Statistics is the science of collecting, analyzing, interpreting, and presenting data. It helps students make informed decisions, identify patterns, and solve real-world problems by applying mathematical concepts to data from various fields like business, science, and social studies.

1. Business Statistics
(Unit – II)
Q1.What do you mean by Time series? State the importance of Time Series Analysis
Q2. What do you mean by components of Time Series? Also explain the models of analysing
Time Series.
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2. Q1. What do you mean by Time series? State the importance of Time Series Analysis
Ans.
Time Series
When some information is obtained according to time, then such type of series is called Time
Series. In other words, the numerical data which we get at different points of time thus which
series we find that is called Time Series.
Importance of Analysis of Time Series
OR
Utility of Time Series Analysis
The analysis of Time Series is extremely useful in each and every sphere because of the
following reasons:
1. Helpful in the Analysis of Past Behaviour:By recording data over a period of time
we can easily understand the changes that have taken place in the past.
2. Helpful in Forecasting and Planning: With the help of Time Series, we can also
forecast the estimated sales or production or profits etc. for future time period if all
the things remain same.
3. Helpful in Comparative Study:
Once the Time Series data are recorded, the comparison between the values of the
variable at different time points become possible. It helps to compare variations in the
values of a variable over time and analyses the causes of such variations.
4. Evaluation of Performance: With the help of Time Series Analysis, we can estimate
future production or sale or profit etc. In this way in the coming time when actual
production or sale or profits will be earned in the coming future it may be compared
with estimated figures. Thus, we can analyse the performance of the company.
5. Estimation of Trade Cycle: Trade cycle may be estimated on the basis of cyclical
fluctuations and it helps the businessmen to plan and regulate his activities.
6. Uses in Other Fields: Utility of Time Series Analysis is not limited to economist and
businessmen only but also to the scientist, astronomist, geologist, sociologist,
biologist, research worker etc. It is applicable to all such fields of humanities and pure
sciences where studies are undertaken on the basis of data related to time.
Q2. What do you mean by components of Time Series? Also explain the models of
analysing Time Series.
Ans.
Components of Time Series
The changes or variation in the values of any phenomenon over a period of time are due to a
number of forces or factors. These forces or factors are called “Component of Time Series”.
These components throw light on some distinct characteristics of change both long-term or
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3. short-term, regular or irregular, repetitive or non-repetitive etc. The main components of
Time Series are as under:
 Trend or Secular Trend (T).
 Seasonal Variation (S).
 Cyclical Variation (C).
 Irregular or Random Variations (I).
1. Trend or Secular Trend (T):The general tendency of the time series data to increase
or decrease or stagnate during a long period of time is called the ‘Secular Trend’ or
‘Trend’. It is denoted by “T”.For Example, an upward tendency is usually observed
in time series relating to population, production, prices, income, money in circulation
etc.
2. Cyclical Variation (C): Cyclical variation is a periodic or repetitive movement in
Time Series in long-term. These variations are called cyclical because they occur in
cyclical nature which includes four stages: (i) Prosperity, (ii) Recession, (iii)
Depression and (iv) Recovery.
3. Seasonal Variation (S): It is a special case of Cyclical Variation in which
fluctuations are repeated usually within a year (e.g., weekly, monthly, quarterly).
Thus, seasonal variations are periodic patterns of movements in a time series. For
example, average sales for a retail store may increase greatly during festival season,
demand of woollen cloths increase during November to February every year etc. It is
denoted by “S”.
4. Irregular or Random Variance (I): Irregular variations arise owing to unforeseen
and unpredictable forces at random and affect the data. These are caused by war,
flood, strike,lockouts, revolution etc. Normally, these are short-term variations but at
times may leave a long lasting effect. Infect, the irregular variations include all those
variations which are caused by a sudden and unanticipated events.
Analysis of Time Series
OR
Decomposition of Time Series
The main objective of time series analysis is to give a mathematical description of
components of Time Series. In order to meet this objective, it is necessary to break down the
series into its main components e.g., Secular Trend (T), Seasonal Variance (S), Cyclical
Variation (C) and Irregular Movements (I). Thus, the main problem in the analysis of Time
Series are to identify its components and isolate, study and measure them independently.
In simple words, it can be said that, the measurement, analysis and study of T, C, S,
and I is called analysis of Time Series or Decomposition of Time Series.
 Time Series Decomposition Models:
The following are the two mathematical models commonly used for decomposition of a
Time Series into its components:
(A)Additive Model
(B) Multiplicative Model
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4. (A). Additive Model: According to Additive Model, a particular observation in a time series
is the sum of T, C, S and I.
O = T + C + S + I
According to this model, individual factors may be calculated as under:
T = O – C – S – I; C = O – T – S – I ; S = O – T – C – I; I = O – T – C – S
The Additive Model assumes that all the four components of the Time Series operate
independently of each other so that none of these components has any effect on the remaining
three.
However, this assumption is not true in most of the economic and business time series
where the four components of the Time series are not independent of each other.
(B). Multiplicative Model: According to Multiplicative Model, a particular observation in a
time series is the product of four components i.e., T. C. S and I.
O = T x C x S x I
According to this model, individual factors may be calculated as under:
T = O/CSI; C = O/TSI; S = O/TCI; I = O/TCS
Where,
O = Original Values
T = Secular Trend
S = Seasonal Variation
C = Cyclical Variation
I = Irregular Variation
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