ESTIMATING AND REMOVING THE EFFECTS OF CHINESE NEW YEAR AND RAMADAN TO IMPROVE THE SEASONAL ADJUSTMENT PROCESS
INTRODUCTION
A time series of original estimates can be decomposed into a trend, seasonal and irregular component. Seasonally adjusted estimates are derived by estimating and removing the systematic calendar related variation from the original estimates. The seasonally adjusted estimates can be smoothed to obtain an estimate of the underlying direction, referred to as trend estimates. The irregular component is what is left after the trend and seasonal components are removed from the original estimates. Seasonally adjusted and trend estimates can be used to illustrate the short term movements and the underlying level in social and economic time series.
The estimation of the seasonal component is an essential part of the seasonal adjustment process. Regular calendar related events that occur at the same time each year are accounted for when estimating seasonality. Some calendar related events can move between months. These type of events are known as moving holidays. The activity due to some moving holidays can change the pattern of activity in surrounding months and is also referred to as a proximity effect. Since moving holidays do not occur in the same month each year the estimation of the seasonal component may be distorted and systematic variation will remain in the seasonally adjusted estimates. If moving holidays are not taken into account misleading seasonally adjusted and trend estimates will be produced. This will impact on the interpretation of the short term movements and underlying level of a time series.
This article shows how the Australian Bureau of Statistics (ABS) estimates and removes the impact of two moving holidays: 1) Chinese New Year and 2) Ramadan within the seasonal adjustment process. An example of model based corrections for these two moving holidays is given with an application to ABS monthly Overseas Arrivals and Departure (OAD) time series (Overseas Arrivals and Departures, Australia, cat. no. 3401.0).
CORRECTING FOR MOVING HOLIDAYS
The ABS seasonal adjustment process corrects for a range of moving holidays. These include Easter, Father’s Day, Chinese New Year and Ramadan. Different approaches can be used to correct for moving holidays. Easter and Father’s Day are corrected using an iterative approach (See Zhang, McLaren and Leung (2001) for more details). The most appropriate approach is the use of a model. For example, a suitable regression (or intervention) variable can be constructed and the effect estimated in a suitable framework (Regression-ARIMA, Findley et al, 1998). Regression-ARIMA combines regression analysis with time series modelling (ARIMA). For more detail on ARIMA modelling refer to the technical note of the October 2004 edition of Australian Economic Indicators.
Regression variables can be constructed for a wide range of moving holidays. They can represent the changed pattern of activity caused by the occurrence of a moving holiday. Most commonly the change in pattern caused by the movement of a holiday can be described using two different regressors; one regressor aims to model the change in activity prior to the date of interest and the other regressor models the change in activity during or after the date of interest. The number of days of changed activity is taken into account during the construction of these regressors. The daily change in activity may be a constant change or linear change over time. Daily data and model diagnostics can assist in determining how the activity changes over time and what type of regressors should be used. A regression-ARIMA model can then be used to estimate the impact of the moving holiday. If the impact is significant then appropriate factors can be calculated which will remove the impact of the moving holiday from the original time series before seasonal adjustment. This will give appropriate seasonally adjusted and trend estimates.
CHINESE NEW YEAR
The date of Chinese New Year is determined using the Chinese calendar. This is a lunisolar calendar based on movements of the moon and sun. The Chinese New Year holiday starts on the first full moon of each year falling between January the 21st and February the 21st. This holiday can impact on Australian time series, for example, short-term visitor arrivals to Australia from Hong Kong, China, Malaysia, Thailand, Vietnam and Singapore. Chinese New Year mostly falls in February but can sometimes fall in January. If there is not an appropriate correction for Chinese New Year then when it falls in January or early February the seasonally adjusted estimates for January will typically be higher than normal and the February estimates lower than normal. This will provide users with misleading seasonally adjusted and trend estimates.
Daily data and model based tests can be used to determine the type of activity surrounding the holiday. The number of days of the before-holiday period that fall in January and the number of days of the after-holiday period that fall in January are used to construct two regressors. Regression-ARIMA can then be used to estimate regressor parameters and assess their significance.
