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# Seasonal adjustment of debt securities issues

Seasonal adjustment estimates are available for euro area securities issues by sector and maturity (short-term and long-term). Data refer to end-of-month outstanding amounts, net issues, indexes of notional stocks and growth rates.

All debt securities time series

## Background, approach and formulas

Seasonal adjustment is the process of estimating and removing seasonal effects from a time series. Seasonally adjusted data therefore facilitate analysis of short-term dynamics and the identification of changes in trends. The general principles followed by the ECB in the seasonal adjustment of time series are laid down in the ECB publication Seasonal adjustment of monetary aggregates and HICP for the euro area.

The approach used to seasonally adjust the securities issues statistics utilises a multiplicative decomposition using the Census X-12-ARIMA method, Version 0.2.10. Outliers are taken into consideration in order to minimise distortions to the estimated seasonal components. (Technical notes on the seasonal adjustment of securities issues series)

To ensure the additivity of the seasonally adjusted components to the seasonally adjusted aggregates, the seasonally adjusted series for the securities issues total are derived indirectly from the breakdowns by sector and maturity. A direct adjustment of the total is regularly carried out for monitoring purposes. The difference between direct and indirect estimates is generally negligible.

For seasonal adjustments during the year, forecast seasonal factors are used and seasonal factors are reestimated once a year. A review of the seasonal factors in use based on concurrent adjustments which might lead to a revision of seasonal factors takes place once a quarter. In addition, seasonal factors can be reviewed in the case of large data revisions.

### Growth rate formulas

The three-month annualised growth rate is calculated with the formula below:

${R}_{3}^{t}=\left[{\left(\frac{{X}^{t}}{{X}^{t-3}}\right)}^{4}-1\right]\ast 100$

where R3t represents the 3-month annualised growth rate for the reference month t and Xt is the securities issues index in month t.

The six-month annualised growth rate is calculated with the formula below:

${R}_{6}^{t}=\left[{\left(\frac{{X}^{t}}{{X}^{t-6}}\right)}^{2}-1\right]\ast 100$

where R6t represents the 6-month annualised growth rate for the reference month t and Xt is the securities issues index in month t.

### Monthly net issues of debt securities by euro area residents, broken down by sector, seasonally adjusted and non-adjusted

(EUR billions; transactions during the year; nominal values)