4. • I WOULD LIKE TO THANK DR. VANDANA SARIN WALIA FOR
PROVIDING OUR TEAM A WONDERFUL OPPORTUNITY TO
APPLY THE KNOWLEDGE , IN PRACTICAL TERMS .
THROUGH THIS PROJECT WE WERE ABLE TO GET THE
ABSOLUTE PRACTICAL IDEA .
WITH HER HELP AND CONTINOUS GUIDENCE WE WERE ABLE
TO COMPLETE THIS PROJECT,
WE HOPE THAT WE ARE ABLE TO MAKE THIS PROJECT UPTO
HER EXPECTATIONS .
THANK YOU !
5. A time series is a sequence of DATA
POINTS, measured typically at successive
points in time spaced at uniform time
intervals.
Time series analysis comprises methods for
analyzing time series data in order to extract
meaningful statistics and other characteristics of
the data.
Examples of data could be: stock market prices,
currency values, item prices, daily temperatures,
weekly rainfall, population growth ETC.
6. COMPONENTS OF TIME SERIES
• RANDOM• CYCLICAL
• TREND• SEASONAL
ANALYSIS OF
SERIESTIME
11. SECULAR TREND
• The component responsible for the general
behaviour of time series is called trend
• It is a long term tendency of any particular activity to
grow or to decline.
• Trend may be upward or downward.
• Linear or non linear trend.
RANDOM COMPONENT
•Random, irregular, erratic in nature
•Cannot be foreseen
•No reasons , no causes can be attributed
•Causes- strikes,fire,femines etc
12. PERIODIC COMPONENT
PERODIC MOVEMENT
RECCUR AFTER A TIME
PERIOD OF LESS THAN
ONE YEAR
THE PERIOD OF
OSCCILATION IS MORE
THAN ONE YEAR
THE CYLCES CAN BE
OF DIFFERENT
INTENSITY AND
PERIODICITY
13. THERE ARE TWO TYPES OF MODELS
ADDITIVE MODEL
• This is used when the components are independent
• Yt = Tt + St + Ct + Rt
MULTIPLICATIVE MODEL
• This used when components are inter-dependent.
• Yt = Tt * St* Ct* Rt
• logYt = LogTt + LogSt + LogCt + LogRt
14. Advantages of ANALYSING TIME SERIES .
• Understanding the phenomenon under
consideration
• Gaining knowledge about the Past behaviour.
• Evaluate Current behaviour of the time series.
• Preparing and projecting the future of time
series.
15. METHODS FOR MEASURING TRENDS
Free hand curve method
• Plot the given T.S on a graph taking a time variable t on X axis .
• Join the plotted points with dotted lines
• Draw a smooth line by the inspection of above graph
Method of semi averages
• Divide the time series into equal halves with respect to time
• Calculate the average of each halve
• Semi averages are plotted against the mid points
• Join the two averages.
16. METHOD OF MOVING AVERAGES
Moving average represents the central tendency of data in parts.
The extent of moving average is determined by the period of oscillation
whenever the oscillatory movement is regular or average of period of
oscillations when it is irregular.
It is appropriate to use this method when
• Trend is approximately linear.
• Oscillatory movement is regular.
17. METHOD OF FITTING MATHEMATICAL CURVES
There are many mathematical curves that can be fitted to a time series
data. An examination of the plotted data often provides an adequate
basis for deciding upon which type of trend to use.
The different types of curves are
• A straight line
• Second degree parabola
• Kth degree polynomial
• Exponential curves
• Growth curves
Modified exponential curve
Gompertz curve
Logistic curve
39. Gompertz curve can be fitted by two method. These are :
Method of 3 selected points
Method of partial sums :
In this method the time series data is divided into 3 equal parts. For this purpose
one or two values may be ignored from the data depending upon the relevance of
future or past data.
Now the sums of values of 3 equal parts namely S1 ,S2 and S3 are used to estimate
values of k , A and b as shown below.
63. • Seasonal variation is measured in terms of an index, called
a seasonal index. Its an average that can be used to
compare actual observation relative to what it would be if
there were no seasonal variations .
• An index value is attached to each period of time series
within a year.
• The following methods are used
Method of simple averages
Ratio to trend method
Ratio to moving average method
Link relative method
64. • This is the simplest method of measuring
seasonal component
• This method assumes that the data does not
contain trend or cyclic component.
65. • This method is an improvement over the
simple averages method and is based on the
assumption that seasonal variation for any
given month is constant factor of the trend.
66. • Moving averages completely eliminates the
seasonal movements if the extent of the
moving averages is equal to the oscillatory
movements sought to be eliminated.
• Some of the seasonal indices cannot be
determined.
67. • This method is based on averaging the link
relatives.
• Link relative is the value of one season
expressed as a percentage of the value of the
preceding season.