To calculate exponential moving averages in pandas, we can use the pandas **ewm()** function.

`df.ewm(span=10, adjust=False).mean() # Calculate the Exponential Weighted Moving Average over a span of 10 periods`

When working with data, many times we want to calculate summary statistics to understand our data better. One such statistic is the moving average of time series data. With pandas, we can calculate both equal weighted moving averages and exponential weighted moving averages.

To calculate exponential weights moving averages in Python, we can use the pandas **ewm()** function.

Let’s say we have the following DataFrame.

```
df = pd.DataFrame({'Month': [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],
'Weight':[100,110,120,115,105,120,125,100,120,110,105,130,120,135,125,115,120,110,100,115]})
print(df)
# Output:
Month Weight
0 1 100
1 2 110
2 3 120
3 4 115
4 5 105
5 6 120
6 7 125
7 8 100
8 9 120
9 10 110
10 11 105
11 12 130
12 13 120
13 14 135
14 15 125
15 16 115
16 17 120
17 18 110
18 19 100
19 20 115
```

Let’s calculate some exponentially weighted moving averages with the pandas **ewm()** function.

First, let’s start with a moving average with each average spanning 5 periods.

```
df["5 Period EMA"] = df["Weight"].ewm(span=5).mean()
print(df)
# Output:
Month Weight 5 Period EMA
0 1 100 100.000000
1 2 110 106.000000
2 3 120 112.631579
3 4 115 113.615385
4 5 105 110.308057
5 6 120 113.849624
6 7 125 117.797475
7 8 100 111.624108
8 9 120 114.490637
9 10 110 112.967342
10 11 105 110.280498
11 12 130 116.904721
12 13 120 117.941809
13 14 135 123.647417
14 15 125 124.099310
15 16 115 121.061582
16 17 120 120.707362
17 18 110 117.135825
18 19 100 111.421305
19 20 115 112.614562
```

If we want a bigger window, we can adjust the “span” parameter.

```
df["8 Period EMA"] = df["Weight"].ewm(span=8).mean()
print(df)
# Output:
Month Weight 8 Period EMA
0 1 100 100.000000
1 2 110 105.625000
2 3 120 111.658031
3 4 115 112.829327
4 5 105 110.397235
5 6 120 113.137905
6 7 125 116.322207
7 8 100 112.134192
8 9 120 114.085385
9 10 110 113.097489
10 11 105 111.177039
11 12 130 115.575478
12 13 120 116.597668
13 14 135 120.812017
14 15 125 121.764646
15 16 115 120.233939
16 17 120 120.181217
17 18 110 117.893909
18 19 100 113.883645
19 20 115 114.133363
```

## Other Exponential Weighted Functions with pandas ewm()

With the pandas **ewm()** function, we can calculate more than just exponentially weighted moving averages.

We can also calculate exponentially weighted variances, standard deviations, correlations, and covariances.

To do this, we just need to tack on the appropriate function call.

For example, if we have the same dataset from above, we can calculate the exponentially weighted variance by using the pandas var() function.

```
df["5 Period EW Var"] = df["Weight"].ewm(span=5).var()
print(df)
# Output:
Month Weight 5 Period EW Var
0 1 100 NaN
1 2 110 50.000000
2 3 120 97.368421
3 4 115 53.188259
4 5 105 54.839592
5 6 120 62.391316
6 7 125 76.276032
7 8 100 140.828706
8 9 120 111.987911
9 10 110 79.362125
10 11 105 70.280399
11 12 130 155.434896
12 13 120 105.895898
13 14 135 151.521081
14 15 125 101.349800
15 16 115 90.523566
16 17 120 60.616397
17 18 110 72.258521
18 19 100 129.758539
19 20 115 90.044759
```

If we want to calculate an exponentially weighted moving standard deviation, we can use the pandas std() function.

```
df["5 Period EW Std"] = df["Weight"].ewm(span=5).std()
print(df)
# Output:
Month Weight 5 Period EW Std
0 1 100 NaN
1 2 110 7.071068
2 3 120 9.867544
3 4 115 7.293028
4 5 105 7.405376
5 6 120 7.898817
6 7 125 8.733615
7 8 100 11.867127
8 9 120 10.582434
9 10 110 8.908542
10 11 105 8.383341
11 12 130 12.467353
12 13 120 10.290573
13 14 135 12.309390
14 15 125 10.067264
15 16 115 9.514387
16 17 120 7.785653
17 18 110 8.500501
18 19 100 11.391161
19 20 115 9.489192
```

Hopefully this article has been helpful for you to understand how to use the pandas **ewm()** function to calculate exponentially weighted moving averages and other statistics in your Python code.