ISS (Statistical Services) Statistics Paper III: Questions 54  59 of 96
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Question number: 54
» Econometrics » Autoregressive Linear Regression
Appeared in Year: 2011
Describe in Detail
For the autoregressive scheme , show that if e is a random variable and the series is long, then
and hence show that, variance of the generated series may be much greater than that of e itself.
Explanation
Given autoregressive scheme is a second order Autoregressive series.
……………. . (i)
Since the series is long and , we have
and Var
Squaring both sides of (i) and taking the expectations, we get
→
→…………. . (i)
Multiplying both sides
Question number: 55
» Applied Statistics » Index Numbers » Income DistributionPareto and Engel Curves
Appeared in Year: 2013
Describe in Detail
Explaining Pareto’s law of income distribution, show that the elasticity decreases in the number of persons while passing to a higher income class.
Explanation
Pareto’s law of income distribution:
Pareto’s states that ‘the number of income recipients earning at least a given level of income would tend to fall by a fixed percentage as that given level of income rose by a fixed percentage. ’
Pareto’s law implies that inequality is inescapable and nothing
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 nature of the correlation.

Prediction will be
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
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