# Exponential smoothing

Last updated August 16, 2023

## What is exponential smoothing?

Exponential Smoothing is a popular that assigns different weights to past observations, giving more importance to recent data. It assumes that the future values are influenced by the previous observations exponentially, with the most recent observations having a greater impact. Exponential Smoothing is particularly useful for time series data that do not exhibit strong trends or .

## Types of exponential smoothing

There are different variations of Exponential Smoothing algorithms, including:

### Simple Exponential Smoothing (SES)

Simple Exponential Smoothing forecasts future values by assigning exponentially decreasing weighted average across all time steps to past observations. The method only considers the level component and assumes that the underlying pattern in the data is driven by a constant level. The algorithms is defined by two main components:

- Level: the current level or smoothed value for
*t*, denoted by*Lt.* - Smoothing Parameter: Denoted by the symbol "α", it dictates how much weight is given to past values when being included in the current level estimate.

### Holt’s Linear Exponential Smoothing

Holt’s Linear Exponential Smoothing, also known as Double Exponential Smoothing, is an extension of Simple Exponential Smoothing that incorporates trends into the forecasting process. It involves two main components:

- Level: The level component represents the smoothed value or average of the series at a given time.
- Trend: The trend component captures the rate of change or slope of the series over time.

Holt’s Linear Exponential Smoothing is useful when the data exhibits a trend but does not have significant seasonality.

### Holt-Winters’ Exponential Smoothing

Holt-Winters’ Exponential Smoothing, also known as Triple Exponential Smoothing, extends Holt’s Linear Exponential Smoothing by incorporating not only trends but also seasonality or cyclical patterns.

It consists of three main components:

- Level: The level component represents the smoothed value or average of the series at a given time.
- Trend: The trend component captures the rate of change or slope of the series over time.
- Seasonality: The seasonality component captures the repeating patterns or cycles within the data.

It is particularly useful when the data exhibits trends and seasonality. It enables the forecasting of future values by capturing both long-term trends and short-term seasonal variations.