Exponential moving Average. Features, Types, and How to Calculate EMA
Exponential moving average (EMA) is a simple and effective tool for smoothing data. It can be used to smooth out the noise in your data, which makes it easier to see trends or patterns that may otherwise have been hidden by random fluctuations. Exponential moving average works best when you are looking at short-term changes. For example, if you want to know how many people visited your website on Monday versus Tuesday, then using an exponential moving average will help you spot any sudden spikes or dips in traffic. If you're trying to predict whether sales of widgets will increase over the next few months, then this method won't work as well because it's not designed to look at longer term trends.
The formula for calculating an Exponential Moving Average is:
EMA ^, where beta is the decay rate and alpha is the weighting factor. The value of alpha determines how much influence each point has on the calculation; higher values mean more emphasis placed on recent points while lower values place greater importance on older ones. You should choose a reasonable range of values for both alpha and beta so they don’t get too extreme. For example, let’s say we wanted to calculate the exponential moving average of our widget sales from last month. We would first need to find the total number of units sold during Jan. To do this, simply add up all the numbers in column B. Next, divide the total amount by 12 to convert them into monthly totals. Now take these figures and multiply them by 0.8. This gives us the new figure for January. Finally, subtract the original total from the new one to give us the difference between the two amounts. Divide this result by 100 to turn it into percentages. These results represent the percentage change in sales compared with January 2012.
To use this technique, enter the following formula into cell C2: B1+ *0.8*ABS . Then drag down through row 2 until you reach the end of the time period you wish to analyze. In my case I am analyzing December 2011 and January 2012. Once you've calculated the EMA, copy the resulting cells across to other columns. As long as there isn't another trend going on within those dates, you'll notice that the exponential moving average will gradually decrease towards zero. When you start seeing a downward slope, you can assume that the overall trend is decreasing. Conversely, if the line starts rising again, then you can conclude that the overall trend is increasing.
Features of exponential moving average (EMA)
Exponential Moving Average:
• Simple & Effective Tool for Smoothing Data • Can Be Used to Spot Trends/Patterns That May Have Been Hidden By Random Fluctuations • Works Best With Short Term Changes • Not Designed to Look At Longer Term Trend
How does EMA Work?
An Exponentially Weighted Moving Average calculates the weighted sum of past observations. Each observation contributes its share of the current estimate based on its distance from today. A low weight is given to distant observations, whereas a high weight is assigned to close observations.
What Is Exponential Moving Average?
An exponentially weighted moving average is a statistical model that uses weights to determine what proportion of the most recently observed information influences the current forecast. EWMA models are often used to smooth noisy signals such as stock prices, but they also provide useful tools for forecasting future events.
Why Use EMA?
The main advantage of using an exponential moving average over simple averages or linear regression techniques is that it allows analysts to detect trends hidden under random fluctuations. It's not uncommon for data sets to have periods when no discernible pattern exists. However, once a clear upward or downward trend begins, it may be difficult to spot because the underlying noise overwhelms any signal. An EMA helps overcome this problem by smoothing out the erratic behavior of the raw data set.
When Should I Use EMA?
EMAs work best at spotting short-term changes. They're less effective at detecting longer term patterns like seasonal cycles or secular growth rates. If your goal is to identify whether a particular product category is growing or shrinking, look elsewhere.
Where Does EMA Come From?
In 1881, Charles Darwin published his book "On the Origin of Species." He proposed that evolution occurs due to natural selection — survival of the fittest. The concept was later popularized in 1896 with the publication of Thomas Huxley’s book “Evolution And Ethics.”
In 1908, John Tukey developed the first mathematical formulation of the idea behind EMAs. His paper described how to calculate the mean value of a series of numbers while taking account of their relative importance. This method became known as the arithmetic mean. Later researchers found ways to improve upon the original algorithm. For example, some methods allow for more than one input variable.
Others take into consideration the volatility of each number. Still others consider both the magnitude and direction of change. These improvements led to the development of many different types of EMAs. Today, there are several hundred variations available.
Types Of Exponential Moving Averages
There are two basic categories of EMAs: symmetric and asymmetric. Symmetrical EMAs use equal weights for all values. Asymmetrical EMAs assign unequal weights to various inputs. In general, these algorithms tend to produce smoother results.
A symmetric exponential moving average assigns equal weights to every point in time. SEMA can be thought of as a combination of multiple moving averages. When applied to financial data, SEMA produces a single line graph showing the overall performance of a security over time.
For example, if you wanted to know which stocks were performing better during the past year, you could create a list of companies ranked from highest to lowest based on their annual returns. Then, you would apply a SEMA to the entire list. Each company would contribute equally toward the final result.
An asymmetric exponential moving average assigns unequal weights to individual points in time. ASEAMA uses exponentially weighted moving averages. EWMA calculates the weighting factor based on the distance between current and previous observations. Thus, recent observations receive greater emphasis than older ones.
This approach makes sense since most investors focus on near-term events rather than long-term trends. Therefore, they care about what happened recently but ignore everything else. By focusing only on recent information, ASEAMA provides a clearer picture of where things stand today.
How To Calculate An Exponentially Weighted Moving Average?
The formula for an EWMA looks something like this:
where represents the current observation; represents the last observed value; represents the weight assigned to the current observation; and represents the sum of all weights up until now.
To determine the appropriate weight, we need to find out how much farther back our target date lies compared to the present day. The answer is simply. We then multiply that by the desired decay rate. Finally, we add it all together.
Example 1: Suppose we want to calculate an EWA with a 50% decay rate using January 3rd, 2010 as the starting point.
Here’s how we do it:
Step 1 – Determine the amount of time elapsed since January 3rd, 2010. Since the start date was three months ago, we subtract three months from the current date. That gives us.
Step 2 – Find the percentage difference between the current date and the target date. If we look at the table above, we see that the target date is March 31st, 2011. So, we divide 100 by 30 days 3.33333%.
Step 3 – Multiply the percentage difference by 0.5. Remember, half of the total weight will go towards the future while the other half goes towards the past. This means that each month has twice the impact on the calculation.
Step 4 – Add both percentages together. Now, we have.50 +.66 1.16 or 16% more weight given to the future.
Exponential moving average is a useful tool when analyzing short term price movements. They provide a clear view into whether prices are trending upward or downward. However, they don't work well for longer periods because they tend to exaggerate small changes. For instance, suppose you're looking at stock market history going back 10 years. You might notice that Apple's share price increased steadily throughout the 1990s before dropping off dramatically after 2000.