# How to Calculate an Exponential Moving Average in R

In time series analysis, a moving average is simply the average value of a certain number of previous periods.

An exponential moving average is a type of moving average that gives more weight to recent observations, which means it’s able to capture recent trends more quickly.

This tutorial explains how to calculate an exponential moving average in R.

### Example: Exponential Moving Average in R

Suppose we have the following data frame in R:

```#create data frame
df <- data.frame(period=1:10,
sales=c(25, 20, 14, 16, 27, 20, 12, 15, 14, 19))

#view data frame
df

period sales
1       1    25
2       2    20
3       3    14
4       4    16
5       5    27
6       6    20
7       7    12
8       8    15
9       9    14
10     10    19
```

We can use the movavg() function from the pracma package to calculate the exponentially weighted moving average for a certain number of previous periods.

This function uses the following syntax:

movavg(x, n, type=c(“s”, “t”, “w”, “m”, “e”, “r”))

where:

• x: Time series as numeric vector
• n: Number of previous periods to use for average
• type: Type of moving average to calculate. We will use “e” for exponential weighted moving average.

For example, here’s how to calculate the exponentially weighted moving average using the four previous periods:

```library(pracma)

#create new column to hold 4-day exponentially weighted moving average
df\$EWM_4day <- movavg(df\$sales, n=4, type='e')

#view DataFrame
df

period	sales	4dayEWM
0	1	25	25.000000
1	2	20	23.000000
2	3	14	19.400000
3	4	16	18.040000
4	5	27	21.624000
5	6	20	20.974400
6	7	12	17.384640
7	8	15	16.430784
8	9	14	15.458470
9	10	19	16.875082```

We can also use the ggplot2 visualization library to visualize the sales compared to the 4-day exponentially weighted moving average:

```library(ggplot2)
library(reshape2)

#melt data into format for easy plotting
df <- melt(df ,  id.vars = 'period', variable.name = 'series')

#plot sales vs. 4-day exponentially weighted moving average
ggplot(df, aes(period, value)) +
geom_line(aes(colour = series))
```

The red line displays the sales during each period and the blue line displays the exponentially weighted moving average.

## 3 Replies to “How to Calculate an Exponential Moving Average in R”

1. Lucas says:

How do we choose the weights of the “exponentially weighted moving average”? for example 0.25 or 0.5. Thank you.

2. Bautista Penayo says:

Hey Zach, thank you for this. I just have a question:
I imported an excel file where I have dates instead of the number of days in the column that would be equivalent to Periods in your data frame. Would the function recognize these as days? And also, what if my excel file did not have all data for each consecutive day? What if it jumps from 1/01/2022 to 3/01/2022 instead of 1/01/2022, 2/01/2022, 3/01/2022?

3. Geofract says:

Hi, this was useful to read, thank you.

Though I wonder if it’s possible to ignore the first ‘n’ rows, leave them blank, until ‘n’ rows of the series have passed. Otherwise I would suggest the ema calculation is incorrect in the first 4 iterations of your example, though I don’t claim to be an expert!