In order to understand the time series dataset, let's randomly generate a normalized dataset:

1. We can generate the dataset using the numpy library:

import os
import numpy as np
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns

zero_mean_series = np.random.normal(loc=0.0, scale=1., size=50)
zero_mean_series

We have used the NumPy library to generate random datasets. So, the output given here will be different for you. The output of the preceding code is given here:

array([-0.73140395, -2.4944216 , -1.44929237, -0.40077112,  0.23713083, 0.89632516, -0.90228469, -0.96464949, 1.48135275,  0.64530002, -1.70897785,  0.54863901, -1.14941457, -1.49177657, -2.04298133, 1.40936481,  0.65621356, -0.37571958, -0.04877503, -0.84619236, -1.46231312,  2.42031845, -0.91949491,  0.80903063,  0.67885337, -0.1082256 , -0.16953567,  0.93628661,  2.57639376, -0.01489153, 0.9011697 , -0.29900988,  0.04519547,  0.71230853, -0.00626227, 1.27565662, -0.42432848,  1.44748288,  0.29585819,  0.70547011, -0.6838063 ,  1.61502839, -0.04388889,  1.06261716,  0.17708138, 0.3723592 , -0.77185183, -3.3487284 ,  0.59464475, -0.89005505])

2. Next, we are going to use the seaborn library to plot the time series data. Check the code snippet given here:

plt.figure(figsize=(16, 8))
g = sns.lineplot(data=zero_mean_series)
g.set_title('Zero mean model')
g.set_xlabel('Time index')
plt.show()

We plotted the time series graph using the seaborn.lineplot() function which is a built-in method provided by the seaborn library. The output of the preceding code is given here:

3. We can perform a cumulative sum over the list and then plot the data using a time series plot. The plot gives more interesting results. Check the following code snippet:

random_walk = np.cumsum(zero_mean_series)
random_walk

It generates an array of the cumulative sum as shown here:

array([ -0.73140395,  -3.22582556,  -4.67511792,  -5.07588904,-4.83875821,  -3.94243305,  -4.84471774,  -5.80936723,-4.32801448,  -3.68271446,  -5.39169231,  -4.8430533 ,-5.99246787,  -7.48424444,  -9.52722576,  -8.11786095,-7.46164739,  -7.83736697,  -7.886142  ,  -8.73233436, -10.19464748,  -7.77432903,  -8.69382394,  -7.88479331,-7.20593994,  -7.31416554,  -7.4837012 ,  -6.5474146 ,-3.97102084,  -3.98591237,  -3.08474267,  -3.38375255,-3.33855708,  -2.62624855,  -2.63251082,  -1.35685419,-1.78118268,  -0.3336998 ,  -0.03784161,   0.66762849,-0.01617781,   1.59885058,   1.55496169,   2.61757885, 2.79466023,   3.16701943,   2.3951676 ,  -0.9535608 ,-0.35891606,  -1.2489711 ])

Note that for any particular value, the next value is the sum of previous values.

4. Now, if we plot the list using the time series plot as shown here, we get an interesting graph that shows the change in values over time:

plt.figure(figsize=(16, 8))
g = sns.lineplot(data=random_walk)
g.set_title('Random Walk')
g.set_xlabel('Time index')
plt.show()

The output of the preceding code is given here:

Note the graph shown in the preceding diagram. It shows the change of values over time. Great – so far, we have generated different time series data and plotted it using the built-in seaborn.tsplot() method.