ISS Statistics Paper III: Questions 54 - 59 of 90

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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… (66 more words) …

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… (190 more words) …

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… (175 more words) …

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 function Equation 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… (281 more words) …

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… (230 more words) …

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