Revision history

Revisions are calculated as differences between the first (earliest) adjustment of an observation at time $t$, computed when this observation is the last observation of the time series (concurrent adjustment, denoted as $A_{t|t}$) and a later adjustment based on all future data available at the time of the diagnostic analysis (the most recent adjustment, denoted as $A_{t|N}$).

In the case of the multiplicative decomposition the revision history of the seasonal adjustment from time $N_{0}\ $to $N_{1}$ is a sequence of $R_{t|N}^{A}$ calculated in the following way :

$R_{t|N}^{A} = 100 \times \frac{A_{t|N} - A_{t|t}}{A_{t|t}}$ [1]

The revision history of the trend is computed in the same manner.

With an additive decomposition $R_{t|N}^{A}$ is calculated in the same way if all values $A_{t|t}$ have the same sign. Otherwise differences are calculated as:

$R_{t|N}^{A} = A_{t|N} - A_{t|t}$ [2]

The analogous expression for the trend component is:

$R_{t|N}^{T} = T_{t|N} - T_{t|t}$ [3]

Revision in the period-to-period (month-on-month or quarter-to-quarter) change in the seasonally adjusted series at time $t$ calculated from the series $y_{1},y_{2},\ldots y_{n}$ is defined as:

$R_{t}^{A} = C_{t|N} - C_{t|t}$ [4]

where $\text{C}_{t|n}^{A} = \frac{A_{t|n} - A_{t - 1|n}}{A_{t - 1|n}}$.

Revisions for the period-to-period changes in the trend component are computed in the same manner.