GNDU B.Com (Bachelor of Commerce)

Chapter 5: Time Series Analysis and Index Numbers

Summary

A time series is a set of observations recorded at successive intervals of time, such as monthly sales or annual production. Analysing it helps in understanding past behaviour and forecasting the future. A time series is made up of four components: the secular trend (the long-term general direction), seasonal variations (regular changes within a year), cyclical variations (medium-term ups and downs of a business cycle) and irregular or random variations (caused by unpredictable events). The trend can be estimated by several methods: the graphical or free-hand method, the semi-average method (dividing the data into two halves and joining their averages), the moving-average method (smoothing by averaging successive groups of values) and the method of least squares, which fits the straight-line trend \(y = a + bx\) by minimising the sum of squared deviations. The second topic is index numbers, which are specialised averages that measure the relative change in a variable, such as prices, over time compared with a base period. They are important for measuring changes in the price level, the cost of living and production. Price index numbers are constructed by weighted methods: Laspeyres' index uses base-year quantities as weights, Paasche's index uses current-year quantities, and Fisher's ideal index is the geometric mean of the two, \(P_{01}=\sqrt{L\times P}\). Index numbers should satisfy tests of consistency such as the time-reversal and factor-reversal tests, and the consumer price index measures changes in the cost of living of a defined group.

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Practice quiz