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Time-Series3

Time series examines a series of data over timeIn studying the series, patterns become evident andthese patterns are used to assist with future decisionmakingTime series relies on the following;Identification of the underlying trend line

Measurement of past patterns and the assumptionthat these patterns will be repeated in the futureForecast of future trends of data

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Components4

The four main components of time series are;Secular trendCyclical movementSeasonal movementIrregular movement

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Methods of measuring trend values5

Freehand Curve Method

Semi-Average MethodLeast Squares MethodMoving Average Method

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Least Square Method6

This method uses the given series of data todevelop a trend line for predictive purposesThe least-squares method establishes a trend linefrom;

y = na+b x

xy = a x+b x²

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Concept7

Straight line trend is given byY = a+bx in order to determine the values of

constant a and b. The following two normal

equations are to be solvedy = na+b xxy = a x+b x²

Y= sum of actual values of y variable

x = representation sum of deviationsx² = representation sum square of deviationsxy = representation of the products sum ofdeviations

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Cont·d8

Y represents the estimated value of the trend .

X represents the deviations in time period.a and b is constant.

a represent intercept of line.b represent slope of line.

Y-axis

X-axis}Intercept

Y= a + bx

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Merits9

This is the only method of measuring trend whichprovides the future values authentically veryconvincing and reliable.This method is used for forecasting the series forexampleThis method has no scope for personal bias of theinvestigator.It is only method which gives the rate of growth perannum

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Demerits10

The method requires mathematical ability. Sometime it involves tedious and complicatedcalculations.The method has no flexibility i.e., if even a singleterm is added to series it makes necessary to doall the calculations again.Estimated and prediction by this method arebased only on long term variations and the impactof cyclical, seasonal and irrigation variation arecompletely ignored.

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Case Study11

From the information provided by Smith Company.Fit a straight line trend by using Least SquaresMethod.Further find the gap between calculated and actualvalue and convert the equation into monthly basis

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869 =13a+7 8 b5629 =7 8 a+ 6 50b

a= 50. 88

b= 2 .28 0

Yc = 50. 8846 + 2 .28 022* X

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Yc = 50. 8846 + 2 .28 022* X

B. Convert the equation monthly basis:

Yc = 4 .24 03 8 3 + 0.1 9 001 8* X

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