Seasonal Adjustment of China’s Monthly Data to Take into Account the Effect of Mobile Holidays

Based on the X-13-ARIMA-SEATS model, aiming at the problem of mobile holidays in China’s economic data, this paper introduces a new method of seasonal adjustment based on the AICC criterion to objectively select the parameters of dummy variables of mobile holidays. Taking the current total value of China’s import and export as an example, we expound a new method for seasonal adjustment of mobile holidays such as Spring Festival, Dragon Boat Festival and Mid-Autumn Festival. Finally, the model is used to predict the total value of China’s import and export in and out of the sample. The prediction results show that the relative error of the out of sample data is less than 5%. The new method has advantages in the processing of macroeconomic data.


Research Background
In order to better monitor the operation of the national economy, it is necessary to scientifically process the economic data, especially the monthly and quarterly high-frequency data. Developed countries generally use the seasonally adjusted data as the basis for economic analysis and forecasting. Most monthly and quarterly macroeconomic data are influenced by seasonal factors. Taking the total value of import and export in the current period ($10 billion) as an example, the "advance of export and delay of import" could theoretically lead to a higher export growth rate and a lower import growth rate in the month during the Spring Festival. The purpose of seasonal adjustment of monthly data and quarterly data occurs between January 21 and February 20 each year, which will cause some distortion in the data of monthly year-on-year growth rate. If the Spring Festival of the adjacent two years does not happen in January or February at the same time, the volatility of year-on-year data may be very large. At present, the latest outcome is the X-13-ARIMA-Seats, which is supported by the bank of Spain and developed by the census bureau. Based on the latest version of X-12-ARIMA (proposed by US Census Bureau's X-12-ARIMA for seasonal adjustment), this program adds the TRAMO/SEATS seasonal adjustment procedure, which has been widely used in the economic analysis process of central Banks and research institutions of various countries. Despite that the X-12-ARIMA regARIMA in program used in the pretreatment of the raw data of the adjustment module can be achieved, which eliminate the calendar effect (such as trading day effect, mobile holiday effect, etc.), but most of the built-in program X-12-ARIMA designed aiming at the condition of the western countries, such as Easter, Thanksgiving, for China the Spring Festival, the Dragon Boat Festival, Mid-Autumn Festival and so on did not provide a direct calculation program. In addition, in the existing seasonal adjustment studies considering the effect of mobile holidays in China, the pre-holiday, mid-holiday and post-holiday influence periods are selected in a subjective way, and the same influence periods are adopted for different time series. Therefore, there is a lack of relevant studies on the possible effects of different mobile holidays on different time series data. In view of this, this paper takes the current total value of China's import and export (RMB 10 billion) data as an example, and based on the X-13-ARIMA-SEATS program package, designs a direct calculation program for the Spring Festival, Dragon Boat Festival and Mid-Autumn Festival, and makes seasonal adjustment to the monthly data of China. At the same time, in view of the Spring Festival effect, this paper selected the parameters before, during and after the Spring Festival according to the AICC criterion, obtained the seasonally adjusted data excluding the Spring Festival effect by using the R, and used the adjusted data for prediction.

Literature Review
The idea of seasonal adjustment of time series can be traced back to 100 years ago. In 1919, Persons explicitly proposed to divide the time series into four parts: Shiskin of the US census bureau first developed a program called X-1 that USES computers to adjust the seasons. In 1955 an improved seasonal adjustment procedure was announced, known as X-2; By 1965 the X-11 method had been developed. The X-11 method was the international seasonal adjustment method at that time, and was also the core of X-11-ARIMA and X-12-ARIMA.
Currently, the X-12-ARIMA model is one of the most popular models for seasonal adjustment.  Festival effect, the number of days before, during and after the festival are set to 20 days, 5 days, and 10 days, which is still subjective. Since different time series may be affected by the mobile holiday effect differently, it is necessary to use reasonable indicators to judge the influence period of the mobile holiday effect objectively. In view of this, Roberts and White (2015) [3] use AICC criterion to objectively select the influence period of the Spring Festival effect. In this paper, to be specific, X-13-ARIMA-SEATS program package is used to adjust China's current value of import and export data as an example to seasonally adjust the time series data of China and France.

The Principle and Method of Seasonal Adjustment
Based on the principle of seasonal adjustment, we will discuss how to introduce the regression variables of outliers, stock trading days and China mobile holiday effect into X-13ARIMA-SEATS program.

Basic Principles of Seasonal Adjustment
Essentially, seasonal adjustment is the estimation and elimination of seasonal with the formula as follows: In this paper, the seasonal adjustment of the money supply is based on the us RegARIMA model can be expressed as: Among them is the lag operator L, s is the seasonal cycle, ( )

Identification Method of Outlier Effect
The X-13-Arima-Seats program can automatically detect four types of outliers, means that there is a mobile holiday effect in that month and must be overcome.
In addition, the fewer outliers there are, the more concise the model tends to be.

