ISS (Statistical Services) Statistics Paper III: Questions 87  93 of 96
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Question number: 87
» Applied Statistics » Time Series Analysis » Illustration, Additive and Multiplicative Models
Appeared in Year: 2014
Describe in Detail
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
Represents the Seasonal value
Question number: 88
» Econometrics » Heteroscedastic Disturbances
Appeared in Year: 2014
Describe in Detail
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
Question number: 89
» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives
Appeared in Year: 2014
Describe in Detail
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
Question number: 90
» Applied Statistics » Index Numbers » Fisher Index Numbers: Chain Base Index Number & Tests for Index Number
Appeared in Year: 2014
Describe in Detail
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
Question number: 91
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Describe in Detail
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.
Question number: 92
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Write in Short
Discuss a onedimensional random walk.
Question number: 93
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Describe in Detail
Define a Poisson process. Stating the regularity conditions, Show that P_{n} (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 nonnegative integer values continuous time process. Assume that

X (t + h) X (t) is independent of X (t) X (0) with