What does exponential smoothing mean

The formula for the single exponential smoothing is given by:. DES adds support particularly for trends in the univariate time series. The name is derived from the name of developer of the method Charles Holt.

This method aids changing trends with time in different ways, either additively or multiplicatively, counted on if the trend is linear or exponential correspondingly, i.

When the forecasts have longer range or multi forecasting steps, the trend approaches to become unrealistic such that assisting in dampening the trend over time.

Here dampening implies the decreasing the size of the trend over future time steps down to a straight line no trend. Dampening the trend takes place the same as modelling the trend, in particular with additively or multiplicatively for linear or exponential dampening effect respectively.

In this case, a damping coefficient phi is used to determine and control the dampening rate, i. Additive Dampening: Make a damped trend linea r. TES explicitly adds support to the univariate time series for seasonality; it is also referred to as Holt-Winters Exponential Smoothing on the name of two contributors Charles Holt and Peter Winters.

The Holt-Winters exponential smoothing model permits the level, trend and seasonality patterns to change over time as it is an adaptive method. In correspondence with the trend, seasonality can be modeled in the particular of additive or multiplicative process for the linear and exponential variation in the seasonality. Multiplicative Seasonality: TES with an exponential seasonality. Being an advanced variation of exponential smoothing, TES can construct single and double exponential smoothing models through configuration.

In addition to that, in order to make and ensure the accuracy of seasonality models, one should specify the number of time steps in a seasonal period. These methods are the family of traditional forecasting algorithms that work efficiently when time series data exhibit a clear and seasonal pattern.

Exponential smoothing has the elements as Error, Trend, and season that can be either additively or multiplicatively. In order to find the trend, season or error, time series decomposition is an accurate approach as it makes the plot of each component as a distinct subplot. As the trends reflect upward or downward behavior tendency , applied as additively, and if varies exponentially, it is multiplicative.

Brown, R. Statistical forecasting for inventory control. Holt, C. Forecasting seasonals and trends by exponentially weighted averages O. Memorandum No. Winters, P. Forecasting sales by exponentially weighted moving averages.

For the methods that follow there is usually more than one smoothing parameter and more than one initial component to be chosen. In some cases, the smoothing parameters may be chosen in a subjective manner — the forecaster specifies the value of the smoothing parameters based on previous experience.

However, a more reliable and objective way to obtain values for the unknown parameters is to estimate them from the observed data. In Section 5. Similarly, the unknown parameters and the initial values for any exponential smoothing method can be estimated by minimising the SSE. Unlike the regression case where we have formulas which return the values of the regression coefficients that minimise the SSE , this involves a non-linear minimisation problem, and we need to use an optimisation tool to solve it.

In this example, simple exponential smoothing is applied to forecast oil production in Saudi Arabia. In Table 7. The black line in Figure 7. Figure 7. The forecasts for the period — are plotted in Figure 7.

Also plotted are one-step-ahead fitted values alongside the data over the period — The prediction intervals shown here are calculated using the methods described in Section 7.