# 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.