Presentation is loading. Please wait.

Presentation is loading. Please wait.

Time-Series Analysis and Forecasting – Part III To read at home.

Similar presentations


Presentation on theme: "Time-Series Analysis and Forecasting – Part III To read at home."— Presentation transcript:

1 Time-Series Analysis and Forecasting – Part III To read at home

2 Time-Series Data

3 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 19-3 Time-Series Plot  the vertical axis measures the variable of interest  the horizontal axis corresponds to the time periods A time-series plot is a two-dimensional plot of time series data

4 The problem of comparability of levels of time series Jointing (смыкание) of time series

5 Since time series is formed during the long period of time, its levels are frequently incomparable

6 Reasons of the incomparability 1.Change of prices. 2.Different methods of calculation of the same indicator. 3.Change of «borders» (organizational, administrative)

7 The method of jointing time series is often used to ensure the comparability of data. It is necessary to have a transitional link (переходное звено) for jointing time series. Transitional link – is the period of time, for which the investigated indicator was calculated using the old method (in old borders) and the new method (in new borders). A transitional coefficient for this transitional is calculated, the transitional coefficient spreads over all the previous period of time

8

9 Transitional coefficient

10

11

12 Analysis of the main tendency of time series

13 The levels of time series are formed under the influence of lots of factors. They can be divided into 5 groups

14 Time-Series Components Time Series Cyclical Compo- nent Irregular Compo- nent Trend Compo- nent Seasonality Component Secular Compo- nent

15 1. Determining ( Определяющие) factors have a constant and strong influence on the examined indicator. They determine the main tendency (the trend) of time series

16

17 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Upward trend Trend Component  Long-run increase or decrease over time (overall upward or downward movement)  Data taken over a long period of time Sales Time

18 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Downward linear trend Trend Component  Trend can be upward or downward  Trend can be linear or non-linear Sales Time Upward nonlinear trend Sales Time (continued)

19

20 There are 4 kinds of charge or variations involved in time series analysis. They are: 2.Secular trend U t. In the secular trends the value of variable tends to increase or decrease over a long period of time. The steady increase of the cost of living recorded by the Сonsumer price index is an example of secular trend. From year to year, the cost of living varies a great deal, but if we examine long-period, we see that the trend is toward a steady increase.

21 3. Cyclical fluctuation V t. The most common example of cyclical fluctuation is the business cycle. Over time, there are years when the business cycle hits a peak above the trend line. At other times, business activity is likely to slump, hitting a low point below the trend line. The time between hitting peaks and falling to low points is at least one year and it can be as many as 15 or 20 years.

22 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Cyclical Component  Long-term wave-like patterns  Regularly occur but may vary in length  Often measured peak to peak or trough to trough Sales 1 Cycle Year

23 4. Seasonal variation S t involves pattern of change within year that tend to be repeated from year to year. For example the consumption of drinks, juices, ice cream and other. Seasonal factors give rise to oscillations relative to the main tendency

24 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Seasonal Component  Short-term regular wave-like patterns  Observed within 1 year  Often monthly or quarterly Sales Time (Quarterly) Winter Spring Summer Fall Winter Spring Summer Fall

25 5. Irregular variation ε t. The value of variable may be completely unpredictable changing in random manner. For example, the Iraqi situation in 1990, the ruble devaluation in 1998 and the others. Random factors cause the random fluctuations of levels of series (for example, weather factor) Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 19-25

26 5. Irregular variation ε t. The value of variable may be completely unpredictable changing in random manner. For example, the Iraqi situation in 1990, the ruble devaluation in 1998 and the others. Thus each value of time series could be presented as follows: Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 19-26

27 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Irregular Component  Unpredictable, random, “residual” fluctuations  Due to random variations of  Nature  Accidents or unusual events  “Noise” in the time series

28 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Time-Series Component Analysis  Used primarily for forecasting  Observed value in time series is the sum or product of components  Additive Model  Multiplicative model (linear in log form) whereT t = Trend value at period t S t = Seasonality value for period t C t = Cyclical value at time t I t = Irregular (random) value for period t

29 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap Smoothing the Time Series  Calculate moving averages to get an overall impression of the pattern of movement over time  This smooths out the irregular component Moving Average: averages of a designated number of consecutive time series values

30 Method of interval enlargement

31 Method of interval enlargement consists in replacement of initial levels of series by the average values, which are calculated for the enlarged intervals

32 Month ytyt Quarterly sums Average monthly value (per quarter)

33 The End of Part III  To be continued Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chap 19-33


Download ppt "Time-Series Analysis and Forecasting – Part III To read at home."

Similar presentations


Ads by Google