EWMA

Edited byAshish Kumar Srivastav
Reviewed byDheeraj Vaidya, CFA, FRM

What Is EWMA?

The Exponentially Weighted Moving Average (EWMA) refers to an average of data used to track the portfolio’s movement by checking the results and output by considering the different factors and giving them the weights. Then, tracking results to evaluate the performance and make improvements.

EWMA

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Weight for an EWMA reduces exponentially for each period that goes further in the past. Also, since EWMA contains the previously calculated average, hence the result of the Exponentially Weighted Moving Average will be cumulative. Because of this, all the data points will contribute to the result, but the contribution factor will go down as calculated in the next EWMA period.

Key Takeaways

  • The Exponentially Weighted Moving Average (EWMA) is a data average that one can use to discover the portfolio’s development by determining the outcome and output by considering the diverse factors and enabling them with the weights. Moreover, one may know the results to calculate the performance and improve.
  • It displays the data geometrically, so data only get affected a little when outliers occur.
  • It is an instrument for finding more minor shifts in the time-bound process.

EWMA Explained

EWMA is a tool for detecting smaller shifts in the mean of the time-bound process. An exponentially weighted moving average is also highly studied and used as a model to find a moving average of data. It is also very useful in forecasting event based on past data.

The Exponentially Weighted Moving Average is an assumed basis that observations are normally distributedNormally DistributedNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more. It considers past data based on their weightage. As the data is more from the past, its weight for the calculation will decrease exponentially.

Users can also give weight to the past data to find a different set of EWMA basis different weightage. Also, because of the geometrically displayed data, data doesn’t get affected much because of the outliers. Hence, more smoothed data can be achieved using this method.

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Formula

This EWMA formula shows the value of the moving average at a time t. Its application would help us understand the EWMA volatility and its implications.

EWMA(t) = a * x(t) + (1-a) * EWMA(t-1)
 

Where,

  • EWMA(t) = moving average at time t
  • a = degree of mixing parameter value between 0 and 1
  • x(t) = value of signal x at time t

This formula states the value of moving averageMoving AverageMoving Average (MA), commonly used in capital markets, can be defined as a succession of mean that is derived from a successive period of numbers or values and the same would be calculated continually as the new data is available. This can be lagging or trend-following indicator as this would be based on previous numbers.read more at time t. Here, a parameter shows the rate at which it will calculate the older data. The value of a will be between 0 to 1.

Suppose a=1 means only the most recent data used to measure EWMA. If a is nearing 0, that means more weightage is to older data. If a is near 1, newer data has given more weightage.

Examples

Below are the examples of Exponentially Weighted Moving Average or EWMA filter. These examples shall help us understand the concept in depth.

You can download this EWMA Excel Template here – EWMA Excel Template

Example #1

Let’s consider 5 data points as per the below table:

Time (t)Observation (x)
140
245
343
431
520

And parameter a = 30% or 0.3

So EWMA(1) = 40

EWMA for time 2 is as follows:

EWMA Example 1.2
  • EWMA(2) = 0.3*45 + (1-0.3)*40.00
  • = 41.5

Similarly, calculate the exponentially weighted moving average for given times:

Example 1.3
  • EWMA(3) = 0.3*43 + (1-0.3)*41.5 = 41.95
  • EWMA(4) = 0.3*31 + (1-0.3)*41.95 = 38.67
  • EWMA(5) = 0.3*20 + (1-0.3)*38.67 = 33.07

Example #2

We are having the temperature of a city in degrees Celsius from Sunday to Saturday. Using =10%, we will find the moving average temperature for each day of the week.Using a =10%, we will find an exponentially weighted moving average for each day in the below table:

Weekday (t)Temperature oc (x)
Sunday24
Monday30
Tuesday36
Wednesday25
Thursday22
Friday29
Saturday30

Using a =10%, we will find an exponentially weighted moving average for each day in the below table:

Example 2.2

Below is the graph showing a comparison between the actual temperature and EWMA:

Example 2.3

As we can see, smoothing is quite strong, using =10%. In the same way, we can solve the exponentially weighted moving average for many kinds of time series or sequential datasets.

Importance

Below are a few points to consider when discussing EWMA:

  • One can use this method in chemical and day-to-day accounting processes in the real world.
  • One can also use it to show website visitors’ fluctuations on days of the week.

Advantages & Disadvantages

The EWMA volatility has its own set of advantages and disadvantages. Let us understand them through the discussion below.

Advantages

Disadvantages

  • One can only use it when continuous data is available.
  • One can use it only when we want to detect a small shift in the process.
  • One can use this method to calculate the average. Monitoring variance requires the user to use some other technique.

Frequently Asked Questions (FAQs)

What does EWMA stand for?

The Exponentially Weighted Moving Average, or EWMA, is a statistic for knowing the technique that averages the data. In addition, it also facilitates less weight to data as they are further discarded in time.

What is half-life in EWMA?

Half-life means the phase for the exponential weight to minimize to one-half. In addition, alpha is the smoothing factor.

What is the difference between EWMA and CUSUM?

The EWMA is suitable for deciding where the process follows a signal. At the same time, one may use the CUSUM to determine how to estimate when the shift may occur.

What is EWMA volatility?

The exponentially weighted moving average (EWMA) volatility model is recommended for predicting the RiskMetrics group volatility. In addition, for monthly data, the EWMA model parameter is suitable to place 0.97.

Recommended Articles

This article has been a guide to what is EWMA. Here we explain its formula, along with step-by-step examples, and discussed its importance. You can learn more from the following articles: –