Application of SARIMA Model on Money Supply

In the paper, the data of the narrow money supply of China from January 2005 to March 2016 as sample, ( ) ( ) SARIMA 4,1, 4 0,1,1 model is established by using Eviews6.0. Upon inspection, the model has good fitting effect (MAPE = 1.09) and high prediction accuracy. According to the results of the model, the paper forecasts the development trend of the narrow money supply of China and puts forward some suggestions to provide reference for monetary policy of China.


Introduction
As the intermediate target of monetary policy, money supply is one of the important means of macroeconomic regulation.It includes narrow money supply and broad money supply.The difference between the two is that the former does not include guasi-money.For a country or a region, money supply will affect its inflation rate.Generally, the central bank will take the total money supply as the main means of regulation to keep the currency stable.In addition, money supply is also crucial to the development of capital market.Changes in money supply will lead to the changes of market interest rates, which have an effect on the investment costs and profits of listed companies and ultimately make the company stock change.Chen Riqing and Wang Tongtong (2011) [1] analyzed the nonlinear effects of the money supply on Chinese insurance market by building the Markov regime switching model.Gu Liubao and Chen Bofei (2013) [2], by building the VAR model, used impulse response function and variance decomposition to analyze the dynamic affection of the changes of money supply and interest rate on the price of real estate market.Zhang Xiuli (2011) [3] analyzed the correlation between money supply and stock price.In fact, scholars had less research on the trend of narrow money supply in the past.But narrow money supply is central bank's key regulatory object because of its strong liquidity.Therefore, it is of great significance to predict its development trend.In the paper, based on the data of the narrow money supply of China from January 2005 to March 2016 as sample, SARIMA (Seasonal Auto Regressive Integrated Moving Average) model is established by using Eviews6.0.According to the results of the model, we predicted the development trend of the narrow money supply of China and put forward some suggestions to provide reference for monetary policy of China.

Data Preprocessing
The line chart (see Figure 1) of t Y shows that the narrow money supply has a certain trend.It shows that the sequence is a non-stationary series.In order to reduce the fluctuation of the series and eliminate the heteroscedasticity that may exist in the data, the natural logarithm of t Y is taken as Ln t Y .To confirm the stationarity of Ln t Y , the ADF test is performed, and the result is as follow (see Table 1).
The ADF test of t W is taken to judge whether the processed series t W , is stationary or not.And the result of the ADF test is shown in Table 2. From the result, we can know that the value of T statistic is −39.92772, which is smaller compared with the critical values at 1%, 5% and 10% confidence level.In addition, the P value is almost 0, so the original hypothesis is rejected and there is no unit root in t W .Therefore, it is a stationary series and its autocorrelation graph and partial autocorrelation graph are shown in Figure 3.

Model Recognition
Box-Jenkins method is an important method to identify SARIMA model N is the sample size of t W , is 54.55% or 63.64% which are all less than 68.3%.
And the proportion of  an independence test of model residual t a .It is used for judging whether this model is suitable for describing the time series and it is necessary to further improve the model or not.The results of the Chi-square test are as follows (see Figure 4).The sample size of the residual series is 120.So its maximum lag period can be taken as ( ) . The P value of the corresponding Q sta- tistic is 0.904, so the original hypothesis that the residual series is independent can't be rejected.This indicates that the residual series of the model is purely random.That is to say, it is a white noise series.

The Prediction Based on the Model
The model is reasonable through the above test.It can be used for short-time prediction.In order to test the prediction accuracy of the model, firstly we use the mean absolute percentage error (MAPE) and Theil inequality coefficient (TIC) to test the fitting effect of the model.Among them,

Figure 5 .
Figure 5.Comparison between the real values and predicted values in sample.

Figure 6 .
Figure 6.The graph of early values (Y) and predicted values about future (YF).

Table 1 .
ADF test about Ln t Y .According to the Table 1, the value of T statistic is −0.964622, which is relatively bigger compared with the critical values at 1%, 5% and 10% confidence level.It means that Ln t Y has a unit root.So it is a non-stationary series.In or- der to make it stationary, it is processed by the first order difference.The processed series is marked as Ln t Y ∇ .Its autocorrelation graph and partial autocorrelation graph are shown in Figure 2. We can see that the trend of Ln t Y ∇ has been eliminated by Figure 2.But when k = 122,436, the autocorrelation coefficient and partial autocorrelation coefficient of Ln t Y ∇have significant difference compared with 0. This shows that it is seasonal time series.After the first order seasonal difference for the sequence, the new series is marked as

Table 2 .
ADF test about t W .

Table 4 .
Parameters estimation of

Table 6 .
Forecast the narrow money supply of China.