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The passenger transportation, as an important index to describe the scale of aviation passenger transport, prediction and research, can let us understand the future trend of the aviation passenger transport, according to it, the airline can make corresponding marketing strategy adjustment. Combining with the knowledge of time series let us understand the characteristics of passenger transportation change, the R software is used to fit the data, so as to establish the ARIMA(1,1,8) model to describe the civil aviation passenger transport developing trend in the future and to make reasonable predictions.

In recent years, with the improvement of people’s living, travel distance extension, travel mode is no longer confined to the car and train traffic. And taking into account the cost of time, more and more people choose the aircraft as means of transportation to travel. Some scholars have done research on the characteristics of China’s air transport development [

Now prediction methods that have complete theoretical basis mainly include: regression analysis, time series analysis, input-output method, inductive method and Markov chain prediction method. At present, China has already done the research and forecast of aviation passenger traffic. In terms of influence factors, Wang Cui (2008) [

Because there are many factors influencing the air passenger volume, we need in-depth study of the internal and external environment of the aviation industry. The influence factors include the non quantifiable factors which are not easy to treatment, so this paper selects the self factor model focuses on its internal rules. In economic forecasting process, the ARIMA model (i.e., autoregressive moving average model) not only considers the economic phenomena in time series dependence, but also considers the interference of random fluctuations. On this problem of short-term trend forecast for the economic operation, this model has the high accuracy rate. The ARIMA model is widely used in economic research. Because of many factors such as holidays and climate factors, the aviation passenger transport industry has the market volatility. The passenger volume can be regarded as a stochastic time series formed with the passage of time. By analysing the time series is stochastic, stationary and seasonal factors or not, we can use the ARIMA model to fit civil aviation passenger transport. Therefore, this paper will use the time series analysis of the ARIMA model and R software to fit the data to achieve passenger transport turnover forecast. Air passenger traffic turnover is a composite index that can describe air transport enterprises in a certain period of time. It is a composite index of transport volume and distance. Air passenger traffic turnover is not only an important index of civil aviation enterprises, but also one of the main indicators of the national assessment of air transport enterprises. Therefore, this paper will study the problem of air passenger transport turnover forecast.

In the domestic and foreign well-known materials or works, modeling method of time series is basically uniform that the steady but autocorrelation sequence to establish ARMA model and the non-stationary time series (with unit root) to establish ARIMA(p,d,q) model [

The ARIMA(p,d,q) model includes the autoregressive model AR(p), moving average model MA(q) and the mixed autoregressive moving average model ARMA(p,q) of these three cases [

The first one, the AR(p) model corresponding to the algebraic expression is:

The second, the MA(q) model of the corresponding algebraic expression is:

Third, the ARMA(p,q) model corresponds to the logarithmic expression is:

If

Among them, both

The STL [

The STL decomposition method corresponds to the logarithmic expression is:

Among them,

This article studies on the index (civil aviation passenger transport volume [

It can be seen from

The change of seasons can make the time series of passenger turnover change regularly, which is the seasonal periodicity seen in

From January 2010 to August 2015 passenger turnover data into R software, based on the Loess method to do seasonal trend decomposition. This trend decomposition method is STL decomposition method, which is a time series decomposition method with generality and robustness. Thus it gets the seasonal trend decomposition map (it is shown in

Month | Seasonal variation value |
---|---|

January | −90,584.3 |

February | −70,172.9 |

March | −17,375.3 |

April | −71,211.5 |

May | −156,815 |

June | −216,210 |

July | 445,438.6 |

August | 606,397.1 |

September | 7611.507 |

October | 116,642.3 |

November | −306,071 |

December | −247,649 |

As can be seen from

After understanding the basic trend of the civil aviation passenger transport, in order to effectively predict the future trend of development, we need to fit the passenger transport turnover curve. First, we need to remove the seasonal changes in the time series. And then we make the remaining part of the data for ADF test.

When the ADF level is 0.01, 0.05 and 0.1, the critical value of them is −3.99, −3.45 and −3.13 respectively (the smaller the value of the more significant). And the test results show that the test statistic value of the original sequence is 0.1015, there is no sufficient evidence to reject the original hypothesis. It can not say that the original sequence is smooth. Then after the first order difference of the original data, the test statistic obtained is −5.6418, which is significant at 0.01 level, that is to reject the original hypothesis. Therefore, before the construction of the ARMA model to the data for the first order difference.

