Unit
– 4: Time Series analysis:
Q.N.1. Define time
series. What are its utilities? What the components of time series?
Ans: - Definition: - A time series is a set
of statistical observations arranged is chronological order. Time
series may be defined as collection of magnitudes of some variables belonging
to different time periods. It is commonly used for forecasting.
Utility of
Time Series Analysis
The analysis of Time Series
is of great significance not only to the economist and businessman but also to
the scientist, geologist, biologist, research worker, etc., for the reasons
given below:
a) It helps
in understanding past behaviors: By observing
data over a period of time one can easily understanding what changes have taken
place in the past, Such analysis will be extremely helpful in producing future
behavior.
b) It helps
in planning future operations: Plans for the
future cannot be made without forecasting events and relationship they will
have. Statistical techniques have been evolved which enable time series to be
analyzed in such a way that the influences which have determined the form of
that series to be analyzed in such a way that the influences which have
determined the form of that series may be ascertained.
c) It helps
in evaluating current accomplishments: The
performance can be compared with the expected performance and the cause of
variation analyzed. For example, if expected sale for 1995 was 10,000
refrigerators and the actual sale was only 9,000, one can investigate the cause
for the shortfall in achievement. Time series analysis will enable us to apply
the scientific procedure for such analysis.
d) It
facilitates comparison: Different time series
are often compared and important conclusions drawn there from. However, one should not be led to believe that by time
series analysis one can foretell with 100percnet accuracy the course of future
events.
The four components of time series
are:
1.
Secular trend
2.
Seasonal variation
3.
Cyclical variation
4.
Irregular variation
Secular trend: A time
series data may show upward trend or downward trend for a period of years and
this may be due to factors like increase in population, change in technological
progress, large scale shift in consumer’s demands etc. For example, population
increases over a period of time, price increases over a period of years,
production of goods on the capital market of the country increases over a
period of years. These are the examples of upward trend. The sales of a
commodity may decrease over a period of time because of better products coming
to the market. This is an example of declining trend or downward trend. The
increase or decrease in the movements of a time series is called Secular trend.
Seasonal variation: Seasonal
variation are short-term fluctuation in a time series which occur periodically
in a year. This continues to repeat year after year. The major factors that are
responsible for the repetitive pattern of seasonal variations are weather
conditions and customs of people. More woolen clothes are sold in winter than
in the season of summer .Regardless of the trend we can observe that in each
year more ice creams are sold in summer and very little in Winter season. The
sales in the departmental stores are more during festive seasons that in the
normal days.
Cyclical variations: Cyclical
variations are recurrent upward or downward movements in a time series but the
period of cycle is greater than a year. Also these variations are not regular
as seasonal variation. There are different types of cycles of varying in length
and size. The ups and downs in business activities are the effects of cyclical
variation. A business cycle showing these oscillatory movements has to pass
through four phases-prosperity, recession, depression and recovery. In a
business, these four phases are completed by passing one to another in this
order. It has four important characteristics: i) Prosperity ii)
Decline iii) Depression iv) Improvement
Irregular variation: Irregular
variations are fluctuations in time series that are short in duration, erratic
in nature and follow no regularity in the occurrence pattern. These variations
are also referred to as residual variations since by definition they represent
what is left out in a time series after trend, cyclical and seasonal variations.
Irregular fluctuations results due to the occurrence of unforeseen events like floods,
earthquakes, wars, famines, etc.
Q.N.2. What are the different models of time
series?
Ans: - In
Traditional time series analysis, it is ordinarily assumed that there is a
multiplicative relationship between the components of time series. Symbolically, Y=T X S X C X I
Where T= Trend
S= Seasonal
component
C= Cyclical
component
I=
Irregular component
Y= Result of
four components.
Another
approach is to treat each observation of a time series as the sum of these four
components Symbolically, Y=T + S+ C + I
Q.N.3. Mention the different methods of
measuring trend and seasonal variation.
Ans: - The
following four methods are commonly used for measuring trends:-
i)
Graphic method
ii)
Semi-average method
iii)
Moving average method
iv)
Method of least squares.
Again,
The following methods are commonly used for measuring seasonal variation:-
i)
Method of simple averages
ii)
Ratio to trend method
iii)
Ratio to moving average
iv)
Link relative method.
i) Graphic method: - This is
the simplest method of studying trend. The procedure of obtaining a straight
line trend is:
a)
Plot the time series on a Graph.
b)
Examine the direction of the trend based on the plotted information.
c)
Draw a straight line which shows the direction of the trend.
The
trend line thus obtained can be extended to predict future values.
Merits:-
i)
This method is simplest method of measuring trend.
ii)
This method is very flexible. I can be used regardless of whether the trend is a
straight line or curve.
Demerits:-
i) This
method is highly subjective because it depends on the personal judgement of the
investigator.
ii) Since this method is subjective in nature it
cannot be used for predictions.
ii)
Semi-average method: - Under this method, the given data is divided
into two parts. After that an average of each part is obtained which gives two
points. Each point is plotted at the mid-point of the class interval covered by
the respective part and then the two points are joined by a straight line which
gives the required trend line.
Merits:-
i)
This method is simple to understand as compared to the moving average method
and the method of least square.
ii)
This is an objective method of measuring trend as everyone who applies this
method gets the same result.
Demerits:-
i)
It is affected by extreme values.
ii)
This method assumes straight relationship between the plotted points whether
this exist or not.
iii) Method of moving average: - Under
this method the average value for a certain time span is secured and this
average is taken as the trend value for the unit of time falling at the middle
of the period covered in the calculation of the average. While using this
method it is necessary to select a period for moving average.
Merits:-
i) This method is simple to understand and apply.
ii) It is particularly effective if the trend of a series is very
irregular.
iii) It is a flexible method of measuring trend because all
figures are not changed if a few figures are added to the data.
Demerits:-
i) Trend values cannot be computed for all years.
ii) No there is no hard and fast rule for selecting the period of
moving average.
iii) this method is not appropriate if the trend situation is not
linear.
iv) Method
of Least Square: - This method is most commonly used method of
measuring trend. It is a mathematical method and a trend line is fitted to the
data in such a manner that the following two conditions are satisfied:-
i) the sum of deviation of the actual values from their respective
mean is zero.
ii) the sum of square of the deviations of the actual and compute
values is least from this line. That is why this method is called method of
least square.
The straight line trend is represented by the equation: Y = a + bx
Where, y = denotes the trend values
a = represents the intercept on
y axis.
b= represents slope of the trend
line.
Merits:-
i) This is a mathematical method of measuring trend.
ii) Trend values can be obtained for all the given time periods in
the series.
Demerits:-
i) This method is more tedious and time consuming.
ii) This method cannot be used to fit the growth curves.
Q.N.4. What is meant by shifting of trend
origin and deseasonalised data?
Ans: - Shifting:-Shifting of trend origin
means replacing the origin with new base. Shifting can be done by using the
following formula: Y = a + b (X + k)
Where k is
the number of time units shifted. If the origin is shifted forward in time, k
is positive and if shifted backward in time, k is negative.
Deseasonalised Value: - The
value which show how things would have been or would be if there were no
seasonal fluctuations is called Deseasonalised data. In order to obtain
Deseasonalised data, the effect of seasonal variations have to be removed. For
this purpose, the actual data is divided by the appropriate seasonal indices.
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