The method of measuring trend of time series using only averages is ______ - Mathematics and Statistics

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The method of measuring trend of time series using only averages is ______

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Solution

moving average method

Concept: Measurement of Secular Trend
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Chapter 2.4: Time Series - Q.2

RELATED QUESTIONS

Obtain the trend values for the data in using 4-yearly centered moving averages.

Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985
Index 0 2 3 3 2 4 5 6 7 10

Fit a trend line to the data in Problem 7 by the method of least squares. Also, obtain the trend value for the year 1990.


State whether the following is True or False :

Least squares method of finding trend is very simple and does not involve any calculations.


State whether the following is True or False :

All the three methods of measuring trend will always give the same results.


Solve the following problem :

The following table shows the production of pig-iron and ferro- alloys (‘000 metric tonnes)

Year 1974 1975 1976 1977 1978 1979 1980 1981 1982
Production 0 4 9 9 8 5 4 8 10

Fit a trend line to the above data by graphical method.


Obtain trend values for the following data using 4-yearly centered moving averages.

Year 1971 1972 1973 1974 1975 1976
Production 1 0 1 2 3 2
Year 1977 1978 1979 1980 1981 1982
Production 3 6 5 1 4 10

Solve the following problem :

Following data shows the number of boxes of cereal sold in years 1977 to 1984.

Year 1977 1978 1979 1980 1981 1982 1983 1984
No. of boxes in ten thousand 1 0 3 8 10 4 5 8

Fit a trend line to the above data by graphical method.


Solve the following problem :

Obtain trend values for data in Problem 10 using 3-yearly moving averages.


Solve the following problem :

Obtain trend values for data in Problem 13 using 4-yearly moving averages.


Solve the following problem :

Following table shows the all India infant mortality rates (per ‘000) for years 1980 to 2010.

Year 1980 1985 1990 1995 2000 2005 2010
IMR 10 7 5 4 3 1 0

Fit a trend line to the above data by graphical method.


Solve the following problem :

Fit a trend line to data in Problem 16 by the method of least squares.


Solve the following problem :

Following tables shows the wheat yield (‘000 tonnes) in India for years 1959 to 1968.

Year 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968
Yield 0 1 2 3 1 0 4 1 2 10

Fit a trend line to the above data by the method of least squares.


The complicated but efficient method of measuring trend of time series is ______


The simplest method of measuring trend of time series is ______


State whether the following statement is True or False:

The secular trend component of time series represents irregular variations


State whether the following statement is True or False: 

Moving average method of finding trend is very complicated and involves several calculations


State whether the following statement is True or False:

Least squares method of finding trend is very simple and does not involve any calculations


The following table gives the production of steel (in millions of tons) for years 1976 to 1986.

Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986
Production 0 4 4 2 6 8 5 9 4 10 10

Obtain the trend value for the year 1990


Obtain the trend values for the data, using 3-yearly moving averages

Year 1976 1977 1978 1979 1980 1981
Production 0 4 4 2 6 8
Year 1982 1983 1984 1985 1986  
Production 5 9 4 10 10  

Use the method of least squares to fit a trend line to the data given below. Also, obtain the trend value for the year 1975.

Year 1962 1963 1964 1965 1966 1967 1968 1969
Production
(million barrels)
0 0 1 1 2 3 4 5
Year 1970 1971 1972 1973 1974 1975 1976  
Production
(million barrels)
6 8 9 9 8 7 10  

Following table shows the all India infant mortality rates (per ‘000) for years 1980 to 2010

Year 1980 1985 1990 1995
IMR 10 7 5 4
Year 2000 2005 2010  
IMR 3 1 0  

Fit a trend line by the method of least squares

Solution: Let us fit equation of trend line for above data.

Let the equation of trend line be y = a + bx   .....(i)

Here n = 7(odd), middle year is `square` and h = 5

Year IMR (y) x x2 x.y
1980 10 – 3 9 – 30
1985 7 – 2 4 – 14
1990 5 – 1 1 – 5
1995 4 0 0 0
2000 3 1 1 3
2005 1 2 4 2
2010 0 3 9 0
Total 30 0 28 – 44

The normal equations are

Σy = na + bΣx

As, Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx2

As, Σx = 0, b =`square`

∴ The equation of trend line is y = `square`


Obtain the trend values for the following data using 5 yearly moving averages:

Year 2000 2001 2002 2003 2004
Production
xi
10 15 20 25 30
Year 2005 2006 2007 2008 2009
Production
xi
35 40 45 50 55

Following table shows the amount of sugar production (in lakh tonnes) for the years 1931 to 1941:

Year Production Year Production
1931 1 1937 8
1932 0 1938 6
1933 1 1939 5
1934 2 1940 1
1935 3 1941 4
1936 2    

Complete the following activity to fit a trend line by method of least squares:


The complicated but efficient method of measuring trend of time series is ______.


Fit a trend line to the following data by the method of least square :

Year 1980 1985 1990 1995 2000 2005 2010
IMR 10 7 5 4 3 1 0

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