Exponential Smoothing models are a broad class of forecasting models that are intuitive, flexible, and extensible.

Members of this class include simple, single parameter models that predict the future as a linear combination of a previous level and a current shock. Extensions can include parameters for linear or non-linear trend, trend damping, simple or complex seasonality, related series, various forms of non-linearity in the forecasting equations, and handling of irregular time series.

Exponential Smoothing assumes that a series extends infinitely into the past, but that influence of past on future, decays smoothly and exponentially fast. The smooth rate of decay is expressed by one or more smoothing constants. The smoothing constants are parameters that the model estimates. The assumption is made practical for modeling real world data by using an equivalent recursive formulation that is only expressed in terms of an estimate of the current level based on prior history and a shock to that estimate dependent on current conditions only.The procedure requires an estimate for the time period just prior to the first observation, that encapsulates all prior history. This initial observation is an additional model parameter whose value is estimated by the modeling procedure.

Components of ESM such as trend and seasonality extensions, can have an additive or multiplicative form. The simpler additive models assume that shock, trend, and seasonality are linear effects within the recursive formulation.

Simple Exponential Smoothing assumes the data fluctuates around a stationary mean, with no trend or seasonal pattern.

In simple exponential smoothing model, each forecast (smoothed value) is computed as the weighted average of the previous observations, where the weights decrease exponentially depending on the value of smoothing constant α. Values of the smoothing constant, α, near one, put almost all weight on the most recent observations. Values of α near zero allows the distant past observations to have a large influence.

The preferred form of additive (linear) trend is sometimes called Holt’s method or double exponential smoothing.

Models with trend add a smoothing parameter γ and optionally a damping parameter φ. The damping parameter smoothly dampens the influence of past linear trend on future estimates of level, often improving accuracy.

When the time series average does not change over time (stationary), but is subject to seasonal fluctuations, the appropriate model has seasonal parameters but no trend.

Seasonal fluctuations are assumed to balance out over periods of length m, where m is the number of seasons, For example, m=4 might be used when the input data are aggregated quarterly. For models with additive errors, the seasonal parameters must sum to zero. For models with multiplicative errors, the product of seasonal parameters must be one.

Holt and Winters introduced both trend and seasonality in Exponential Smoothing Model(ESM). The original model, also known as Holt-Winters or triple exponential smoothing, considered an additive trend and multiplicative seasonality. Extensions include models with various combinations of additive and multiplicative trend, seasonality and error, with and without trend damping.

To compute prediction intervals, Exponential Smoothing Model (ESM) is divided into three classes.

The simplest class is the class of linear models, which include, among others, simple ESM, Holt’s method, and additive Holt-Winters. Class 2 models (multiplicative error, additive components) make an approximate correction for violations of the Normality assumption. Class 3 modes use a simple simulation approach to calculate prediction intervals.

Time Series analysis, requires ordered input data. Hence, each data row must consist of an [index, value] pair, where the index specifies the ordering.

When the CREATE_MODEL procedure is used to initiate an Exponential Smoothing (ESM) model build, the CASE_ID_COLUMN_NAME specifies the column used to compute the indices of the input and the TARGET_COLUMN_NAME specifies the column used to compute the observed time series values. The time column bears Oracle number, or Oracle date, timestamp, timestamp with time zone, or timestamp with local time zone. The input time series are sorted according to the values of CASE_ID (time label). The case id column cannot contain missing values. The value column can contain missing values indicated as NULL. ESM also supports partitioned models and in such cases, the input table contains an extra column specifying the partition. All [index, value] pairs with the same partition ID form one complete time series. Exponential Smoothing constructs models for each partition independently, although all models use the same model settings.

Properties of the data can result in a warning message or settings are ignored. Settings are ignored when If the user specifies a model with either multiplicative trend, multiplicative seasonality or both and the data contains values Y_t<= 0, then the model type is set to the default. If the series contain fewer values than the number of user-specified seasons, then the seasonality specifications are ignored with a warning.

For Exponential Smoothing algorithms, the accumulation procedure is applied when the column is a date type (date, datetime, timestamp, timestamp with timezone, or timestamp with local timezone).

The case id can be a NUMBER column whose sort index represents the position of the value in the time series sequence of values. The case id column can also be a date type. A date type is accumulated in accordance with a user specified accumulation window. Regardless of type, the case id is used to transform the column into an equally spaced time series. No accumulation is applied for a case id of type NUMBER. As an example, consider a time series about promotion events. The time column contains the date of each event, and the dates can be unequally spaced. The user must specify the spacing interval, which is the spacing of the accumulated or transformed equally spaced time series. In the example, if the user specifies the interval to be month, then an equally spaced time series with profit for each calendar month is generated from the original time series. Setting EXSM_INTERVAL is used to specify the spacing interval. The user must also specify a value for EXSM_ACCUMULATE, for example, EXSM_ACCU_MAX, in which case the equally spaced monthly series would contain the maximum profit over all events that month as the observed time series value.

Input time series can contain missing values. A NULL entry in the target column indicates a missing value. When the time column is of the type datetime, the accumulation procedure can also introduce missing values. The setting EXSM_SETMISSING can be used to specify how to handle missing values. The special value EXSM_MISS_AUTO indicates that, if the series contains missing values it is to be treated as an irregular time series.

Exponential Smoothing Model (ESM) can be applied to make predictions by specifying the prediction window.

Setting EXSM_PREDICTION_STEP can be used to specify the prediction window. The prediction window is expressed in terms of number of intervals (setting EXSM_INTERVAL), when the time column is of the type datetime. If the time column is a number then the prediction window is the number of steps to forecast. Regardless of whether the time series is regular or irregular, EXSM_PREDICTION_STEP specifies the prediction window.

Oracle Advanced Analytics supports parallellism by partition.

For example, a user can choose PRODUCT_ID as one partition column and can generate forecasts for different products in a model build. Although a distinct smoothing model is built for each partition, all partitions share the same model settings. For example, if setting EXSM_MODEL is set to EXSM_SIMPLE, all partition models will be simple exponential smoothing models. Time series from different partitions can be distributed to different processes and processed in parallel. The model for each time series is built serially.