Chapter 13 Time series and index numbers

13.1 Time series

13.1.1 Flow and stock

13.2 Absolute and relative change

13.3 Index numbers

13.3.1 Chain index

13.3.2 Fixed-based index

13.4 Average Rate of Change

13.5 Aggregate Price and Quantity Indices

13.5.1 Laspeyres Index

\[\begin{equation} I = \frac{\sum p_n q_0}{\sum p_0 q_0}\cdot 100, \tag{13.1} \end{equation}\]

13.5.2 Paasche Index

\[\begin{equation} I = \frac{\sum p_n q_n}{\sum p_0 q_n}\cdot 100, \tag{13.2} \end{equation}\]

13.5.3 Fisher Index

13.6 Exercises

Exercise 13.1 According to the Gapminder website (https://www.gapminder.org/topics/guitars-per-capita/), the number of guitars per million inhabitants of the Earth increased from 200 guitars per million in 1962 to 11,000 guitars in 2014. What was the average annual rate of change?

Exercise 13.2 Using the Central Statistical Office’s Local Data Bank (Bank Danych Lokalnych GUS), find the average ticket price for cinemas and theatres for each available year. Then calculate the average annual rate of change for both series over the full period covered by the data.