Question

In: Statistics and Probability

Problem 6 (14 Marks) The unemployment rate (UR) for PEI by quarter was as follows: &nb

Problem 6

The unemployment rate (UR) for PEI by quarter was as follows:

UR T (Time)

Year Quarter Rate For Regression

2018 Q1 12.0 1

Q2 7.1 2

Q3 8.2 3

Q4 10.2 4

2019 Q1 12.2 5

Q2 6.9 6

Q3 7.1 7

Q4 9.9 8

Sketch this data on a graph. Is there seasonality in the data?
Use a four quarter moving average to determine the seasonal factors for the four quarters.

Calculate the four quarter moving average;
Centre the data if necessary;
Calculate the seasonal factors for each Quarter.
Calculate the average seasonal factors for each quarter.
What percentage is the rounding error in this calculation?

Expert Solution

Solution)

Excel work :

from the graph we have seen that there is a seasonality in unemployment rate.

1	2	3	4	5	6	7	8	9
					base line	Yt/CMA(4)	seasonal average	Yt/St
T	Years	Quarters	(UR)Unemployment rate(Yt)	MA(4)	CMA(4)	St,It	St	Deseasonalize
1	2018	Q1	12.0				1.320703654	9.086065574
2		Q2	7.1				0.76137931	9.325181159
3		Q3	8.2	9.4	9.4	0.872340426	0.872340426	9.4
4		Q4	10.2	9.4	9.4	1.085106383	1.085106383	9.4
5	2019	Q1	12.2	9.4	9.2	1.320703654	1.320703654	9.2375
6		Q2	6.9	9.1	9.1	0.76137931	0.76137931	9.0625
7		Q3	7.1	9.0			0.872340426	8.13902439
8		Q4	9.9				1.085106383	9.123529412

Since this is time series data we make

Our first column as "T" and enter values 1 to 8.

Our second column is ” Years “

Our third column is “ Quarters”

Our fourth column is “unemployement rate(UR)”

Our fifth column is “MA(4)” since our data is quarterly. We find moving average of Q1 to Q4 of 2018year in the cell corresponding to Q3 of 2018year and hit enter .

Then drag this value from 2018year Q3 to 2019year Q3 only as we find MA(4) so we have to take four values to find it . leave the above 2 cells and last one cell empty .

Formula to calculate average is

=average()

Our sixth column is ” CMA(4)” which is centered moving average this is our base line .

It is average of first 2 values of MA(4) column .

=Average()

Find average of first two values using average formula above and drag this value within column last cell value is empty because it is the average of two values.

Our seventh column is “(St, It)” which is seasonal and irregular obtained by (UR) divided by CMA(4)

=(UR)/CMA(4)

Our Eight column is “St” which is average of only seasonal values. For example average of only quarter 1 of 2018 and 2019.

Average of only quarter 2 of 2018 and 2019

Similarly average of only quarter 3 and only quarter 4 of 2018 and 2019 respectively.

For this we have to take values of Quarters from the column “(St, It)”

After find average of all quarters separately right the values in the column “St”

Our ninth column is “ Deasonalise “

=(UR)/St

orchestra answered 1 year ago

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