**BCom 1st Year Analysis Of Time Series Notes** :-

**Section A**

**SHORT ANSWER QUESTIONS **

**Q.1. Explain the meaning and importance of time series.**

**Or What is meant by time series? **

**Ans. Meaning of Time Series:** An arrangement of statistical data in accor occurrence or in a chronological order is called a time series. The numerical data which we get at different points of time, i.e. the set of observations is known as time series.

Mathematically, a time series is defined by the values Y1, Y), Y2, …, Yn of a variable y at time t1, T2, …) tr. Here, Y is a function of time t and Y, tends the value of the variable Y at time.

A time series consists of data arranged chronologically.

‘Time series consists of statistical data which are collected, recorded or observed over successive increments.

**Importance of Time Series Analysis**

The importance of time series analysis are as under:

**1. It Helps in the Analysis of Past Behaviour of a Variable: **Analysis of past data discloses the effect of various factors on the variable under study.

isolate and analyse the effects of various sets of homogeneous factors on the problem under study.

**2. It Helps in Forecasting: **The analysis of past conditions is the basis of forecasting the future behaviour of the variable under study, e.g. the analysis of a time series relating to income or wages or production would be the basis for forecasting future income or wages or production. This helps in making future plans of action.

**3. It Helps in Evaluation of Current Achievements: **The review and evaluation of progress made on the basis of a plan are done on the basis of time series data, e.g. the progress of our five-year plans is judged by the annual growth rates in the gross national products.

**4 It Helps in Making Comparative Studies:** Once the data are arranged, chronological comparison between one time period and another is facilitated. It provides a scientific basis fo by studying and isolating the effects of various components of a time series. It also helps in making regional comparison amongst data collected on the basis of time

**Q.2. What is a time series? Explain the objectives of the analysis of a time series.Ans.** Time series is a historian series that discloses relationship between two ve data are arranged in the order of their occurrence, the resulting statistical series is called a time series. Thus the statistics is a major instrument for predictions. In business economics, International trade, etc. the future has to be devised for planning. Whether, it be a case of sales in business, Production in industries or agriculture, nature, national income, population, etc. there are fluctuations in the rate of growth or happenings. Thus, time series is a need in the field of economic activities.

**Objectives: **The main objectives of the analysis of a time series are:

1. To study the past behaviour of the series, past experience is a guide to the future. Time series analysis only brings to light the salient features of this past experience

2. To forecast the future trend.

3. To isolate the effect of various forces that are affecting the series.

A time series is the result of the combined effects of different categories of forces like seasonal variations, cyclical variations, irregular variations, etc.

**Q.3. What are the causes of seasonal variation? Give its utility. **

**Ans.** The main causes of seasonal variation are:

**1 Climatic and Natural Forces:** The climatic changes play an important natic changes play an important role in the seasonal. movements. For example, sales of some goods increase in some season but decrease in the other, h.c. they are affected by natural forces, i.e. weather or season.

**2 Man-made Conventions: **These are the customs, habits, fashion, etc. There is no of wearing new clothes, preparing sweets, etc. in some festivals and during that time there demand for such items.

**Utility of Seasonal Variations: **These are extremely useful for businessmen, sales managers producers, etc. so as to plan future operations and to formulate policy decisions regarding purchase, personnel requirements, production, selling, etc. So, the time series data must be adjusted for seasonal variations so as to understand the behaviour of the phenomenon in a time series properly.

**Q.4. What are the merits and demerits of moving average method? **

**Ans. Merits of Moving Average Method: **These are as follows:

1. This method is simple to understand and use among all mathematical methods.

2. It is flexible that entire calculations are not distributed inspite of adding few more observations to the series.

3. In case, the period of cyclical fluctuation is taken to calculate moving average, such fluctuations will be eliminated.

4. This method follow the general pattern of the movement of time series data and so, the nature of the trend curve is determined by the data.

5. This method is also used to measure seasonal, cyclical and the irregular fluctuations.

**Demerits of Moving Average Method: **These are as follows:

1. Trend values cannot be determined for some of the periods initially and for some at the end.

2. This method cannot be used to find future values as they are the main objects of trend analysis to ascertain definitely the period of moving average when the time series

3. It is not required to ascertain definitely the period of does not exhibit cycles.

**Q.5. Explain how you would obtain estimates of the constant of a straight line fitted to time series data.**

**Ans. Fitting of Linear or Straight Line Trend:** The simplest type of trend equation is the linear equation of the form,

Y = a +bX

X represents time and Y be the value of the variables. Here, Y is the dependent and X is the independent variable. Now, for the set of given data (X1,Y1), (X2, Y2), …, (Xn, Yn) the constants a and b e determined by solving simultaneously the equation,

EY = Na + b2X

EXY = a£X+b3X2

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