Seasonal index is a measure of how a particular season compares with the average season.

Irregular variations do not have particular pattern and there is no regular period of time of their occurrences. Normally they are short terms variations but its occurrence sometimes has its effect so intense that they may give rise to new cyclic or other movements of variations.
For example floods, wars, earthquakes, Tsunami, strikes, lockouts etc.

Cyclic uniformly periodic in nature. They may or may not follow exactly similar patterns after equal intervals of time. Generally one cyclic period ranges from 7 to.9 years and there is no hard and fast rule in the fixation of years for a cyclic period. For example, every business cycle has a Start-Boom-Depression- Recover maintenance during booms and depressions, changes in government monetary policies, changes in interestrates.

Since the number of years is even(eight), we can equally divide the given data it two equal parts and obtain the averages of first four years and last four years.

Fisher’s price index number
\({ P }_{ 01 }^{ F }=\left( \sqrt { \frac { \sum { { p }_{ 1 }{ q }_{ 10 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } } \right) \times 100=\left( \sqrt { \frac { 623\times 517 }{ 584\times 484 } } \right) \times 100=106.74\)
Time Reversal Test: P₀₁ × P₁₀ = 1
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 0 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 0 } } } \right) } \)
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { 623\times 517\times 484\times 584 }{ 584\times 487\times 517\times 623 } \right) } \)
P₀₁ x P₁₀ = 1
Factor Reversal Test
\({ P }_{ 01 }\times { Q }_{ 01 }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\sqrt { \left( \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } \times \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } \times \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } \right) } \)
\({ P }_{ 01 }\times { P }_{ 10 }=\sqrt { \left( \frac { 623\times 517\times 484\times 517 }{ 584\times 484\times 584\times 623 } \right) } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\sqrt { \left( \frac { 517\times 517 }{ 585\times 584 } \right) } =\frac { 517 }{ 584 } \)
\({ P }_{ 01 }\times { P }_{ 01 }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \)

Laspeyre’s price index number
\({ P }_{ 01 }^{ L }=\frac { \sum { { p }_{ 1 }{ q }_{ 0 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } } \times 100=\frac { 487}{ 376} \times 100=129.5212\)
Paasche’s price index number
\({ P }_{ 01 }^{ P }=\frac { \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 1 } } } \times 100=\frac { 709 }{ 565 } \times 100=125.4867\)
Fisher’s price index number
\({ P }_{ 01 }^{ F }=\sqrt { \frac { \sum { { p }_{ 1 }{ q }_{ 0 } } \times \sum { { p }_{ 1 }{ q }_{ 1 } } }{ \sum { { p }_{ 0 }{ q }_{ 0 } } \times \sum { { p }_{ 0 }{ q }_{ 1 } } } } \times 100=\sqrt { \frac { 487\times 709}{ 376\times 565} } \times 100=127.4879\)
On an average, there is an increase of 29.52%, 25.48% and 27.48% in the price of the commodities by Laspeyre’s, Paasche’s, Fisher’s price index number respectively, when the base year compared with the current year.

Computation of Seasonal Index by the method of simple averages.

S.I for I Quarter = \(\frac{Average\ of \ I\ quarter }{Grand\ average} \times100\)
Grand Average = \(\frac{1304.333}{4}=326.0833\)
S.I for I Q = \(\frac{243.8333}{326.0833} \times100= 74.77;\) 
S.I for II Q = \(\frac{312}{326.0833} \times100=95.68;\)
S.I for III Q = \(\frac{361.6667}{326.0833} \times 100=110.91; \) 
S.I for IV Q = \(\frac{386.833}{326.0833} \times 100=118.63\)

Computation of trend values by the method of least squares (ODD Years).

\(a=\frac { \sum { Y } }{ n } =\frac { 316 }{ 7 } =45.143;\quad b=\frac { \sum { XY } }{ { \sum { X } }^{ 2 } } =\frac { 29 }{ 28 } =1.036\)
Therefore, the required equation of the straight line trend is given by
Y = a + bX
Y = 45.143 + 1.036 (x - 2003)
The trend values can be obtained by
When X = 2000 , Yt = 45.143 + 1.036(2000–2003) = 42.035
When X = 2001, Yt = 45.143 + 1.036(2001–2003) = 43.071,
similarly other values can be obtained.