# Time Series Transformation Functions

**Difference.** Nonseasonal
difference between successive values in the series. The order is the
number of previous values used to calculate the difference. Because
one observation is lost for each order of difference, system-missing
values appear at the beginning of the series. For example, if the
difference order is 2, the first two cases will have the system-missing
value for the new variable.

**Seasonal difference.** Difference between series values a constant span apart. The span
is based on the currently defined periodicity. To compute seasonal
differences, you must have defined date variables (Data menu, Define
Dates) that include a periodic component (such as months of the year).
The order is the number of seasonal periods used to compute the difference.
The number of cases with the system-missing value at the beginning
of the series is equal to the periodicity multiplied by the order.
For example, if the current periodicity is 12 and the order is 2,
the first 24 cases will have the system-missing value for the new
variable.

**Centered moving
average.** Average of a span of series values surrounding
and including the current value. The span is the number of series
values used to compute the average. If the span is even, the moving
average is computed by averaging each pair of uncentered means. The
number of cases with the system-missing value at the beginning and
at the end of the series for a span of *n* is equal to *n*/2 for even span
values and (*n*–1)/2 for
odd span values. For example, if the span is 5, the number of cases
with the system-missing value at the beginning and at the end of the
series is 2.

**Prior moving average.** Average of the span of series values preceding the current value.
The span is the number of preceding series values used to compute
the average. The number of cases with the system-missing value at
the beginning of the series is equal to the span value.

**Running medians.** Median of a span of series values surrounding and including the
current value. The span is the number of series values used to compute
the median. If the span is even, the median is computed by averaging
each pair of uncentered medians. The number of cases with the system-missing
value at the beginning and at the end of the series for a span of *n* is equal to *n*/2 for even span values and (*n*–1)/2 for odd span values. For example, if the span is 5,
the number of cases with the system-missing value at the beginning
and at the end of the series is 2.

**Cumulative sum.** Cumulative sum of series values up to and including the current
value.

**Lag.** Value of a previous case, based on the specified lag order. The
order is the number of cases prior to the current case from which
the value is obtained. The number of cases with the system-missing
value at the beginning of the series is equal to the order value.

**Lead.** Value of a subsequent case, based on the specified lead order. The
order is the number of cases after the current case from which the
value is obtained. The number of cases with the system-missing value
at the end of the series is equal to the order value.

**Smoothing.** New series values based on a compound data smoother. The smoother
starts with a running median of 4, which is centered by a running
median of 2. It then resmoothes these values by applying a running
median of 5, a running median of 3, and hanning (running weighted
averages). Residuals are computed by subtracting the smoothed series
from the original series. This whole process is then repeated on the
computed residuals. Finally, the smoothed residuals are computed by
subtracting the smoothed values obtained the first time through the
process. This is sometimes referred to as **T4253H smoothing**.