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

Essay Question▾

Describe in Detail

For the auto-regressive scheme Equation , show that if e is a random variable and the series is long, then

Equation

and hence show that, variance of the generated series may be much greater than that of e itself.

Explanation

Given auto-regressive scheme Equation is a second order Auto-regressive series.

Equation ……………. . (i)

Since the series is long and Equation , we have

Equation and VarEquation

Squaring both sides of (i) and taking the expectations, we get

Equation

Equation

Equation …………. . (i)

Multiplying both sides

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Question number: 55

» Applied Statistics » Index Numbers » Income Distribution-Pareto and Engel Curves

Appeared in Year: 2013

Essay Question▾

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

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Question number: 56

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Discuss the practical consequences of autocorrelation. Show that

Equation

Explanation

Practical consequences of autocorrelation:

  1. OLS estimators are still unbiased and consistent. Equation

  2. The variance of the estimators are underestimated. In the presence of autocorrelation Equation , but Equation Thus, variance of Equation may be either over estimated or under estimated depending upon the nature of the correlation.

  3. Prediction will be

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Question number: 57

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2012

Short Answer Question▾

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 Distribution-Pareto and Engel Curves

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Discuss Engel’s curve. Explain the Engel’s curve for constant price of a demand functionEquation where Equation 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

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Question number: 59

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2012

Essay Question▾

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 Semi-Averages

(iii) Method of Curve fitting by principles of Least Squares

(iv) Method of moving averages

Fitting a straight line using least squares method:

Let Equation be

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