Time Series Analysis 6th lecture Dr. Varga Beatrix

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.

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

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

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

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

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

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.

Average netto income in Hungary Period Ft/cap./year 2011= 100% Prev. year =100% 2011 996 548 100.00 … 2012 996 153 99.96 2013 1 049 206 105.28 105.29 2014 1 099 710 110.35 104.85 2015 1 150 303 115.43 104.60 2016 1 199 094 120.32 104.24 2017 1 300 079 130.46 108.42

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 

Average income in Hungary Period Ft/cap./year 2010= 100% Prev. year =100% 2011 996 548 100.00 … 2012 996 153 99.96 2013 1 049 206 105.28 105.29 2014 1 099 710 110.35 104.85 2015 1 150 303 115.43 104.60 2016 1 199 094 120.32 104.24 2017 1 300 079 130.46 108.42 Average absolute change:

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.

Average income in Hungary Period Ft/cap./year 2010= 100% Prev. year =100% 2011 996 548 100.00 … 2012 996 153 99.96 2013 1 049 206 105.28 105.29 2014 1 099 710 110.35 104.85 2015 1 150 303 115.43 104.60 2016 1 199 094 120.32 104.24 2017 1 300 079 130.46 108.42 Average relative change:

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

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.

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

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

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.

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.

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

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

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.

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.

Base period-weighted volume index (Laspeyres volume index)

Current period-weighted volume index (Paasche volume index)

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.

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.

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

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

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

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.

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

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

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.

Thank You for Your Attention stbea@uni-miskolc.hu