# Natural language details for time series

Details for time series provide text insights based on the analysis of the time series data and corresponding forecasting models.

## Overview

IBM® Cognos Analytics with Watson reports details for time series for a visualization that is created in an exploration whenever the visualization data contains a single time series and a forecasting model is computed. If the data is suitable, time series insights are generated even if the Forecasting dialog box is not present on the visualization. When the Forecasting dialog box is present, it produces the same default model upon activation as the time series insights. Time series points are automatically sorted in chronological order for purpose of the insights detection, but unlike in the forecasting feature, the time points displayed in the visualization are not sorted.

## Algorithms

Details for time series are based on an exponential smoothing model for the observed time series data. Observed time series values and computed model components are used to create insights for the time series: unusual values, seasonal effects, and trend insight. Each type of insight depends on a different combination of data and corresponding exponential smoothing model components.

## Details

**Unusual values**

An exponential smoothing model provides a predicted value for each observed time point. A predicted value at a time point is the one-step ahead forecast at the previous time point. A confidence interval for each predicted value is computed that uses the corresponding predicted value variance that depends on the model. An observed time series value that is found outside of the confidence interval for corresponding predicted value based on the model is considered to be an unusual value.

Unusual values are detected based on the selected exponential smoothing model for the time series. The confidence level that is used for computing the prediction confidence intervals is 99.74%. Up to five unusual values are reported by listing the corresponding time points. Cognos Analytics does not list the points in chronological order but rather in decreasing order of distance from the confidence interval. More unusual points are listed first. Unusual values are specified as unusually high or unusually low when possible.

An unusual value that is detected at the last time point is reported separately. This might indicate that data is incomplete. For example, summarized value for the last month might reflect daily data halfway through the month only.

**Seasonal effects**

The seasonal effects insight reveals the seasonal length for a time series that is identified by the model. Seasonal length corresponds to a fixed duration of a seasonal pattern established in the time series. For example, average temperature variation across 12 months establishes an annual pattern. This insight also provides the strength of the seasonal effects and reports periods with the largest and the smallest seasonal values.

The seasonal length is obtained from the selected model. It is derived from the seasonal period and date or time interval that is reported in the forecasting statistical details. A seasonal model is selected only if it provides a fit superior to all non-seasonal models. The seasonal period for the selected seasonal model is obtained by comparing models with multiple candidate seasonal periods.

Seasonal effects are reported as weak, moderate, or strong depending on the computed strength value. Strength of seasonal effects is computed as a reduction in model error by the seasonal model compared to matching non-seasonal model and divided by the non-seasonal model error. This is different from the seasonality strength reported in the forecasting statistical details where the difference in accuracy between the two models is reported.

The largest and the smallest seasonal values are computed based on the underlying seasonal model component averages across all seasonal patterns in the time series. Corresponding periods are reported if the average values are consistently the largest, or the smallest, over majority of the seasonal patterns.

**Trend**

The trend insight reports an overall positive or negative direction of the time series values when present. It also reports the strength of the trend.

Both level and trend components are extracted from the corresponding exponential smoothing model. Only the level component is used if the model has no trend component. This defines a trend curve for the time series data. Kendall’s tau measure of association and corresponding statistical test are then computed for the trend curve. They detect an overall positive or negative direction of the time series values. Different tau value ranges define reported strength degree for the trend: weak, moderate, or strong.

For more information on exponential smoothing models, see Forecasting models.