Unit 3: Time Series
Points to Remember

Year
1
2
3

In case of 3 yearly moving averages
Data
In case of 4 yearly moving averages
4 yearly sums
2 item Sums
Trend
Start Here
In case of 5 yearly moving averages
Year Data
1
2
3

Trend
Start Here
Year Data
1
2
3
4

3 yearly sums
5 yearly sums
Trend
Start Here
In case of 2 yearly moving averages
Year Data
1
2
2 yearly sums
2 item Sums
Trend
Start Here

Year
For equation y=a+bx
y
∑y

x2
x
∑x
∑x2
xy
∑xy
For equation y =a+bx+cx 2
Remember the following
na+b∑x+c∑ x2 =∑y
a∑x +b∑x2+c∑ x3=∑xy
a∑x2 +b∑x3+c∑ x4=∑x2y
Here ‘n’ is the number of values.
Year
y
∑y
x2
x
∑x
∑x2
x3
∑x3
x4
∑x4
xy
∑xy
x2 y
∑x2y
For questions in the equation format, substitute the values of x in the equation once you arrive at the
solution to get the trend values.
Exponential Trend
This is given as:
y=abx
Where ‘y’ denotes time series data, x denotes time, a and b are constants
log y = log a + x log b
log 𝑎 =
log 𝑏 =
∑ log 𝑦
𝑛
∑ 𝑥 log 𝑦
∑ 𝑥2
𝑎 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 [
𝑏 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 [
Year
y
x
x2
log y
∑ 𝑙𝑜𝑔 𝑦
]
𝑛
∑ 𝑥 𝑙𝑜𝑔 𝑦
]
∑ 𝑥2
x log y
When they ask you to find trend, solve the equation for log y by taking antilog of the answer.