RAMADAN
Ramadan is the ninth month of the Islamic calendar. This is a lunar calendar based on cycles of the moon. The end of Ramadan is celebrated with a festival known as Eid al-Fitr which begins approximately eleven days earlier each year on the Gregorian calendar. This means that Ramadan can fall in any month. This holiday can impact on Australian time series. Short-term visitor arrivals to Australia from Indonesia and Malaysia increase at times corresponding to the end of Ramadan when the Eid al-Fitr celebrations occur. If there is not an appropriate correction the months which correspond to the end of Ramadan will typically have larger than normal seasonally adjusted estimates. A correction is needed to avoid misleading seasonally adjusted and trend estimates.
Daily data and model based tests can be been used to determine the type of activity surrounding the holiday. If the end of Ramadan occurs at the beginning of a month then the proportion of the activity that falls in the preceding month is used to construct a before-holiday regressor. If the end of Ramadan falls at the end of a month the proportion of activity falling in the following month is used to construct an after-holiday regressor. Regression-ARIMA can then be used to estimate regressor parameters and assess their significance.
APPLICATION TO OVERSEAS ARRIVAL AND DEPARTURE SERIES
Short-term visitor arrivals from Hong Kong and Indonesia are used to demonstrate the application of Chinese New Year and Ramadan moving holiday corrections. Identical methods can also be applied to other time series.
SHORT TERM VISITOR ARRIVALS FROM HONG KONG
Chinese New Year is celebrated in Hong Kong. This celebration influences short-term visitor arrivals to Australia from this country. Figure 1 shows the seasonally adjusted and trend series for short-term visitor arrivals from Hong Kong with no correction for the effect of the Chinese New Year holiday. The large January and low February seasonally adjusted estimates in 1993, 1995, 1998, 2001, 2003 and 2004 all correspond to years in which the Chinese New Year holiday started in January or early February. The systematic behaviour in the seasonally adjusted estimates would provide users with misleading information. The trend estimates will also be distorted.
FIGURE 1: SHORT TERM VISITOR ARRIVALS FROM HONG KONG, (WITHOUT CHINESE NEW YEAR PROXIMITY CORRECTION)
Figure 2 shows the irregular values for January and February ordered by the start date of Chinese New Year. This is referred to as a proximity chart. The irregular component of a time series should display no distinct pattern with a mean of one. When Chinese New Year begins in January or early February, the January irregulars are mostly above one and the February irregulars are less than one. This indicates there are residual effects from Chinese New Year and that the seasonal adjustment process has not removed all systematic variation.
FIGURE 2: CHINESE NEW YEAR PROXIMITY CHART FOR SHORT TERM VISITOR ARRIVALS FROM HONG KONG, (WITHOUT CHINESE NEW YEAR PROXIMITY CORRECTION)
Using daily data of short-term visitor arrivals from Hong Kong two regressors were constructed to reflect the impact of Chinese New Year. The before Chinese New Year holiday activity showed that there was a linear daily increase in arrivals for seven days leading up to the holiday. The during and after-holiday activity showed a linear daily decrease in arrivals for six days after the start of Chinese New Year.
Table 1 shows the regression-ARIMA results in terms of the daily percentage change in activity. The coefficients of the before and after Chinese new year regressors were both significant. The before Chinese New Year parameter indicated that there was a 13.4% daily increase in arrivals for the seven days leading up to Chinese New Year. For the six days after the Chinese New Year holiday there was a 16% daily decrease in arrivals.
This series was also tested for a Ramadan proximity effect. As expected, Ramadan did not have a significant effect on short-term visitor arrivals from Hong Kong.
TABLE 1: REGRESSION-ARIMA RESULTS FOR SHORT TERM VISITOR ARRIVALS FROM HONG KONG
|
| Regressors | Daily rate | t-value |
|
| Before Chinese New Year activity | 13.4% increase | 5.05 |
| During and after Chinese New Year activity | 16% decrease | 5.31 |
|
| Note: If the absolute value of the t-statistic is higher than a critical value of approximately 2.0 then this effect is significant at the 95% level. |
Figure 3 shows the seasonally adjusted and trend series once the Chinese New year proximity correction was applied. The large January and low February seasonally adjusted estimates shown in Figure 1 have been corrected. This can also be seen in the proximity chart (Figure 4). The irregulars are randomly scattered about one as opposed to the systematic pattern that was present before the correction was implemented. Figure 5 illustrates the seasonally adjusted estimates of short-term visitor arrivals from Hong Kong both before and after the correction. There is a significant improvement in the seasonally adjusted estimates after applying an appropriate correction for Chinese New Year.
