These are a versatile family of models for modeling and forecasting time series data. Seasonal ARIMA models have a special form for efficiently modeling many kinds of seasonal time series and are heavily used in seasonal adjustment. ARIMA is an acronym for AutoRegressive Integrated Moving Average.

A comprehensive term for trading day, holiday, working day, and length of month/quarter effects. These are all effects that are related to changes in the calendar, i.e., the date of a moving holiday or the number of weekdays in a given calendar month.

Time series measuring consecutive changes over a unit of time, such as monthly sales or monthly cash flows, or monthly changes in any stock series.

This is the residual time series that results from the removal of estimated seasonal and other systematic calendar-related components of an observed time series, along with the removal of an estimated trend-cycle component.

These are systematic changes in the values of a time series that are associated with the timing of moving holidays, i.e. holidays whose dates vary from year to year, such as Easter, Passover, Ramadan, Chinese New Year and U.S. Labor Day. Estimates of one or a combination of such effects define the moving holiday component of time series.

Data from an abrupt, untypical movement in the time series, e.g. from a hurricane, a strike, etc., that are likely to distort the estimates of seasonal, trading day or holiday effects. For seasonal adjustment, the software's generic outlier regressors are used to estimate and temporarily (approximately) remove the outliers, in order to prevent distortion of the desired estimates. These protected estimates are removed from the original series to obtain the adjusted series. Consequently, the seasonal and perhaps trading day and holiday effect adjusted series still shows the expected outlier movements. Extreme Value Adjustment refers to the X-11 procedure's more limited form of temporary adjustment, not requiring regression estimation, to protect seasonal effect estimates from distortion by outliers.

In the seasonal adjustment context, a hybrid model in which some features of the time series, such as moving holiday, trading day and outlier effects, are modeled with linear regression variables while the remaining features (those of the regression residuals, including trend, cycle and seasonal components) are modeled with a seasonal ARIMA model.

The estimation of the seasonal component and, when applicable, also trading day and moving holiday effects, followed by their removal from the time series. The goal is usually to produce series whose movements are easier to analyze over consecutive time intervals and to compare to the movements of other series in order to detect co-movements.

A time series whose values quantify (usually in percents or in the units of data measurement, e.g. dollars) variations in the level of the observed series that recur with the same direction and a similar magnitude at time intervals of length one year. (Length is measured in the calendar units of the observed series-- usually quarters or months, sometimes semesters, weeks, or other units.)

This approach is used within TRAMO-SEATS and also within the X-13A-S seasonal adjustment packages. It can simultaneously estimate the different components of a time series.

For the unit of time of the series, months for example, these are time series like end-of-month inventories that arise as the cumulative sum of inflows and outflows (i.e. monthly net flows) starting from some initial value in the past.

A sequence of measurements of an economic (or other) variable made at approximately equally spaced times. It is important that the definition of the variable and the method used to measure it be consistent over time.

As practical concerns, these are systematic effects in monthly times series related to changes in the day-of-week composition of each month and, in some cases, also to changes in the length of February. For flow series (monthly accumulations of daily activity e.g. monthly sales), the increases or decreases from average day-of-week activity associated with the days that occur five times in the month in a given year are important. (If they are days of high sales volumes, the monthly value will be inflated, etc.) For flow series, the length of February can have an impact. (More days than average should produce more sales than average for February.) For stock series, such as end-of-month inventories, the extent to which inventories tend to rise or fall on the day of measurement (e.g. the last day of the month) can have an impact that is different from year to year. Attempts to measure analogous effects in quarterly series are seldom successful. A series of estimated trading day effects defines a trading day component for the time series.

Short for Time Series Regression with ARIMA Noise, Missing Observations, and Outliers.  This approach is used within the TRAMO-SEATS seasonal adjustment software.  It is an approach to estimate and prior correct time series before seasonal adjustment.

Seasonal adjustment software developed by the Bank of Spain. It uses models to estimate the different time series components.

Seasonal adjustment software originally developed by United States Census Bureau. It is based on an iterative application of linear filters.

This is an estimate of the local level of the time series that is expected to include the effects of moderately short- and well as long-term movements associated with the "business cycle". It is often obtained by applying a customized smoothing procedure (a data-dependent "trend filter") to the seasonally adjusted series to suppress its oscillatory movements over short time intervals, i.e. its higher frequency movements.

Seasonal adjustment software developed by Statistics Canada. It incorporates ARIMA modelling to improve estimation of the different time series components.

Seasonal adjustment software developed by the United States Census Bureau. It incorporates regression techniques and also ARIMA modelling to improve estimation of the different time series components.

Seasonal adjustment software developed by the U. S. Census Bureau in collaboration with the Bank of Spain that integrates an enhanced version of X-12-ARIMA with an enhanced version of SEATS to provide both X-11 method seasonal adjustments and ARIMA model-based seasonal adjustments and diagnostics. This is the seasonal adjustment software currently used by the Census Bureau.