to the cycle of change, the influence of periodic change can be eliminated. In practice, the mean square error S of prediction for past data is generally adopted to be the criterion for choosing N. However, because of the accumulation of errors, the predictive error is bigger for the prediction of more distant periods. Therefore, the first moving average method is usually adapted to the  
Figure 1: Flowchart of the time series prediction methods of bank cash flow.  
stationary model and only a period prediction (_i.e._, predicting the \(t+1\) period). So when the basic mode of predicted variables changes, the adaptability of the first moving average method will be relatively poor.  
Figure 3: Predictive results of the first moving average method in 2012.  
Figure 2: Predictive results of the first moving average method in 2011.