1. “ TIME SERIES ANALYSIS- Measurement of Trend”
A Lecture on
“ TIME SERIES ANALYSIS- Measurement of Trend”
for B.Sc(Statistics) 3rd year VI th semester, Paper-VII
Title of the paper : Applied Statistics By
Dr.G.Varalakshmi M.Sc.,Ph.D.
Lecturerin Statistics
D. K. Govt. College for women (A)
Nellore
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2. “ TIME SERIES ANALYSIS- Measurement of Trend
Objectives:
To know the Definition of Time Series Analysis with examples
To study the Components of Time Series
To understand the Models of Time Series
To know the Uses of Time Series Analysis
To study the “Measurement of Trend-Methods”
To solve the problems using the above said Methods
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3. DEFINITION OF TIMESERIES DATA
There are three types of data
CROSS SECTION DATA: Data collected on a variable at same point of time
Ex: State-Population, Height- Weight
TIME SERIES DATA: Data collected on a variable at different time periods
Here time may be year or month or week or hour etc.,
Ex: Year-Population, Month-Sales, Week-Profits, Hour-Temparature
PANEL DATA: A Combination of Cross Section Data and Time Series Data
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4. Example
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5. A Set of data depending on the time is called Time series - Kenny& Keeping A Time Series consists of data arranged in chronoligical - Croxton & Cowden t yt t1 Y1 t2 Y2 t3 Y3 . tn Yn
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6. ANALYSIS OF TIME SERIES
When data relating to a variable are segregated by time there will be variations in the values of the variable from time to time
The decomposition or seperation of time series value into its components is called Analysis of Time Series
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7. COMPONENTS OF TIME SERIES
The various factors affecting a time series variable can be broadly classified into the following four categories
Trend (Long Term Fluctuations) (T)
Seasonal variations(Short Term Fluctuations) (S)
Cyclical Variations (C)
Irregular Variations (I )
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8. TREND (LONG TERM FLUCTUATIONS)
It is the general nature of the variable to show an increasing or decreasing tendency over a long period
Trend is the slowly changing component of a time series
Sudden and short term changes can’t be considered as due to trend
Ex: Year-Population Year-Production Year- Profits
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9. SEASONAL VARIATIONS
Seasonal variations are periodic variations which tend to repeat themselves at regular intervals of time(Season)
The season may be a Quarter or Month or Day
Ex:1. The Demand for A.Cs, Cool drinks etc increases during
summer and will be bleak during rest of the year
2.Prices of certain seasonal crops will be low during that
season and high during the rest of the year
3.Deposits in Banks during Croping Season
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10. CYCLICAL VARIATIONS
Cyclical Variations are the oscillatory moments in a time series where the period of oscillation is more than a year
Every kind of Business and Economic activity is susceptible to business cycles
A Business Cycle consists of Four Phases or Periods
1. Prosperity : Material Cheap, Wages low, Prices High, So Profits High
2. Decline : Material high, wages increase, Price discounts offered , Purchasers wait for further reduction of prices-so profits reduced gradually
3.Depression: Increasing Pessimism in trade leads to closure of factory , since no profits leads to unemployment, low wages, low profits
4.Recovery : A period of improvement or recovery- Material low, Demand High, Production High
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11. IRREGULAR VARIATIONS (RANDOM VARIATIONS)
Variations due to unforeseen events such as floods, droughts, earthquakes, wars, Lockouts, Strikes, Migrations
These variations are purely random and beyond human control
They do not repeat in a definite pattern
Even then we need to study them
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12. Example
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13. MODELS OF TIME SERIES Additive Model : Yt =Tt +St + Ct + It
Multiplicative Model : Yt =Tt St Ct It
Mixed Model : Yt =Tt St + Ct + It
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14. USES OF TIME SERIES ANALYSIS
This Analysis is useful for the Governments, Business Persons,NGOs, Banks, Private Organizations as follows
Helps in understanding the PAST SITUATIONS
Helps in finding the FUTURE PREDICTIONS
Comparison of Actual data with the Predicted data and find the reasons for the difference
Comparison of different TIMESERIES DATA
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15. METHODS OF MEASURING TREND
Graphical Method
Semi Averages Method
Moving Averages Method
Curve Fitting Method
METHODS OF MEASURING SEASONAL VARIATIONS
Simple Averages Method
Ratio to Trend Method
Ratio to Moving Averages Method
Link Relatives Method
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16. GRAPHICAL METHOD YEAR SALES (in thousands) 2001 38 2002 40 2003 49
2004 45
2005 47
2006 52
2007 55
2008
2009 50
2010 53
2011 56
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17. SEMI AVERAGES METHOD YEAR SALES (in thousands) SEMI AVERAGES 2001 38
2002 40
2003 49
43.8
2004 45
2005 47
2006 52
2007 55
2008
2009 50
53.8
2010 53
2011 56
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20. MOVING AVERAGE METHOD ODD MOVING PERIOD
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21. MOVING AVERAGE METHOD EVEN MOVING PERIOD
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22. MOVING AVERAGE METHOD EVEN MOVING PERIOD
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23. MOVING AVERAGE METHOD EVEN MOVING PERIOD
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24. CURVE FITTING Fitting of a straight line Fitting of a Parabola
Fitting of Exponential curve
Fitting of Power curve
Fitting of growth curves
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25. FITTING OF STRIGHT LINE (ODD NUMBER OF OBSERVATIONS)
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27. FITTING OF STRIGHT LINE (EVEN NUMBER OF OBSERVATIONS)
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29. Normal Equations: y = n a+b ∑ x + c ∑ x2 y = a ∑ x+b ∑ x2+ c ∑ x3
FITTING OF PARABOLA
y =a +b x + c x2
Normal Equations:
y = n a+b ∑ x + c ∑ x2
y = a ∑ x+b ∑ x2+ c ∑ x3
y = a ∑ x2+b ∑ x3+ c ∑ x4
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30. QUESTIONS ????
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31. THANK YOU
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