ISS (Statistical Services) Statistics Paper III: Questions 52 - 56 of 109

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Question number: 52

» Applied Statistics » Time Series Analysis » Exploratory Time Series Analysis

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

Give the various steps for finding the variance of the random component using variate difference method. Is F-test used for testing the significance of homogeneity of two successive estimates of variance? If yes, ok, otherwise which ‘test can be used? Discuss.

Explanation

To find the variance of the random component using variate difference method:

let us consider a series represented as the sum of functional part and random component

Here are considered as independently identically distributed with

…. (i)

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Question number: 53

» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives

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Appeared in Year: 2010

Short Answer Question▾

Write in Short

What are the three tests of index numbers? Verify whether the following index number satisfies any of these tests:

I=

Where L = Lasperaye’s Price Index Number

P = Paasche’s Price Index Number.

Question number: 54

» Econometrics » Autoregressive Linear Regression

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Appeared in Year: 2011

Essay Question▾

Describe in Detail

For the auto-regressive 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 auto-regressive scheme is a second order Auto-regressive series.

……………. . (i)

Since the series is long and , we have

and Var

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

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Question number: 55

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

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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 coiuld be done about it.

pareto’s law is only true for h

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Question number: 56

» Econometrics » Ordinary Least Squares (OLS)

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Appeared in Year: 2012

Essay Question▾

Describe in Detail

Discuss the practical consequences of autocorrelation. Show that

Explanation

Practical consequences of autocorrelation:

  1. OLS estimators are still unbiased and consistent.

  2. The variance of the estimators are underestimated. In the presence of autocorrelation , but Thus, variance of may be ei

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