Question

Question 3: The following table shows the monthly minimum temperature (degree Celsius C)) of a city in Australia for 3 consequent years Mean of Minimum Temperature Month 2010 2011 2012 18 15.5 12.9 12.5 10 8.1 6.4 7.6 8.7 9 12.2 13.9 15.6 16 14.5 11.8 9.8 7.9 7.1 7.8 9.2 10.6 12.6 14.1 17.7 17.7 13.5 12.3 9.5 7.3 7.6 7.2 10.1 Jan Feb Mar Ma Jun Jul Aug Sep Oct Nov Dec 11.9 13.7 1. Propose a visualisation method to compare the mean of minimum temperature in monthly manner for three given years 2. Aggregate the information to provide a table and visualisation of the temperature in seasonal bases

Answer 1

1 question answer

Time series visualization:

Visualization plays an important role in time series analysis and forecasting.

Plots of the raw sample data can provide valuable diagnostics to identify temporal structures like trends, cycles, and seasonality that can influence the choice of model.

A problem is that many novices in the field of time series forecasting stop with line plots.

They are 6 different types of visualizations that you can use on your own time series data. They are:

1. Line Plots.
2. Histograms and Density Plots.
3. Box and Whisker Plots.
4. Heat Maps.
5. Lag Plots or Scatter Plots.
6. Auto correlation Plots.

The focus is on univariate time series, but the techniques are just as applicable to multivariate time series, when you have more than one observation at each time step.

Download the dataset and place it in the current working directory

Source code

Below is an example of loading the dataset as a Panda Series.

from pandas import Series
from matplotlib import pyplot
series = Series.from_csv('daily-minimum-temperatures.csv', header=0)
print(series.head())

1. Time Series Line Plot

The first, and perhaps most popular, visualization for time series is the line plot.

In this plot, time is shown on the x-axis with observation values along the y-axis.

Below is an example of visualizing the Pandas Series of the Minimum Daily Temperatures dataset directly as a line plot.

from pandas import Series

from matplotlib import pyplot

series = Series.from_csv('daily-minimum-temperatures.csv', header=0)

series.plot()

pyplot.show()

2. Time Series Histogram and Density Plots

Another important visualization is of the distribution of observations themselves.

This means a plot of the values without the temporal ordering.

Some linear time series forecasting methods assume a well-behaved distribution of observations (i.e. a bell curve or normal distribution). This can be explicitly checked using tools like statistical hypothesis tests. But plots can provide a useful first check of the distribution of observations both on raw observations and after any type of data transform has been performed.

The example below creates a histogram plot of the observations in the Minimum Daily Temperatures dataset. A histogram groups values into bins, and the frequency or count of observations in each bin can provide insight into the underlying distribution of the observations.

from pandas import Series

from matplotlib import pyplot

series = Series.from_csv('daily-minimum-temperatures.csv', header=0)

series.hist()

pyplot.show()

3. Time Series Box and Whisker Plots by Interval

Histograms and density plots provide insight into the distribution of all observations, but we may be interested in the distribution of values by time interval.

Another type of plot that is useful to summarize the distribution of observations is the box and whisker plot. This plot draws a box around the 25th and 75th percentiles of the data that captures the middle 50% of observations. A line is drawn at the 50th percentile (the median) and whiskers are drawn above and below the box to summarize the general extents of the observations. Dots are drawn for outliers outside the whiskers or extents of the data.

Box and whisker plots can be created and compared for each interval in a time series, such as years, months, or days.

Below is an example of grouping the Minimum Daily Temperatures dataset by years, as was done above in the plot example. A box and whisker plot is then created for each year and lined up side-by-side for direct comparison.

   
from pandas import Series
from pandas import DataFrame
from pandas import TimeGrouper
from matplotlib import pyplot
series = Series.from_csv('daily-minimum-temperatures.csv', header=0)
groups = series.groupby(TimeGrouper('A'))
years = DataFrame()
for name, group in groups:
   years[name.year] = group.values
years.boxplot()
pyplot.show()