ISS (Statistical Services) Statistics Paper III: Questions 56  61 of 96
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Question number: 56
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2012
Describe in Detail
Discuss the practical consequences of autocorrelation. Show that
Explanation
Practical consequences of autocorrelation:

OLS estimators are still unbiased and consistent.

The variance of the estimators are underestimated. In the presence of autocorrelation , but Thus, variance of may be either over estimated or under estimated depending upon the n
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Question number: 57
» Sampling Techniques » Simple Random Sampling and Systematic Sampling
Appeared in Year: 2012
Write in Short
Show that mean of a systematic sample is more precise than the mean of a simple random sample of size n under a certain condition to be obtained by you.
Question number: 58
» Applied Statistics » Index Numbers » Income DistributionPareto and Engel Curves
Appeared in Year: 2013
Describe in Detail
Discuss Engel’s curve. Explain the Engel’s curve for constant price of a demand functionwhere is national income and p is price.
Explanation
Engel’s curve: The graphic representation of the basic relationship between household income and its expenditure on a particular item of consumption is known as Engel’s curve. The Engel curves shows the effect of a change in income on the expenditure for each good at fixed prices. If price change, the result will be shift in each of the Engel cur
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Question number: 59
» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations
Appeared in Year: 2012
Describe in Detail
What are the different methods for measurement of trend? Discuss the method of fitting a straight line using least squares method.
Explanation
Methods of measurement of trend:
Trend can be measured by the following methods:
(i) Graphic method or trend by Inspection
(ii) Method of SemiAverages
(iii) Method of Curve fitting by principles of Least Squares
(iv) Method of moving averages
Fitting a straight line using least squares method:
Let be the trend equation.
Where =
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Question number: 60
» Applied Statistics » Index Numbers » Laspeyre
Appeared in Year: 2013
Describe in Detail
Discuss simple aggregate method of Index number. Why is weighted average of price relative index preferred over simple aggregate method? Show that weighted average of price relative index number is same as that of Paasche’s index number.
Explanation
Simple aggregate method of Index number:
This method consists of expressing aggregate of prices in any year as a percentage of their aggregate i^{th} the base year. The price index, under this method is computed by the formula
Where
= Price index of the current year with reference to the base year
= Total of the prices of the cu
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Question number: 61
» Applied Statistics » Periodogram and Correlogram Analyses
Appeared in Year: 2012
Describe in Detail
Obtain the correlogram for the series with, provided, , and successive values of are independent.
Explanation
It is given that
And hence
Substituting the value in we get,
Where 𝛈s are independent.
Multiplying both sides of the above equation by , taking expectations and dividing by , we g
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