The TIMESERIES procedure analyzes time-stamped transactional data with respect to time and accumulates the data into a time series format. The procedure can perform trend and seasonal analysis on the transactions. After the transactional data are accumulated, time domain and frequency domain analysis can be performed on the accumulated time series.

For seasonal analysis of the transaction data, various statistics can be computed for each season.

*Seasonal Adjustment output from the TIMESERIES Procedure*

The EXPAND procedure converts time series from one sampling interval or frequency to another and interpolates missing values in time series. PROC EXPAND enables you to change time series data from higher frequency intervals to lower frequency intervals, or vice versa. You can also interpolate missing values in a time series, either without changing series frequency or in conjunction with expanding or collapsing the series. The procedure automatically accounts for calendar effects such as the differing number of days in each month and leap years.

The EXPAND procedure also handles conversions of frequencies that cannot be defined by standard interval names. For example, if you specify the option FACTOR=(13:2), 13 equally spaced output observations are interpolated for each pair of input observations.

You can also convert an aperiodic series, observed at arbitrary points in time, into periodic estimates. For example, a series of randomly timed quality control spot-check results might be interpolated to form estimates of monthly average defect rates.

*Transformed Series from the Expand Procedure*

Details of the EXPAND Procedure.

The X11 procedure is based on the U.S. Bureau of the Census X-11 seasonal adjustment program. The procedure seasonally adjusts monthly or quarterly time series, makes additive or multiplicative adjustments, and creates an output data set containing the adjusted time series and intermediate calculations.

The X11 procedure also provides the X11-ARIMA method developed by Statistics Canada. This method fits an ARIMA model to the original series and then uses the model forecast to extend the original series. This extended series is then seasonally adjusted by the standard X11 seasonal adjustment method. The extension of the series improves the estimation of the seasonal factors and reduces revisions to the seasonally adjusted series as new data becomes available.

*Model forecasts from the X12 Procedure*

The X11 procedure is used to decompose seasonal monthly or quarterly series into seasonal (S), trend cycle (C), trading-day (D), and irregular (I) components. A seasonally adjusted time series consists of the trend cycle and irregular components. The procedure processes any number of variables at once with no maximum length for a series. It projects the seasonal component one year ahead, allowing reintroduction of seasonal factors for an extrapolated series.

The naming convention used in the X11 procedure for the tables follows the original U.S. Bureau of the Census X-11 Seasonal Adjustment program specification. You can optionally print or store, in SAS data sets, the individual X11 tables showing the various components at different stages of the computation.

Sliding spans analysis is done by the X11 procedure to qualify the stability of the seasonal adjustment process and, hence, quantify the suitability of seasonal adjustment for a given series. Statistical tests for stable seasonal patterns, and for moving and combined seasonality, are computed and printed following table D8.

Details of the X11 Procedure.

The X13 procedure is an adaptation of the US Bureau of the Census X-13ARIMA-SEATS seasonal adjustment program. The X-13ARIMA-SEATS program was developed by the Time Series Staff of the Statistical Research Division, US Census Bureau, by incorporating the SEATS method into the X-12-ARIMA seasonal adjustment program. The X-12-ARIMA seasonal adjustment program contains components developed from Statistics Canada’s X-11-ARIMA program.

The X-13ARIMA-SEATS program incorporates the X-12-ARIMA functionality. It also incorporates improvements on X-12-ARIMA methods. Because the X-12-ARIMA methods and improvements are available in X-13ARIMA-SEATS, the new X13 procedure and the existing X12 procedure use the same X-13ARIMA-SEATS methodology, and PROC X12 and PROC X13 are aliases for the same procedure

The X13 procedure seasonally adjusts monthly or quarterly time series. The procedure makes additive or multiplicative adjustments and creates an output data set that contains the adjusted time series and intermediate calculations.

The X-13ARIMA-SEATS program includes the X-12-ARIMA program, which combines the capabilities of the X-11 program and the X-11-ARIMA/88 program and also introduces some new features. One of the main enhancements in the X-12-ARIMA program involves the use of a regARIMA model, a regression model with ARIMA (autoregressive integrated moving average) errors. Thus, the X-12-ARIMA program contains methods developed by both the US Census Bureau and Statistics Canada. In addition, the X-12-ARIMA automatic modeling routine is based on the TRAMO (time series regression with ARIMA noise, missing values, and outliers) method. The four major components of the X-12-ARIMA program are regARIMA modeling, model diagnostics, seasonal adjustment that uses enhanced X-11 methodology, and post-adjustment diagnostics. Statistics Canada’s X-11 method fits an ARIMA model to the original series, and then uses the model forecasts to extend the original series. This extended series is then seasonally adjusted by the standard X-11 seasonal adjustment method. The extension of the series improves the estimation of the seasonal factors and reduces revisions to the seasonally adjusted series as new data become available.

*Use the X13 procedure to seasonally adjust monthly or quarterly time series.*

Details of the X13 Procedure.