Exponential Smoothing for Time Series Data

Data is considered a collection of facts and statistics put together for research and analysis. It is always said that data can take many forms. I’m sure we all have our experiences with structured, unstructured, and even big data. Did you come across time series data?

Unlike the traditional forms of data such as structured and unstructured which are collections of various information, time series data is all about the information of a single object. Time series data captures how the object varies or progresses with time.

Exponential Smoothing is a concept related to time series data or time series analysis, used for smoothing the weights assigned to the data objects. We are going to take a walk through exponential smoothing and its types in this post.

Feel free to check out our take on Time Series Analysis!

Exponential smoothing is a key technique in time series analysis, primarily used for forecasting when no clear trend is visible. It emphasizes recent data points, assigning them more weight compared to older observations. This method is essential for reducing noise and improving the accuracy of short-term predictions in various fields like stock market analysis and weather forecasting.

Introduction to Time Series Data

Before we jump into exponential smoothing, it is necessary to set a base of what time series data actually is and why there is a need for exponential smoothing in the first place.

Time series data consists of data points that are recorded at regular intervals of time. These data points belong to a single object and help in observing a “trend” or “behavior” of the object.

Can you think of any example of time series data right now?

Stock prices that are recorded every day or month, gold prices for the quarter, and rainfall records in an area over two years can be thought of as time series data.

There are four components of time series data:

• Trend
• Seasonality
• Cycle
• Irregularity(Residual)

Understand these components clearly through this post

Coming back to the topic at hand, why do we need exponential smoothing?

The Role of Exponential Smoothing in Time Series

From the above section, we understood that the time series data follows a certain trend or the data has a certain behavior. What if there is no long-term trend at all?

Exponential smoothing in general is used to make short-term forecasts when there is no clear trend displayed by the data points. In other words, exponential smoothing is used to create another set of smoothed data points from the original time series.

In this process, the recent data points are given more weightage such that the importance of the older observations decreases exponentially as the data points begin to stretch over time. Exponential smoothing proceeds with an assumption that the recent data points are more relevant for making predictions for the future.

It is mainly used to reduce the impact of past observations also smoothing out the noise in the data.

There are three types of exponential smoothing.

Let us discuss each of these types briefly.

Simple or Single Exponential Smoothing(SES)

The simple yet effective method of smoothing a time series data is the SES. It is said to be suitable for data with no clear trend or seasonality. The single exponential smoothing requires a parameter called the smoothing factor or constant(α ) to perform smoothing in order to obtain a smoothed statistic.

The formula for SES is as follows:

st = αxt+α(1-α)xt-1+α(1-α)2xt-2+——-

• α- Smoothing constant(0<α<1)
• st – Smoothed statistic
• st-1– Previous observation

Double Exponential Smoothing

Also known as second-order exponential smoothing and Holt Linear smoothing, double exponential smoothing is used when you observe some sort of trend in the data, but no seasonal pattern. Moreover, SES does not perform well when there is even a slight trend in the data.

Similar to Simple Exponential Smoothing, it uses the smoothing factor(α) and also introduces a new term called trend smoothing factor(β).

The formula is a little complicated, but here it is:

st = αxt+(1-α)(st-1+bt-1)

βt=β(st-st-1)+(1-β)bt-1

• st – Smoothed statistic
• st-1 – a previous smoothed statistic
• α- Smoothing constant(0<α<1)
• β – Trend smoothing factor
• t- time period
• bt– best estimate at time period t

Triple Exponential Smoothing

You may have guessed it right away. Also known as the Holt-Winters exponential smoothing, in this case, the smoothing is applied three times. It is most suitable for the data with a seasonal component and a linear trend. Since there is also a seasonal component, another factor(hyperparameter) is introduced.

The formula is as follows:

While the other parameters are the same as the previous variants, we can see two new terms.

• ct – Sequence of the seasonal factor
• γ – seasonal change smoothing factor(0<γ <1)

Summary

To sum it up, we have talked about the time series data in short along with its components, and discussed the need for exponential smoothing in the first place. Later, we discussed about the exponential smoothing in detail and its types.

References

Exponential Smoothing – Wikipedia