models

1. Analysis of
TimeSeries

2. TimeSeries-
Meaning
A time series refers to
the values of a variable,
which are ordered
chronologically, over a
successive period of
time.
It is a sequence taken
at successive equally
spaced points in
time.
It discloses relationship
between two variables,
one being time.
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3. TimeSeries-Examples
Climat
e
Rainfall,
Wind,
Tide
Financi
al
Nationa
l
Incom
e
Busine
ss
Profit,
Inventor
y
Demograp
hy
Populatio
n, Birth
rate
Market
Sensex,
Nifty,
Dow
Jones
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4. Importance of Time Series Analysis
Understanding past
behavior
Predicting,
Forecasting and
Planning
Evaluation of
currentprograms
Facilitates
Comparison
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5. Componentsof Time series
The statistical series are usually affected by a multiplicity of causes.
Such forces can be changes in population, tastes and habits of
people, changes in income etc.
The effects of these forces on the time series are called the
components of a time series
Secul
ar
Trend
Cyclic
Variation
s
Seasona
l
Variation
Irregular
Variation
s 5

6. SecularTrend
Trend refers to long
period changes.
It shows the definite
and basic tendency of
statistical data with the
passage of time.
The trend can be
Rising/Falling/Const
ant.
The concept of trend
does not include short
term oscilations.
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7. Seculartrend- Examples
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8. Seculartrend- Examples
Irrespectiveoftheshortterm
minoroscillations,the trend
remainsrising overa longer
periodoftime.
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9. Freehand
Curve
Method
Semi
Average
Method
Moving
Average
Method
Method of
Least
Squares
Methodsof
measuringtrend
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10. 1.Freehandcurvemethod
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11. 2.SemiAveragemethod
15
1
15
0
14
9
15
2
15
6
15
5
15
4
15
3
1990-
1991
1994-
1995
TREND
LINE
TREND
LINE
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12. 3.MovingAverageMethod
Year Value
1994 2
1995 5
1996 2
1997 2
1998 7
1999 6
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13. Equation of straight line; y = a
+ bx
4.LinearTrend/Lineofbestfit.
• Here, we are trying to establish a mathematical equation and
using that equation to find the trend values.
• We are fitting a straight line to match the trend using a linear
equation derived from the available data.
Year (t) Value (y) Deviation from Mid
year; t – mid year
(x)
xy 𝒙2
𝒂=
𝒚
𝒏
𝒙
𝒚
b = 𝒙𝟐
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14. Drawingagraph–Things to remember!
0
1
2
3
4
5
6
200
1
2002
200
3
200
4
Series
1
Series
2
Title for the graph
Axis Description
Axis
Description
Line description
Line description
Intersectio
n
highlightin
g
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15. Seasonal
Variation
These are the variations
which occur with some
degree of regularity
within a specific period
of one year or shorter.
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16. Simple
Average
Method
Ratio to
trend
Method
Ratio to
Moving
Average
Method
Method of
link
relatives
Methodsofmeasuring
SeasonalVariations
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17. • A seasonal index is calculated by the average of each season.
• Here, a season means a month or a quarter or any other time
period for which the fluctuations happen.
 Step 1: Make a season wise arrangement of
data
 Step 2: Calculate the average for each season
 Step 3: Calculate the average of averages
 Step 4: Calculate seasonal index using the
formula.
1.SimpleAverage Method.
Seasonal
Index=
𝑨𝒗𝒆𝒓𝒂𝒈𝒆𝒐𝒇𝒕
𝒉
𝒂
𝒕𝒔𝒆𝒂𝒔𝒐𝒏
𝑨𝒗𝒆𝒓𝒂𝒈𝒆𝒐𝒇𝒂𝒗𝒆𝒓𝒂𝒈𝒆𝒔
×
100
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18. 2.Ratiototrendmethod
Firstly, we have to find the trend eliminated values using
method of least squares
Then method of simple average is applied on these trend
eliminated values
We will then be getting the seasonal indices
This method is recommended only when there is absence
of cyclical movements
3.RatiotoMovingaveragemethod
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19. LorenzCurve
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20. LorenzCurve
It is a graphic method of studying dispersion in a series
It was developed by Max O. Lorenz in 1905for
representing inequality of the wealth distribution..
It can also be used for studying the dispersion in series
such as wages, production, populationetc..
If there is no inequality in the distribution, lorenz curve
will coincide with the line of equal distribution
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21. 21

22. THANKYOU
Manu Antony
+91 9567 320 002
cmanuantony@gmail.co
m
www.contoso.co
m
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