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In the paper, the data of the narrow money supply of China from January 2005 to March 2016 as sample, 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.

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) [

This paper takes the narrow money supply of China from January 2015 to March 2016 as sample, which denoted as Y t (Unit: billion yuan). The prediction model is established by using Eviews6.0. [

The line chart (see

t-Statistic | Prob. | |||
---|---|---|---|---|

Augmented Dickey-Fuller test statistic | −0.964622 | 0.7645 | ||

Test critical values: | 1% level | −3.479656 | ||

5% level | −2.883073 | |||

10% level | −2.578331 |

According to the

The ADF test of W t is taken to judge whether the processed series W t , is stationary or not. And the result of the ADF test is shown in

Box-Jenkins method is an important method to identify SARIMA model [

t-Statistic | Prob. | |||
---|---|---|---|---|

Augmented Dickey-Fuller test statistic | −39.92772 | 0.0000 | ||

Test critical values: | 1% level | −2.584375 | ||

5% level | −1.943516 | |||

10% level | −1.614956 |

| ρ k + i | ≤ [ 1 N ( 1 + 2 ∑ l = 1 m ρ ^ l 2 ) ] 1 2 where i = 1 , 2 ⋯ M , M = [ N ] = [ 122 ] = 11 and

N is the sample size of W t , is 54.55% or 63.64% which are all less than 68.3%. And the proportion of ρ k + 1 , ρ k + 2 , ⋯ , ρ k + M satisfying

| ρ k + i | ≤ 2 [ 1 N ( 1 + 2 ∑ l = 1 m ρ ^ l 2 ) ] 1 2 ( i = 1 , 2 ⋯ M ) is 63.64%, 81.82% or 90.91%, which

are all less than 95.5%. So ρ k is tailing. When k = 1 , 2 , 3 , 4 , 5 or 6 the propor-

tion of φ k + 1 , k + 1 , φ k + 2 , k + 2 , ⋯ φ k + M , k + M satisfying | φ k k | > 1 N is greater than 31.7% and the proportion of ρ k + 1 , ρ k + 2 , ⋯ , ρ k + M satisfying | φ k k | > 2 N is greater than

4.5%. So φ k k is tailing. In summary, autocorrelation and partial autocorrelation function are both tailing. This is consistent with the result of subjective recognition from the correlogram graph of W t series. So SARIMA ( p , 1 , q ) ( 0 , 1 , 1 ) 12 ( p ≠ 0 and q ≠ 0 ) model should be established.

The p and q in SARIMA ( p , 1 , q ) ( 0 , 1 , 1 ) 12 model can’t be determined directly. Because the order of SARIMA model should not be high, p can be chosen as 5 and q can be chosen as 4 preliminarily by

The adjusted R 2 , AIC, and SC criteria are considerable important factors when we choose a SARIMA model. Generally, we consider that the model making the value of AIC and SC function smaller is better. From

According to the above we initially judge SARIMA ( 4 , 1 , 4 ) ( 0 , 1 , 1 ) 12 as the appropriate model, and we should also test the applicability of the model. This is

Models | Inverted Roots | Adjusted | AIC | SC |
---|---|---|---|---|

0.564752 | −5.470924 | −5.259601 | ||

0.523222 | −5.387604 | −5.199761 | ||

0.547155 | −5.453272 | −5.289795 |

Variable | Coefficient | Std. Error | t-Statistic | Prob. |
---|---|---|---|---|

AR(1) | 0.124123 | 0.068902 | 1.801455 | 0.0744 |

AR(2) | 0.475486 | 0.069742 | 6.817791 | 0.0000 |

AR(3) | 0.479315 | 0.061410 | 7.805100 | 0.0000 |

AR(4) | −0.564442 | 0.063236 | −8.925930 | 0.0000 |

MA(1) | −0.319742 | 0.018708 | −17.09109 | 0.0000 |

MA(2) | −0.536473 | 0.030100 | −17.82320 | 0.0000 |

MA(3) | −0.318432 | 0.019858 | −16.03577 | 0.0000 |

MA(4) | 0.968683 | 0.011388 | 85.05812 | 0.0000 |

SMA(12) | −0.887606 | 0.022645 | −39.19585 | 0.0000 |

R-squared | 0.594513 | Mean dependent var | 0.000578 | |

Adjusted R-squared | 0.564752 | S.D. dependent var | 0.022935 | |

S.E. of regression | 0.015131 | Akaike info criterion | −5.470924 | |

Sum squared resid | 0.024956 | Schwarz criterion | −5.259601 | |

Log likelihood | 331.7845 | Hannan-Quinn criter. | −5.385120 | |

Durbin-Watson stat | 2.061025 | |||

Inverted AR Roots | 0.74 − 0.29i | 0.74 + 0.29i | −0.68 + 0.66i | −0.68 − 0.66i |

