# 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)

… (411 more words) …

## Question number: 53

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

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Appeared in Year: 2010

### 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

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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

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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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