# Applied Statistics-Time 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

Essay Question▾

### 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

Essay Question▾

### 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

Essay Question▾

### 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

Essay Question▾

### 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:

(ii) Multiplicative 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

Essay Question▾

### 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 + s1) −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 one-dimensional random walk.

## Question number: 14

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

Essay Question▾

### Describe in Detail

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 t

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## Question number: 15

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

Essay Question▾

### Describe in Detail

If Xn is a branching process with

and σ2= Var (X1), then show that

1. E (Xn) =mn

### Explanation

Let X0=1. It is evident

Let Zij be i. i. d with the offspring distribution P [Zij=k] =pk, k = 0,1, 2, . . Such a process {Xn} is called branching process and Xn denotes the number of individual in the nth generation.

(i)

Since these are independent

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