1. Time Series Analysis
6th lecture
Dr. Varga Beatrix

2. Consumer prices were 3.1% higher on average in February 2019 than a year earlier.
The Dow Jones Industrial Avared closed to 25,928 today in heavy trading.
Nowadays, the world’s population is increasing by 1.1% per year.
The volume of Gross Domestic Product was 5.1% higher in the 4th quarter of 2018 than in the corresponding period of the previous year.

3. Time series
Numerical data that are calculated, measured, or observed sequentially on a regular chronological basis are called: time series

4. The simple tools of time series analysis
graphical presentation
ratio statistics
means
weighted composite index numbers

5. The Types of Time series
Flow time series: our temporal observations refer to a period of time
Stock time series: our temporal observations refer to a specific point of time

6. Graphical presentation Population number in Hungary*
Stock time series : Bar Charts: the temporal observations refer to a point

7. Graphical presentation Live births and deatrhs per thousand population in Hungary
Flow time series : Line Charts: the temporal observations refer to a period

8. Dynamic ratio Base ratio:
Every piece of data of the time series is correlated to the base temporal data.
Chain ratio:
Each piece of data of the time series is correlated to the previous temporal data.

9. Average netto income in Hungary
Period
Ft/cap./year
2011= 100%
Prev. year =100%
2011
100.00 …
2012
99.96
2013
105.28
105.29
2014
110.35
104.85
2015
115.43
104.60
2016
120.32
104.24
2017
130.46
108.42

10. Average Absolute Change
During the definition of the average degree of the change we need only the first and the last data of the actual time series.
Used if the change from time to time has similar degree, with an approximately linear development 

11. Average income in Hungary
Period
Ft/cap./year
2010= 100%
Prev. year =100%
2011
100.00 …
2012
99.96
2013
105.28
105.29
2014
110.35
104.85
2015
115.43
104.60
2016
120.32
104.24
2017
130.46
108.42
Average absolute change:

12. Average Relative Change
Based on the geometric mean of the relative increments
The rate of change of a variable over time. The nth root of the product of n values.

13. Average income in Hungary
Period
Ft/cap./year
2010= 100%
Prev. year =100%
2011
100.00 …
2012
99.96
2013
105.28
105.29
2014
110.35
104.85
2015
115.43
104.60
2016
120.32
104.24
2017
130.46
108.42
Average relative change:

14. Weighted composite index numbers
How did the output value, the sales revenue, the sales turnover, or the total cost of production change?
How did quantities of production and sales change?
How did the price of a group of products change, how did the price level change? 14

15. Weighted composite index numbers
They are composite comparative ratio of data that cannot be aggregated directly.
They are descriptive indicators, used as a characteriser of change in the magnitude of business activity over time.

16. Notations: v: output value, sales turnover, total cost p: price
q: quantity
Iv; Ip; Iq : Weighted composite indexes:

17. Weighted composite Value index
It shows the average change in the composite(?) value of all commodities. 17

18. Weighted composite Price index
It shows the average change in the price of various products and commodities, briefly it shows the change of the price level.
It measures the average price change of goods, by giving different weights for each item.
If the time series variables are prices, then the weights are quantities purchased.

19. Weighted composite price index
For the calculation of the price index you can also use the quantities of the base period and you can use the actual quantities too.

20. Base period weighted composite Price-index (Laspeyres price index)

21. Current period weighted composite Price-index (Paasche price index)

22. Weighted composite Volume index
It shows the average change in the volume of different products and services.
It measures the composite changing of the quantity of production (or sales, or consumption, etc.) of a given set of goods or services over a period of time.

23. Weighted composite Volume index
For the calculation of the volume index you can use the prices of the base period and the prices of the current period too.

24. Base period-weighted volume index (Laspeyres volume index)

25. Current period-weighted volume index (Paasche volume index)

26. The Methods of Time Series Analysis
Different “n” probability variables belong to each point of time (or to each period of time), but we have only one of these.
The time series is the result of the common effect of several factors. The time factor is the collector of many of the factors.

27. The Methods of Time Series Analysis
Deterministic time series analysis:
The time series follow an already given pre-determined path over a long period of time.
The aim of the analysis is to determine this path, and to separate its components.
Used to predict the probable formation of the time series in the long run.

28. The Methods of times Series Analysis
Stochastic time series analysis:
Deals with the analysis of the short-term effects.
Time phenomena change only randomly compared to their previous state.
Accidental events change the temporal processes
The whole model needs the backup of probability theory

29. Deterministic time series analysis
Decomposition model:
Basic tendency or trend,
Seasonality,
Cycling,
Irregularity

30. Basic tendency or trend
apermanent tendency
the most important component of the development
result of the common effect of several factors
it is defined basically by social-economic laws

31. Seasonality regularly repeating fluctuation in the time series
the fluctuation has regular period length
mainly in time series where the data refer to a period shorter than a year.

32. The cycle is less regular than seasonality
occurs within a longer time series

33. Irregularity a probability variable
the final result of several individually not important components
of the causal effect that the time series data fluctuate stochastically around the trend line

34. Promlem
data only regarding the factual time series evolved by the common effect of all the components
based on the empirical data and based on abstractions.

35. Thank You for Your Attention