# Applied Statistics-Time Series Analysis (ISS (Statistical Services) Statistics Paper III): Questions 1 - 7 of 17

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## Question number: 1

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2015

### Describe in Detail

List the main components of a times series. Explain the method of link relative for measurement of seasonal fluctuations of a times series.

### Explanation

The main components of a times series are the following:

(i) __Secular Trend (T) __: Long term movements in the mean

This measures smooth and regular long-term movements of a times series delineating the increasing, decreasing or stagnant trend over a long span of time.

__ (ii) __ __Seasonal Variation (S) __: Cyclical fluctuations related to the calenda

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## Question number: 2

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2009

### Describe in Detail

Explain ratio to moving average method for calculating seasonal indices.

### Explanation

Ratio to moving average method is an improvement over the ‘ratio to trend’ method as it removes the cyclic fluctuations, which remain closely mixed with the seasonal indices calculated under ‘ratio to trend method’. Here seasonal indices are calculated based on the moving average trend instead of a least square trend.

Further, both the trend and

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## Question number: 3

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2009

### Write in Short

Describe the Yule -Slutsky effect of moving average operation on the random component of a time series.

## Question number: 4

» Applied Statistics » Time Series Analysis » Exponential and Moving Average Smoothing

Appeared in Year: 2011

### Describe in Detail

Explain moving average [m, p]. Let with p = 1 and m = 2k + 1, obtain the coefficient of and [m, p]

### Explanation

Moving average: moving average method is a simple and flexible method for measuring trend. It consists in measurement of trend by smoothing out the fluctuations of the data by means of a moving average.

The first element of the moving average is obtained by taking the average of the initial fixed subset of the number series i. e. the first averag

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## Question number: 5

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2010

### Write in Short

Discuss the ratio to trend method for separating the seasonal component in a time series.

## Question number: 6

» Applied Statistics » Time Series Analysis » Exploratory Time Series Analysis

Appeared in Year: 2011

### Describe in Detail

Give the various steps for finding the variance of the random component using variate difference method. Is F-test used for testing the significance of homogeneity of two successive estimates of variance? If yes, ok, otherwise which ‘test can be used? Discuss.

### Explanation

To find the variance of the random component using variate difference method:

let us consider a series represented as the sum of functional part and random component

Here are considered as independently identically distributed with

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## Question number: 7

» Applied Statistics » Time Series Analysis » Determination of Trend, Seasonal and Cyclical Fluctuations

Appeared in Year: 2012

### 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 be the trend eq

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