Inverted MA Roots | 0.99 | 0.88 − 0.47i | 0.88 + 0.47i | 0.86 − 0.50i |

0.86 + 0.50i | 0.50 − 0.86i | 0.50 + 0.86i | 0.00 + 0.99i | |

−0.00 − 0.99i | −0.50 + 0.86i | −0.50 − 0.86i | −0.72 + 0.69i | |

−0.72 − 0.69i | −0.86 + 0.50i | −0.86 − 0.50i | −0.99 |

an independence test of model residual a t . 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

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,

MAPE = 100 n ∑ i = 1 n | y i − y ^ i y i | (1)

TIC = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 1 n ∑ i = 1 n y i 2 + 1 n ∑ i = 1 n y ^ i 2 (2)

The static predicted values the narrow money supply of China from January 2005 to March 2016 gained by SARIMA ( 4 , 1 , 4 ) ( 0 , 1 , 1 ) 12 model. Then we compare them with the real values (see

At the same time, we use the model to forecast the narrow money supply of China from April to September 2016 and compare the forecast values with the real values. The dynamic predicted values and relative errors are as follows (see

From

The above analysis shows that SARIMA ( 4 , 1 , 4 ) ( 0 , 1 , 1 ) 12 model is appropriate for forecasting narrow money supply. We forecast the narrow money supply of China from October 2016 to February 2018 (see

1) SARIMA ( 4 , 1 , 4 ) ( 0 , 1 , 1 ) 12 model, based on the narrow money supply of China from January 2005 to March 2016 as sample, eventually is established after comparative analysis. Its numerical value of mean absolute percentage error (MAPE) is 1.09 and the value of theil inequality coefficient (TIC) is 0.00768. The data from April 2016 to September 2016 are predicted, and the predicted values

Time | Real values | Dynamic predicted values | Relative errors |
---|---|---|---|

2016.04 | 413,504.84 | 416,171.96 | 0.65% |

2016.05 | 424,250.70 | 426,252.46 | 0.47% |

2016.06 | 443,643.70 | 441,477.73 | 0.49% |

2016.07 | 442,934.43 | 437,336.70 | 1.26% |

2016.08 | 454,543.60 | 444,481.38 | 2.21% |

2016.09 | 454,340.25 | 442,756.64 | 2.55% |

Time | Predicted values | Time | Predicted values |
---|---|---|---|

2016.10 | 462,084.98 | 2017.07 | 528,081.20 |

2016.11 | 472,496.81 | 2017.08 | 536,912.25 |

2016.12 | 491,533.81 | 2017.09 | 536,505.71 |

2017.01 | 492,726.39 | 2017.10 | 547,061.04 |

2017.02 | 484,342.35 | 2017.11 | 558,134.97 |

2017.03 | 502,012.32 | 2017.12 | 578,256.43 |

2017.04 | 504,697.96 | 2018.01 | 575,961.67 |

2017.05 | 514,090.71 | 2018.02 | 563,187.20 |

2017.06 | 531,929.28 |

are compared with the reserved real values. The result shows that the forecasting precision is 98.73%. These results show that the model has good fitting effect and high prediction accuracy.

2) The narrow money supply of China from October 2016 to February 2018, which is forecasted based on SARIMA ( 4 , 1 , 4 ) ( 0 , 1 , 1 ) 12 model, is compared with the historical data. The results are as follows. In the next fifteen months, the overall trend is the same with the last two years’, which shows the same proportion of growth. While compared with the money supply before 2015, it shows a substantial growth.

According to the above conclusions, this paper puts forward the following suggestions for the formulation of China’s monetary policy: 1) In the next year, the money supply will continue to grow. The stock demand is expected to increase which would stimulate the stock prices. It can be appropriate to guide funds into the stock market, stimulate consumption and promote economic growth. 2) With the money supply growing constantly, the central bank should be alert to the risks and improve the control for it. It is necessary to implement a moderately tight monetary policy to avoid the emergence of rapid inflation and hyperinflation phenomenon. 3) The coordination between monetary policy and other economic policies should be strengthened to achieve the balance between the demand and supply.

This work is supported by the National Natural Science Foundation of China (No. 11561056) and Natural Science Foundation of Qinghai (No. 2016-ZJ-914).

Shen, S.C. and Chen, S. (2017) Application of SARIMA Model on Money Supply. Open Journal of Statistics, 7, 112-121. https://doi.org/10.4236/ojs.2017.71009