Time serious

8/7/2019 Time serious

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Definition Time serious:

Arrangement of statistical data according to its time of accurance is called time serious, if T1, T2, T3,« Tn

is the successive time interval and y1, y2, y3,« yn are the observation in that time period then y = f(T) +

e.Where f (t) is the complete determine that follows a systematic pattern of variation and e is random error,

that follows an irregular pattern of variation.

Example of time serious:

The hourly temperature recorded at a weather burro.

The total annual yield of veet our a number of years.

The monthly sales of fertilizer of a store.

Definition of signal and noise:

The signal is systematic component of variation in a time serious.

The noise is an ir-regular component of variation in a time serious (e).

Definition of historigram?

The graph of tie serious data is as historigram, in constracting historigram time is taken on horizontal x-axis

and factor y is on vertical y-axis then joint the piloted point by line segment to the require historigram.

Components of time serious:.

1. Secular trend

2. Seasonal variation

3. Cyclical fluctuation

4. Irr-regular movement

1. Secular trend:

It is a line or curve that shows the journal tendency of time serious. It represent are relatively smoothand gratiual movement of time serious in the same direction. It shows the journal increase or decrease

in sequence of observation. For example,

I. The decline in the death rate due to development in science.

II. A continuously increase demand for smaller automobiles.

III. A need for increase veet production due to a constant increase in population.

2. Seasonal variation:



The seasonal variation are short run movement. These variation indicate a repeated pattern of

identical changes in the data, that tend to occur regularly during a period of one year or less. For

example,

I. An increase in consumption of electricity in the summer.

II. An after Eid sale of departmental store.

III. An increase in the sale of cold drinks in the summer.

3. Cyclical fluctuation:

Cyclical fluctuation are the long term ocilation, the business following four faces,

I. Trough (Depression)

II. Expansion (Recovery)

III. Peak

IV. Contraction

4. Irr-regular movement:

The irr-regular movements are un-predictable changes, that indicate the effect of random events.

For exampleI. A stedstriker delaying the production for 1 week.

II. A fire in the factory delaying in production for 3 week.

Time serious model:

The time serious has two model:

Multiplicative model

Y = T*S*C*I

Additive model:

Y = T+S+C+I

Estimation of secular trend:

They have four step:

1. Method of free hand curve

2. M

ethod of semi-average3. Method of moving average

4. Method of lest square



1. Method of free hand curve:

Year Y

1990 120

1991 80

1992 70

1993 140

1994 60

1995 50

1996 65

0

20

40

60

80

100

120

140

160

1990 1991 1992 1993 1994 1995 1996

Series 1

Series 1



2. Mehtod of semi average:

The following table show the property damage in punjab from 1973 to 1979.

Year Y Semi total Semi averageCoded year

Xt -1973Trend valueY= 190+87x

1973 201 0 190

1974 238 831 831/3 = 277 1 277

1975 398 2 364

1976 507 3 451

1977 484 4 538

1978 649 1875 1875/3 = 625 5 625

1979 742 6 712

y1 = 277 y2 = 625

x1= 1 x2 = 5

b = y2 ± y1

x2 ± x1

b = 625 ± 277 = 87

5 - 1

a = y1 ± bx1

a = 277- 87(1) = 190

Semi average trend line y = a+bx

y= 190 + 87x



Graph:

3. Method of moving Average:

The method of moving average are base odd or even value

1. Find the 3 year moving average which are odd value

2. Find the 4 year moing average which are the even

0

100

200

300

400

500

600

700

800

1973 1974 1975 1976 1977 1978 1979

Actual value

Trend value



Data given:

Year Y 3year

total

3year

moving

average

5year

total

5year

moving

average

1810 15

1811 17 63 21

1812 31 80 26.67 136 27.2

1813 32 104 34.67 146 29.2

1814 41 98 32.67 156 31.2

1815 25 91 30.33 158 31.6

1816 25 80 26.67 152 30.4

1817 30 86 28.67 167 33.4

1818 31 117 39 177 35.4

1819 56 116 38.67 193 38.6

1820 35 126 42 203 40.6

1821 41 116 38.67 220 44

1822 40 129 43 219 43.8

1824 48 143 47.67 244 48.8

1825 55 163 54.33 251 50.2

1826 60 163 54.33 279 55.8

1827 48 176 58.67

1828 68



Compute 4 quarter moving average:

Year 4 quarter Y

4 year

movingtotal

4 quarter

cenralmoving

total

4 quarter

centralmoving

average

1979 1 72

2 98

355

3 79 717 89.62

362

4 106 748 =93.5

3861980 1 79 794 =99.2

408

2 122 850 =106.25

442

3 101 899 =112.37

457

4 140 933 =103.66

476

1981 1 94 979 =122.37

503

2 141 1026 =128.25

523

3 128 1077 =134.62

554

4 160 1110 =138.75

556

198 1 125 1119 =139.87

563

2 143 1153 =144.12

590

3 135

4 187



4. Method of lest square:

The method of lest square say that the best line of any observe data is that for which, that for sum

of square of residuals is minimum.

In the method of least square two type of question, first is for odd and second for even value.

Origin taking:

X(coding) = Time ± origin

Unit of measurement

Odd:

In case of odd value if no instruction is given for origin then we take the mid year as origin.

Even:

In case no instruction is given and data is given in even value then we take the two mid value in the data

and divided by 2.

If the data is given in that shape 1991, 1992, 1993, 1994, 1995, 1996

X(coded) = 1993 - 1994

2

b = nxy ± (x)(y)

nx2 ± (x)2

b = xy ± (x)(y) / n

x2 ± (x)2 / n



Qno1:

Determine the trend line by the lest square method form data. Plot the actual values and linear trend

on same graph.

Year Y(price) X (coding) xy x2 T.V

y = a+ bxe = y- y

1945 3 -4 -12 16 2.28 .72

1946 6 -3 -18 9 3.96 2.04

1947 2 -2 -4 4 5.64 -3.64

1948 10 -1 -10 1 7.32 2.68

1949 7 0 0 0 9 2

1950 9 1 9 1 9 0

1951 14 2 28 4 12.36 1.64

1952 12 3 36 9 14.04 -2.04

1953 18 4 72 16 15.72 2.28

Total 81 0 101 60

b = nxy ± (x)(y)

nx2 ± (x)2

n = 9 xy = 101 x = 81 x2 = 60 x = 0

b = 9(101) ± (0)81



9(60) ± (0)2

b = 1.68

y = y = 80/9 = 9

n

x = 0

a = y ± bx

a = 9- (1.68)0

Graph:

0

2

4

6

8

10

12

14

16

18

20

1945 1946 1947 1948 1949 1950 1951 1952 1953

Actual value

Trend value



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Time serious