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

Definition and types of time series All processes that are the subject of statistics, are in constant motion and change. The best source of information for analysis of such processes in statistics are the time series TS. We use the term "time series" to refer to any group of statistical information accumulated at regular time slices

Definition and types of time series Time series analysis is the quantitative method we use to determine patterns in data collected over time. Time series TS is the sequence of values varied in time and located in the chronological order

YearProduced Fleet on the 1 st of January Total210 Example 1. Production of ditchers on an island

Each time series consist of two components (elements): - periods or points of time t; - statistical indicator characterizing investigated economic process, which is called a level of time series, we analyze three types of levels – base, current, and previous. Definition and types of TS

Statistics tasks in the field of time series: - define the scope and intensity of analyzed processes by measuring the level of the series and its average parameters; - identify the trend, - determine the magnitude of levels variation around the trend; - identify and measure the seasonal fluctuations; - compare changes in time of selected economic indicators Tasks for TS

Example 2. Production, million units tyiyi ,

There are several classes of TS 1. Concerning the type of data: absolute valuesratiosaverages

JanuaryFebruary MarchApril Sales volume, thousand $ JanuaryFebruary MarchApril Growth rate of GDP per capita, % - DR ,1100.8

JanuaryFebruary MarchApril Average salary (salary per person), thousand $ 4,54,7 4,8

There are several classes of TS 2. Concerning the time slices: TS with equidistant time slices TS with non-equidistant time slices

JanuaryFebruary MarchApril Sales volume, thousand $ JanuaryMarchJulyDecember Sales volume, thousand $

There are several classes of TS 3. Concerning data presentation: TS with indication of date TS without indication of date

Time series are classified on instant time series & interval TS Instant time series (моментные) have levels at a specific time or date. Examples: population size, levels of cash balances

Interval TS have levels which are totals for some time intervals (production for a month, the number of births during a month, a year). A special feature of interval series is that their levels can be split or added

January,1February,1March,1April,1 Size of working capital, thousand $ JanuaryFebruaryMarchApril Average salary (salary per person), thousand $ 4,54,7 4,8

Statistical indicators of time series

Analysis of the rate and intensity of processes over time is performed by means of statistical indicators, which are obtained by comparing different levels. One time period (or a moment of time) is chosen as a base, and the other levels are expressed as a share or a percentage of the base period level Statistical indicators of TS

For each time series some special indicators could be defined and they describe the investigated economic processes. All indicators are classified as: 1. Absolute indicators: absolute increase and absolute value of 1% growth A%; 2. Ratios which include: growth rate R gr, rate of increase R inc, growth factor k gr, increase factor k inc ; 3. Average indicators mentioned above: Statistical indicators of TS

All analytical indicators can be chain and base. Chain indicators characterize the intensity of process changing and can be defined by comparison of the current level and the previous level. Base indicators of time series characterize the total result (decision-result) of process changing during the period of time. Base indicators are defined by comparison of the current level to the first (base) level Statistical indicators of TS

Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Absolute increase shows by how many units the current level is greater or smaller than the previous (base) level: 1.Absolute increase

Year , ,3 13,3 0, ,51,53,51,0881,233108,8123,38,823,30, ,541,0271,266102,7126,62,7 26,60, ,1051,400110,5140,010,540,00,190 ch

2.Growth factor k gr (коэффициент роста К р ) shows by how many times the current level is larger or smaller than the previous or base level: 2.Growth factor k gr

Year , ,3 13,3 0, ,51,53,51,0881,233108,8123,38,823,30, ,541,0271,266102,7126,62,7 26,60, ,1051,400110,5140,010,540,00,190 ch

3.Factor of increase k inc (коэффициент прироста К пр ) shows by how many shares the current level is greater or smaller than the previous or base level: 3.Factor of increase k inc

Year , ,3 13,3 0, ,51,53,51,0881,233108,8123,38,823,30, ,541,0271,266102,7126,62,7 26,60, ,1051,400110,5140,010,540,00,190 ch

4.Growth rate (rate of growth) Rgr shows how many percent the current level makes up concerning the previous or base level: 4.Growth rate R gr

5.Rate of increase R inc shows by how many percent the current level is greater or smaller than the previous or base level: 5.Rate of increase R incr

6. Absolute value of 1 % growth shows how many measure units are conformed to 1% growth

Absolute value of 1% in base growth is the ratio between the base absolute increase and the base rate of increase:

Absolute value of 1% in chain growth is the ratio between the chain absolute increase and the chain rate of increase: :

Year , ,3 13,3 0, ,51,53,51,0881,233108,8123,38,823,30, ,541,0271,266102,7126,62,7 26,60, ,1051,400110,5140,010,540,00,190 ch

End of Part I To be continued…