FIGURE 3: SHORT TERM VISITOR ARRIVALS FROM HONG KONG, (WITH CHINESE NEW YEAR PROXIMITY CORRECTION)
FIGURE 4: CHINESE NEW YEAR PROXIMITY CHART FOR SHORT TERM VISITOR ARRIVALS FROM HONG KONG, (WITH CHINESE NEW YEAR PROXIMITY CORRECTION)
FIGURE 5: SEASONALLY ADJUSTED VISITOR ARRIVALS FROM HONG KONG, (WITH AND WITHOUT THE CHINESE NEW YEAR PROXIMITY CORRECTION)
SHORT TERM VISITOR ARRIVALS FROM INDONESIA
Short-term visitor arrivals to Australia from Indonesia significantly increase each year at the end of Ramadan. The seasonally adjusted and trend series for short-term visitor arrivals from Indonesia are given in Figure 6. The large seasonally adjusted estimates correspond to the end of Ramadan. For example, the end of Ramadan fell in November in both 2003 and 2004. For the years 2000, 2001 and 2002 the end of Ramadan fell in December. As December is already seasonally high for this time series the effects of Ramadan is not as evident in those years as the impact has already been removed during the seasonal adjustment process.
FIGURE 6: SHORT TERM VISITOR ARRIVALS FROM INDONESIA, (WITHOUT RAMADAN PROXIMITY CORRECTION)
Daily data of short-term visitor arrivals from Indonesia were used to determine the change in activity before and after the end of Ramadan. For this time series the before-holiday activity started six days before the end of Ramadan and displayed a linear daily increase in arrivals. The after-holiday activity displayed a linear daily decrease for six days after the end of Ramadan. This daily change in activity may vary for different time series. The before and after regressors were both found to be significant (Table 2). The before-holiday parameter indicated that there was a 11% daily increase in arrivals for the six days leading up to the end of Ramadan. For the six days after the end of Ramadan there was a 4% daily decrease in arrivals.
This time series was also tested for a Chinese New Year proximity effect. As expected, there was no significant effect.
TABLE 2: REGRESSION-ARIMA RESULTS FOR SHORT TERM VISITOR ARRIVALS FROM INDONESIA
|
| Regressors | Daily rate | t-value |
|
| Before-holiday activity | 11% increase | 7.73 |
| After-holiday activity | 4% decrease | 3.03 |
|
| Note: If the absolute value of the t-statistic is higher than a critical value of approximately 2.0 then this effect is significant at the 95% level. |
Figure 7 shows the seasonally adjusted and trend estimates after the Ramadan proximity correction had been applied. The large seasonally adjusted estimates due to the end of Ramadan have been corrected. Figure 8 displays the seasonally adjusted estimates of short-term visitor arrivals from Indonesia both before and after the correction. There is a significant improvement in the seasonally adjusted estimates after applying an appropriate correction for Ramadan.
FIGURE 7: SHORT TERM VISITOR ARRIVALS FROM INDONESIA, (WITH RAMADAN PROXIMITY CORRECTION)
FIGURE 8: SHORT TERM VISITOR ARRIVALS FROM INDONESIA, (WITH AND WITHOUT RAMADAN PROXIMITY CORRECTION)
CONCLUSION
The ABS applies corrections for moving holidays that are assessed to have a significant impact on a time series. Removing the effect of moving holidays improves the estimation of the seasonal component which in turn improves the quality of the seasonal adjusted and trend estimates.
This article has described the application of a model based approach to correcting for the Chinese New Year and Ramadan moving holidays. The Chinese New Year proximity correction is currently applied to short-term visitor arrivals from China, Hong Kong, Vietnam, Thailand, Singapore and Malaysia. The Ramadan proximity correction is currently applied to short-term visitor arrivals from Indonesia and Malaysia.
The regression variables and models used for each time series are reviewed on a regular basis to ensure that corrections that are applied are appropriate. This is because the impact of a holiday on a series can change or evolve over time.
REFERENCES
Australian Bureau of Statistics (2004). Australian Economic Indicators ‘Use of ARIMA modelling to reduce revisions’ cat. no. 1350.0
Australian Bureau of Statistics, Overseas Arrivals and Departures, Australia. cat. no. 3401.0
Findley, D.F. et al (1998) New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program, Journal of Business and Economic Statistics, Vol. 16, No. 2., 127-177.
Zhang, X., Mclaren, C.H. & Leung, C.S. (2001) An Easter proximity effect: modelling and adjustment, Australian & New Zealand Journal of Statistics, Vol 43, No. 3., 269-28
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