Question

In: Statistics and Probability

The unemployment rate (UR) for PEI by quarter was as follows: UR T (Time) Year Quarter...

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

UR T (Time)

Year Quarter Rate For Regression

2018 Q1 11.9 1

Q2 7.0 2

Q3 8.1 3

Q4 10.1 4

2019 Q1 12.1 5

Q2 6.8 6

Q3 7.0 7

Q4 9.8 8

  1. Sketch this data on a graph. Is there seasonality in the data?

  2. Use a four quarter moving average to determine the seasonal factors for the four quarters.

  1. Calculate the four quarter moving average;

  2. Centre the data if necessary;

  3. Calculate the seasonal factors for each Quarter.

  4. Calculate the average seasonal factors for each quarter.

  5. What percentage is the rounding error in this calculation?


Solutions

Expert Solution

(a)

Yes, there is a seasonality from the graph.

(b)

Centered
Moving Ratio to Seasonal UR Rate
t Year Quarter UR Rate Average CMA Indexes Deseasonalized
1 1 1 11.9 1.327 8.97
2 1 2 7.9 0.772 10.24
3 1 3 8.1 9.525 0.850 0.841 9.64
4 1 4 10.1 9.413 1.073 1.061 9.52
5 2 1 12.1 9.013 1.343 1.327 9.12
6 2 2 6.8 8.713 0.780 0.772 8.81
7 2 3 6.0 0.841 7.14
8 2 4 9.8 1.061 9.24
Calculation of Seasonal Indexes
1 2 3 4
1 0.850 1.073
2 1.343 0.780
mean: 1.343 0.780 0.850 1.073 4.047
adjusted: 1.327 0.772 0.841 1.061 4.000

The seasonal factors are:

Calculation of Seasonal Indexes
1 2 3 4
0.850 1.073
1.343 0.780

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