Time-Series Analysis and Forecasting – Part II Lecture on the 5 th of October

Average indicators of TS

Average level of TS should be calculated with the help of arithmetic mean or chronological mean

1.In case of interval TS calculation of the average level is performed using simple arithmetic mean: i y y n

2. In case of instant time series with non-equidistant time slices one should implement weighted arithmetic mean to calculate the average level of TS: where – the longitude of time interval i (interval between two neighbor levels); - average level for time interval i

next year pers.

3. In case of instant time series with equidistant time slices we may use simple chronological mean to calculate the average level of TS: where n – number of dates

thousand

Average absolute increase is determined as simple arithmetic mean of chain absolute increases. It shows an average increase/decrease of analyzed TS level where n – number TS levels; S = n - 1 – number of chain increases

Annual average growth factor is calculated as geometric mean from chain growth factors. If chain growth factors were calculated for a TS with equidistant time slices then simple geometric mean is used. shows an average level growth

In case of non-equidistant time slices the weighted geometric mean is used where k i – growth factor; t i – interval between two neighbor levels

Annual average growth rate can be received in different ways, for instance multiplying average annual growth factor by 100. shows an average level growth in percent

Annual average rate of increase shows an average level of increase or decrease in percent

1.What limits of changes have todays absolute and ratio indicators of dynamics? 2.How to get one of four ratio indicator if you know another indicator? A short quiz for my students

End of Part II To be continued… Parts III-V should be read at home Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 19-21