Exponential smoothing

Exponential smoothing is a popular family of statistical techniques and processes for discrete time series data that is used to forecast the neaIntroducti

This strategy works with time series data that has seasonal components, or systematic trends were past observations were used to construct predictions. 

Exponential smoothing is seen as a peer or alternative to the well-known Box jenkins ARIMA class of time series forecasting algorithms. 

The methods are referred regarded as ETS models since they explicitly model Errors, Trend, and Seasonality.

How does exponential smoothing operate, and what is it

While the most weight is given to current observations, less weight is given to the observations immediately before them, less weight is given to the observation before that, and so on, so that weighted values follow/ represent exponential decay in terms of historical data effect.

. In other words, the larger the related weight, the more recent the observation.” – Principles and Practice of Forecasting

Exponential smoothing has been widely employed in forecasting applications at the strategic, tactical, and operational levels for more than half a century, technologie

At a strategic level The forecasting method is used to plan for investment and growth, as well as the influence of new technologies. 

At the tactical level, forecasting is used to determine spending, inventory concerns, and customer satisfaction. 

At the operational level, forecasting is used to set goals, predict quality, and confirm compliance with standards.

Exponential Smoothing Types 

Exponential smoothing approaches that rely on trends and seasonality are divided into three categories. 

They’re there

Smoothing Exponentials in a Simple WayWa

When the data, in particular, does not support any of the above, SES is utilized for time series anticipation. 

Trend :- A slope that is slanted either uphill or downward.

Seasonality is defined as a pattern that emerges as a result of seasonal factors such as hours,days, years, and downwar

Only the level component is estimated by a single exponential smoothing.

Weighted averages are used by SES. 

Again, the biggest weights correspond to recent data,whereas the smallest weights correspond to previous observations. 

Smoothing parameter (alpha – single parameter/hyperparameter) is always used to determine the weight of each parameter or the decrease in weight. 

A value around 1 suggests quick learning (i.e., just the most recent values influence forecasts), whereas a value near 0 indicates slow learning (past observations have a large influence on forecasts). Practical Time Series Forecasting in R is the source of this information. 

For single exponential smoothing, a hyperparameter information

Alpha is a level smoothing factor)

Smoothing with two exponentials (DES)

DES adds support for patterns in univariate time series in particular. Holt’s linear trend model is the name given to it when it is combined with additive trends. The name comes from the name of the method’s creator, Charles HoHoltD

This strategy assists in modifying trends through time in many ways, either additively or multiplicatively, depending on whether the trend is linear or exponential, i.e.

Smoothing with two exponential (DES)  LinearTrend: Additive Trend 

Smoothing with exponential  an Exponential Trend: Multiplicative Trend 

The trend may continue to be abnormally long in longer-term (multi-step) forecasts. 

As a result, it may be beneficial to slow down the tendency over timtren

Dampening is the process of diminishing the magnitude of a trend over time until it becomes a straight line (no trend).

Holt’s linear approach forecasts show a consistent trend (growing or decreasing) indecently into the future. 

The exponential trend technique generates even more severe forecasts[…] 

In response to this finding, […] created a parameter that “dampens” the tendency to a flatline at a later date.

Smoothing with three exponentials 

Triple Exponential Smoothing is a type of  Smoothing that takes seasonality into account in univariate time series.

Triple Exponential Smoothing with exponential seasonality (Multiplicative Seasonality). 

Triple exponential smoothing is the most complex form of exponential smoothing, and it is achieved by configuring the hyperparameter

Hyperparameters: 

Alpha is a level smoothing factor. 

Beta is a trend smoothing factor. 

Gamma is a seasonality smoothing factor. 

Additive or multiplicative trends. 

Additive or multiplicative dampening. 

Phi stands for damping coefficient. 

Time intervals in a seasonal period

Exponential Smoothing: How to Set It Up 

It is possible to specify all of the model hyperparameters explicitly. 

This can be difficult for both professionals and beginners. 

Instead, numerical optimization is commonly used to find and fund the smoothing coefficients (alpha, beta, gamma, and phi) for the model with the least error. 

[…] Estimating the unknown parameters contained in any exponential smoothing algorithm using observable data is a more robust and objective way to obtain values for them. […] any exponential smoothing method’s unknown parameters and initial values can be calculated by reducing the SSE. [the sum of squared mistake

Conclusion:

Exponential smoothing is a univariate time series forecasting method that can be extended to data with a systematic trend or seasonal component. It’s a powerful forecasting tool that can be employed instead of the well-known Box-Jenkins ARIMA family of algorithms.