# Applied Statistics (ISS (Statistical Services) Statistics Paper III): Questions 1 - 5 of 45

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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 » Index Numbers » Laspeyre

Appeared in Year: 2015

### Describe in Detail

Discuss the considerations in the choice of (i) base period and (ii) the formula (method), for constructing price index numbers.

### Explanation

__ (i) __ __Choice of base period: __ Price index numbers are constructed in reference to a period against which the comparisons are to be made. Such a reference period is known as base period. The index for base period is always taken to be 100. The base primarily depends upon the purpose of the index number. Still there are certain requirements.

(a)

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## Question number: 3

» Applied Statistics » Index Numbers » Link and Chain Relatives Composition of Index Numbers

Appeared in Year: 2015

### Describe in Detail

In the construction of price index numbers, explain the terms ‘time reversal test’ and ‘factor reversal test’. Show that both these tests are satisfied by the Fisher index.

### Explanation

Price index numbers which measure the change in the retail or wholesale prices of a commodity at current period to some previous period. In the construction of price index numbers various test is consider tom find the accuracy of the formula. We explain the following test.

__ (i) __ __Time reversal test: __ An index formula would be accurate if it maint

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## Question number: 4

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

Appeared in Year: 2015

### Write in Short

State the problem of autocorrelation in a general linear model. Why does this problem arise? Demonstrate its effect on ordinary least square estimator (OLSE).

## Question number: 5

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

Appeared in Year: 2015

### Describe in Detail

The following information concerns changes in price and consumption (quantity) of certain major of components of the consumption basket of the labour class:

- | - | - | Year 2000 | Year 2000 | Year 2014 | Year 2014 |

SI. No. | Item | Unit | Price ( Rs. ) | Consumption | Price ( Rs. ) | Consumption |

1 | Rice | Quintal | 500 | 16 | 640 | 20 |

2 | Wheat | Quintal | 240 | 52 | 320 | 10 |

3 | Cloth | Metre | 16 | 50 | 20 | 35 |

Compute price index using

(i) Fisher’s method

(ii) Marshall-Edgeworth method

Also interpret the results.

### Explanation

To compute price index, various index methods is consider. Here for this portfolio we consider two index methods.

Where

And

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