Applied StatisticsTime Series Analysis (ISS (Statistical Services) Statistics Paper III): Questions 8  15 of 17
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Question number: 8
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Appeared in Year: 2013
Describe in Detail
Discuss the relevance of variate difference method in time series analysis data. Show that
Explanation
Relevance of variate difference method:
Although many different formulas are used to measure the random component in a time series, , the variate difference method fits the best, because this method method enables us to estimate the variance of the random component in a series. The variate difference method does not require the specification of a
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Question number: 9
» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations
Appeared in Year: 2012
Describe in Detail
Discuss link relative method to estimate seasonal fluctuations, with appropriate illustrations.
Explanation
link relative is the value of one season expressed as a percentage of the preceding season. The word ‘season’ refers to time period, it means month for monthly data, quarter for quarterly data etc.
Under this method, the seasonal indices are found with the following steps.
Steps:
(i) Find the link relative of all the seasonal data using the fo
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Question number: 10
» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations
Appeared in Year: 2013
Describe in Detail
Discuss various steps of finding adjusted monthly indices of seasonal variations using link relative method.
Explanation
Steps of finding adjusted monthly indices of seasonal variations using link relative method:
(i) Find the link relative of all the seasonal data using the formulae
Where = link relative of the current season
(ii) Arrange the entire link relatives thus obtained seaso
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Question number: 11
» 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
Represents the Cyclic value
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Question number: 12
» 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.

Z (t + s_{1}) −Z (t) is independent
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Question number: 13
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Write in Short
Discuss a onedimensional random walk.
Question number: 14
» 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 X (0) =0 that process with independent increments.

X (t + h) X (t) does not depend on t t
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Question number: 15
» Applied Statistics » Time Series Analysis » Discrete Parameter Stochastic Process
Describe in Detail
If X_{n} is a branching process with
and σ^{2}= Var (X_{1}), then show that

E (X_{n}) =m^{n}

Explanation
Let X_{0}=1. It is evident
Let Z_{ij} be i. i. d with the offspring distribution P [Z_{ij}=k] =p_{k}, k = 0,1, 2, . . Such a process {X_{n}} is called branching process and X_{n} denotes the number of individual in the nth generation.
(i)
Since these are independent
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