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# Time forecasting model algorithms for detecting trends in monotonic data

This topic lists and describes time forecasting model algorithms that are suitable for detecting trends in monotonic data:

## Linear

 Behavior The algorithm fits a linear regression line using the Minimum Least Squares method, and uses the line to predict future points. The model also calculates the 95% confidence interval for the regression line, displaying the upper and lower bounds. This algorithm is widely used, because it is suitable for non-periodic or high-granularity data (for example, day resolution).

An example of a time forecasting model using the Linear algorithm ## Robust Linear

 Behavior A variant of the Linear algorithm that applies outlier filter to input data before estimating the regression. Specifically, the algorithm uses an M-estimation for robust regression. This model also calculates the 95% confidence interval for the regression line, displaying the upper and lower bounds. This algorithm adds robustness to the Linear algorithm, making it suitable for data with outliers (for example, abnormal peaks).

An example of a time forecasting model using the Robust Linear algorithm ## Robust Linear - Last Ramp

 Behavior This algorithm works in two steps: It detects the last ramp in the time series, that is, the part that follows the last statistical change in the time series. The change is detected using mean and variance over a moving window, and analyzing the variation between adjacent windows. It applies the #Robust Linear algorithm to only this last ramp. This algorithm is suitable for time series that present a step-like, or sawtooth-like, behavior. These series reflect rapid variations due to configuration changes. For example, when you modify the configuration, for example, to expand a storage volume and instantly allocate more space or to add bandwidth to a network link, the resource utilization data reflects this configuration change instantaneously. This model filters the data before such as configuration change, which is not useful in predicting behavior and trends with the new configuration.

An example of a time forecasting model using the Robust Linear - Last Ramp algorithm ## Robust Linear - Smoothed Last Ramp

 Behavior The algorithm is similar to #Robust Linear - Last Ramp, except that it applies a smoothing filter on historical data after detecting the last ramp in the time series. The smoothing filter consists of a Seasonal Decomposition, after which only the resulting trend component is considered for the prediction. Seasonal Decomposition works using the LOESS method. This algorithm is also suitable for time series that present a step-like, or sawtooth-like, behavior, and is particularly useful for high variance series and for data containing outliers.

An example of a time forecasting model using the Robust Linear - Smoothed Last Ramp algorithm Behavior This algorithm uses the Minimum Least Squares method to estimate a second-degree polynomial fitting on smoothed data obtained with Seasonal Decomposition (as described in #Robust Linear - Smoothed Last Ramp, and uses the line to predict future points. This algorithm is suitable for time series that reflect non-linear behavior with a quadratic increase.

An example of a time forecasting model using the Quadratic algorithm ## Cubic

 Behavior This algorithm uses the Minimum Least Squares method to estimate a third-degree polynomial fitting on smoothed data obtained with Seasonal Decomposition (as described in #Robust Linear - Smoothed Last Ramp, and uses the line to predict future points. This algorithm is suitable for time series that reflect non-linear behavior with an increase more rapid than quadratic.

An example of a time forecasting model using the Cubic algorithm ## Exponential - Multiplicative Trend

 Behavior This algorithm uses the Minimum Least Squares method to estimate an exponential fitting on smoothed data obtained with Seasonal Decomposition (as described in #Robust Linear - Smoothed Last Ramp, and uses the line to predict future points. This algorithm is suitable for time series that reflect non-linear behavior with an increase more rapid than polynomial.

An example of a time forecasting model using the Exponential - Multiplicative Trend algorithm ## Robust Exponential Damping

 Behavior This algorithm works in two steps: It smoothes the data using Exponential Damping. It forecasts the smoothed data with a robust regression. This algorithm is ideal for forecasting the underlying mean behavior of data that has significant variation.

An example of a time forecasting model using the Robust Exponential Damping algorithm ## Robust Exponential Damping - Last Ramp

 Behavior This algorithm is similar to #Robust Linear - Last Ramp, except that the smoothing is done using Exponential Damping. Similar to Robust Linear - Last Ramp, this algorithm is suitable for time series that present a step-like, or sawtooth-like, behavior. However, models that use this algorithm can result in more pessimistic predictions than models that use the Robust Linear - Last Ramp algorithm.

An example of a time forecasting model using the Robust Exponential Damping - Last Ramp algorithm 