Day Effect Treatment
where ϖ is the smaller values between the observation registration date (correspond to Gregorian calendar date) and the length of the month.

Handling of Mobile Holidays
Mobile holidays are holidays that occur regularly but do not necessarily corres-

Empirical Results
This

Seasonal Adjustment of Current Export Value
According to the AICC criterion, the model finally chooses the pre-festival influence period of 6 days, the mid-festival influence period of 6 days, and the post-holiday impact period is 12 days, which maximize the value of AICC. The ARIMA model selected by the ndiffs function in R is (0, 1, 0) (0, 1, 1). Table 1 shows the result of regARIMA fitting of current value after logarithmic conversion by nidify program.
The results above show that the effects of pre-festival (xreg1), mid-festival  Table 2 is the main statistics of the model adjusted for the last quarter of the total value of the current period after logarithmic conversion, and Table 3 is the QS statistics of the seasonally adjusted diagnostic test. QS is a kind of statistic.
The null hypothesis is that there is no seasonal effect in the series, which is suitable for testing whether there is still seasonal effect in the time series after modeling Finally, by plotting the seasonally adjusted data with the original total amount of import and export in the current period in Figure 1, we can find that the seasonal factors are well removed after seasonal adjustment.

Forecast of Total Export Value
According to the selected final model, the total export value in the current period is predicted, and the forecast time range is from January 2018 to December 2018. Figure 2 shows the comparison between the predicted value and the real value, and it can be seen that the predicted value and the real value trend are consistent. Table 4 is the error table of the prediction phase pairs. The results in Table 4 show that the relative error in other months is small except that the relative error in December reaches 5%, and the total average relative error is 2.22%.

Seasonal Adjustment of Current Total Import Value
According to the AICC criterion, the model finally chooses the pre-festival influence period of 3 days and the mid-festival influence period of 9 days, and the post-festival effect is not significant. The ARIMA model selected by the ndiffs function in R is (0, 1, 0) (0, 1, 1) Table 1 shows the result of regARIMA fitting of current value after logarithmic conversion by ndiffs program (Table 5).
The results show that the effect of xreg1 and xreg2 before the Spring Festival is significant. At the same time, it can be seen from the parameter symbols that the total value of import in the current period is the same as that of export, and the positive effect is brought to export before the festival, while the negative effect is brought to the total value of import during the festival and xreg2. In addition, Boat Festival. Table 6 shows the main statistics of the last seasonally adjusted model of the total output value of the current period after logarithmic conversion, and Table 7 shows the QS statistics of the seasonally adjusted diagnostic test.
The results show that the original time series of export current value has seasonal and significant seasonal effect, the residual of regAERIMA model has no seasonal effect, and the final sequence after seasonal adjustment has no seasonal effect. Finally, the seasonally adjusted data and the original total data of the inlet and outlet in the current period are plotted in Figure 2 and Table 8.

Conclusions
In order to better monitor the operation of the national economy, it is necessary to scientifically process the economic data, especially the monthly and quarterly high-frequency data. Developed countries generally use the seasonally adjusted data as the basis for economic analysis and forecasting. China has developed a version of X-12-ARIMA software and NBS-SA software for seasonal adjustment of economic data, but because the software is not made public, it is not known whether the different economic indicators use reasonable standards to distinguish. The existing studies on seasonal adjustment of China's economic data all adopt a fixed influence period when dealing with the effect of mobile holidays, and do not differentiate different economic indicators, which ignores the fact that there may be different characteristics among indicators, and there will inevitably be deviations in the prediction.
According to Roberts and White (2015) [3] the latest research results, we used AICC criterion on objective selection of the Spring Festival effect, based on China's gross value of import and export, in the use of X-13-ARIMA-SEATS. We finally designed a direct application to make seasonally adjustment for China's monthly data of the Spring Festival, the Dragon Boat Festival, Mid-Autumn Festival. In addition, in view of the Spring Festival effect, this paper selected the parameters before, during and after the Spring Festival according to the AICC criterion, obtained the seasonally adjusted data excluding the Spring Festival effect by using the R sequence, and used the adjusted data for prediction. The results show that the total value of exports in the three periods of the Spring Festival has a significant holiday effect, while the total value of imports in the current period has only a significant holiday effect before and during the Spring Festival. In ad- forecasts the total value of imports and exports in the current period from the out-of-sample data, and the relative error of the prediction is less than 5%, indicating that the accuracy of the model is relatively high. Therefore, the method of using AICC criterion to select the parameters of mobile holiday dummy variable has great advantages.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.