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# Revision of Seasonally Adjusted Data for Currency in Circulation

February 7, 2012
Bank of Japan
Currency Issue Department

The Bank of Japan has revised the seasonally adjusted data for Currency in Circulation. This revision is conducted every year around January, when the final figures for the whole of the previous calendar year become available.

Details of the current seasonal adjustment method are as follows.

1. The Bureau of Census X-12-ARIMA (Version 0.3) is used.
2. A multiplicative model and a logarithmic transformation are adopted for each series. The critical value for additive outliers and temporary changes depends on the length of the time-series data used for seasonal adjustment, which is the most recent 56 years, or 672 months, from January 1956 through December 2011. For the months after December 2011, seasonally adjusted figures are calculated by applying the predicted seasonal factors.
4. Starting with the 2012 revision, data for the most recent 56 years are used instead of data from the beginning of the series (January 1955) to the most recent December.1 This is because the number of data from the beginning of the series has reached the program limit with the X-12-ARIMA model. Accordingly, the data from January 1956 have been revised, and those prior to January 1956 remain unchanged.
Table : Revision of Seasonally Adjusted Data for Currency in Circulation
Indicator ARIMA model2 Level shift and ramp Trading-day
Length of the series
Banknotes in circulation
(average amount outstanding)
(211)(212) February 1989
From February through April 2002
From February through April 2005
None From January 1956 through December 2011
Banknotes in circulation
(amount outstanding at end of period)
(212)(011) March 2002
March 2005
Yes From January 1956 through December 2011

Notes:

1. The maximum number of data that can be used when conducting the revision of seasonally adjusted data with X-12-ARIMA is 720 (monthly data covering 60 years). Among these, 48 data (monthly data covering four years) are used to compile projected figures.
2. The models for "banknotes in circulation (average amount outstanding)" and "banknotes in circulation (amount outstanding at end of period)" have been revised.

## Inquiries

### Operations Management Group, Planning and Coordination Division, Currency Issue Department

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