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# Time forecasting model algorithms for detecting trends in seasonal time series

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

## Linear - By Time Shifts

 Behavior This algorithm works in three steps: It decomposes the series in K subseries, representing the original series components for each time shift. For example, a subseries containing all the points for Monday-8AM, another subseries containing all the points for Tuesday-9AM, and so on. The time shift granularity is hour for hourly resolution models, and day for daily resolution models. The day of the week is always taken into account. It predicts each subseries separately using a linear regression. It builds the output series, selecting the predicted points from each subseries in the correct order. This algorithm is ideal when a sizable amount of historical data is available, and you detect a clearly periodic behavior in the time series to predict.

An example of a time forecasting model using the Linear - By Time Shifts algorithm

## Holt-Winters

 Behavior This algorithm uses the Holt-Winters Additive model with Exponential Smoothing, explained, for example, in Time series Forecasting using Holt-Winters Exponential Smoothing, by Prajakta S. Kalekar, Kanwal Rekhi School of Information Technology, 2004. A confidence band with 90% confidence is also calculated. This algorithm is suitable when the time series shows both trend and additive seasonality.

An example of a time forecasting model using the Holt-Winters algorithm

## Linear - Yearly Time Shift

 Behavior This algorithm works in three steps: It calculates a linear trend on the given data. You can configure the algorithm to use the classic Minimum Least Squares method or the Robust Linear method. It replicates the original signal and adds the calculated trend, assuming a known (configurable) seasonality period, for example, 365 days. It calculates confidence bands using configurable values. This algorithm is suitable when the time series has a known seasonality period. It produces particularly effective results on yearly-based seasonality when you expect to have similarly shaped data over the course of a number of years.

An example of a time forecasting model using the Linear - Yearly Time Shift algorithm