Here we will discuss the graphical representation of time series data, called historigram.

As we have discussed in the introduction to Time Series, given an observed time series, the first step in analyzing a time series is to plot the given series on a graph taking time intervals ($t$) along X-axis (as an independent variable) and the observed value ($Y_t$) on Y-axis (as the dependent variable: as a function of time). Such a graph will show various types of fluctuations and other points of interest.

A historigram is a graphical representation of a time series that reveals the changes that occurred at different time periods. The first step in the prediction (or forecast) of a time series involves an examination of the set of past observations. In this case, the historigram may be a useful tool. The construction of this involves the following steps described below:

- Use an appropriate scale and take time $t$ along the $x$-axis as an independent variable.
- Use an appropriate scale, and plot the observed values of variable $Y$ as a dependent variable against the given points of time.
- Join the plotted points by line segments to get the required graphical representation.

### Historigram Example

Draw a graphical representation of the data to show the population of Pakistan in various census years.

Census Year | 1951 | 1961 | 1972 | 1981 | 1998 | 2017 |

Population (Million | 33.44 | 42.88 | 65.31 | 83.78 | 130.58 | 200.17 |