ISS (Statistical Services) Statistics Paper III: Questions 87 - 93 of 109

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Question number: 87

» Applied Statistics » Time Series Analysis » Illustration, Additive and Multiplicative Models

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Appeared in Year: 2014

Essay Question▾

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What are the two mathematical models employed for time series analysis? Can one model be considered as a particular type of the other one? Which one of the two models is considered to be more useful and why? Discuss each of the above aspects.

Explanation

The two mathematical models employed for time series analysis:

(i) Additive model

(ii) Multiplicative Model

Additive model:

According to the additive model the time series can be expressed as

where

is the time series value at time T

Represents the Trend value

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Question number: 88

» Econometrics » Heteroscedastic Disturbances

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Appeared in Year: 2014

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Discuss the problem of Heteroscedasticity in GLM. Describe Glejser test for detecting hetroscadasticity. What are the difficulties in using Glejser test? How do you overcome these difficulties?

Explanation

Problem of Hetroscadasticity:

  • One of the sources of Heteroscedasticity is grouping. data from large scale surveys are often in grouped form with an different number of entities in different groups. Working with group averages in such cases give rise to Heteroscedasticity disturbance.

  • There may be certain outlying observations in the data w

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Question number: 89

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

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Appeared in Year: 2014

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Discuss how you will proceed for constructing a cost of living index number for a given expenditure group in a city.

Explanation

Steps involved in the construction of cost of living index number.

i) Scope and coverage: Since it is always constructed for a particular community, first step is to specify the particular class of people for which the index number is going to be constructed. such class may be industrial workers of a particular locality, government employees of a

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Question number: 90

» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number

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Appeared in Year: 2014

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Define Fisher index number. Show why Fisher index number is said to be ideal index number. Also, show why Laspeyres’ and Paasche’s index number are not ideal one.

Explanation

Fisher’s index number:

Fisher’s index number is the geometric mean of laspeyer’s and Paasche’s index number. This index number uses bith base and current year quantities as weights. It counter balances the effect of upward and downward bias experienced with the method os Laspeyer’s and Paasche’s by taking into account both the current year’s and

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Question number: 91

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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What is a Wiener process? Obtain the forward diffusion equation of a Wiener process. Also discuss any two application of the process.

Explanation

A stochastic process is a random process that is a function of time. Brownian motion is a stochastic process that evolves in continuous time, with movements that are continuous. So, Brownian motion is a continuous stochastic process, Z (t), with the following characteristics:

  • Z (0) =1

  • Z (t) is continuous.

  • Z (t + s1) −Z (t) is independen

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Question number: 92

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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Discuss a one-dimensional random walk.

Question number: 93

» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process

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Define a Poisson process. Stating the regularity conditions, Show that Pn (t) =P {N (t) =n} is given by the Poisson law

Explanation

Let X (t) denote the number of occurrences of a typical event over [0, t], X (t) is also referred as a counting process. Let X (t) be non-negative integer values continuous time process. Assume that

  1. X (t + h) -X (t) is independent of X (t) -X (0) with X (0) =0 that process with independent increments.

  2. X (t + h) -X (t) does not depend on t

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