Through the R software output the timing diagram of data (it is shown in

For the ARIMA(p,d,q) model identification, it is required to determine the three parameters of p, d, q. The identification of parameter d has been completed, through the

first order difference, the sequence is smooth. So we think the time series is a single integer sequence and it can construct ARMA model after the first order difference. Under normal circumstances, it can be used for the self correlation function ACF map and the partial autocorrelation map PACF map to initially identify p and q. But it is very difficult to see the order in the ACF diagram and PACF diagram. In this paper, we introduce the concept of Bayesian information criterion. BIC is developed from the Bayesian perspective, which is similar to the maximum probability of a posteriori model, and a priori model has a uniform distribution in all models [

The expression formula of BIC is as follows:

Among them, L is the maximum likelihood, n represents the number of data, K said the number of variables in the model.

The BIC criterion is used to describe the loss of information after using a certain model relative to the actual situation. So the smaller the BIC value indicates that the model fitting effect is better. According to the BIC criterion to judge that for different q and p display the corresponding BIC value, the results shown in

As can be seen from

It uses ARMA(1,8) model to fit the data which removed seasonal variation (already through the first order difference) and points out the value of p [

the Ljung-Box test is 1 - 30, ACF diagram and PACF diagram is shown in

The null hypothesis of Ljung-Box test is that the sequence is independent, for the observed value of p which is not related to should be very large. If the value of p is small that it may be correlated. From

In the upper representation,

According to the fitting results of the sequence, the ARIMA(1,1,8) model of civil aviation passenger turnover has passed the test, and the fitting effect is ideal. It can be used to forecast the change of passenger turnover in the future. Using R software to predict the value of passenger turnover in the next 6 months, it draws a forecast figure as shown in

As can be seen from the

Time | Predicted Value | Real Value |
---|---|---|

2015-9 | 6,233,218 | 6,152,663 |

2015-10 | 6,296,824 | 6,420,679 |

2015-11 | 5,948,463 | 5,892,072 |

2015-12 | 6,034,594 | 6,077,000 |

2016-1 | 6,387,065 | - |

2016-2 | 6,448,524 | - |

2016-3 | 6,513,871 | - |

2016-4 | 6,530,472 | - |

2016-5 | 6,515,186 | - |

2016-6 | 6,525,991 | - |

2016-7 | 7,257,721 | - |

2016-8 | 7,488,643 | - |

period of time, but this does not affect the rising trend of the total passenger traffic volume. After comparing with the real data, the prediction error is maintained at about 1%, and the predicted results are in line with the expected results. Same as the predicted results, there is a lower value in November and the overall trend is still maintained steady growth.

This paper draws a line chart of the passenger turnover amount, as shown in

Time series analysis is performed by the civil aviation monthly passenger volume data from January 2010 to August 2015, this article established the ARIMA(1,1,8) model. On the basis of the ARIMA model to predict the trend of passenger turnover from next 6 months, the fitting effect of this model is better. The following conclusions are obtained by the ARIMA model of passenger turnover:

First, as China’s comprehensive national strength and people’s living standards to be better, air passenger volume will maintain a steady upward trend, it will officially break the mark of 6 ten thousand person-kilometers. And air passenger market will become bigger.

Second, the passenger turnover has a certain seasonal fluctuation, the main reasons of which include holidays, climate and so on. For example, summer (that is August) is

the peak of the air passenger.

The premise of rational planning is a clear understanding of the needs of the future. Only by accurately predicting the trend of air passenger turnover, airlines can reasonably adjust the manpower and material resources in the passenger transport market. In the face of the change of civil aviation passenger volume and passenger market on the future, the airlines should make strategic adjustment decisions, such as good routes and configuration, flight attendant recruitment work and so on. These adjustments will improve the operational capacity and service quality of airlines.

Tang, X.X. and Deng, G.M. (2016) Prediction of Civil Aviation Passenger Transportation Based on ARIMA Model. Open Journal of Statistics, 6, 824-834. http://dx.doi.org/10.4236/ojs.2016.65068