Page 249 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 11.4 Keywords

Additive Model: This model is based on the assumption that the value of the variable of a time
series, at a point of time t, is the sum of the four components. Using symbols, we can write
Y = T + S + C + R , where T , S , C and R are the values of trend, seasonal, cyclical and random
t t t t t t t t t
components respectively, at a point of time t.
Cyclical Variations: The oscillatory movements are termed as Cyclical Variations if their
period of oscillation is greater than one year.

Link Relatives Method: This method is based on the assumption that the trend is linear and
cyclical variations are of uniform pattern.
Multiplicative Model: This model assumes that Yt is given by the multiplication of various
components. Symbolically, we can write Yt = Tt × St × Ct × Rt.
Periodic Variations: These variations, also known as oscillatory movements, repeat themselves
after a regular interval of time. This time interval is known as the period of oscillation.

Random or Irregular Variations: As the name suggests, these variations do not reveal any
regular pattern of movements. These variations are caused by random factors such as strikes,
floods, fire, war, famines, etc.
Seasonal Variations: The oscillatory movements are termed as Seasonal Variations if their
period of oscillation is equal to one year.
Secular Trend: Secular trend or simply trend is the general tendency of the data to increase or
decrease or stagnate over a long period of time.

Time Series: A series of observations, on a variable, recorded after successive intervals of time is
called a time series.

11.5 Review Questions

1. Explain the meaning and objectives of time series analysis. Describe briefly the methods
of measurement of trend.
2. What is a time series? What are its main components? How would you study the seasonal
variations in any time series?

3. Distinguish between secular trend and periodic variations. How would you measure
trend in a time series data by the method of least squares? Explain your answer with an
example.
4. Explain the method of moving average for the determination of trend in a time series
data. What are its merits and demerits?
5. Discuss the underlying assumptions of additive and multiplicative models in a time series
analysis. Which of these is more popular in practice and why?

6. Distinguish between the ratio to trend and the ratio to moving average methods of
measuring seasonal variations. Which method is more general and why?
7. “All periodic variations are not necessarily seasonal”. Discuss the above statement with a
suitable example.
8. Determine secular trend by the method of semi-averages from the following data on the
production of sugarcane (in million tonnes). Plot the observed and the trend values on a
graph.

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