QUESTION 4

Consider the following times-series where the data is recorded weekly

Data collected over 36 weeks

t X t X t X t X t X t X

1 9.8 7 36.4 13 53.4 19 99.2 25 105.3 31 141.3

2 9.0 8 51.0 14 66.6 20 90.4 26 116.7 32 151.8

3 10.5 9 51.1 15 70.6 21 91.2 27 113.2 33 151.1

4 20.6 10 46.9 16 76.4 22 94.9 28 120.5 34 156.4

5 28.1 11 50.5 17 88.4 23 94.2 29 124.2 35 155.9

6 28.3 12 58.5 18 98.6 24 104.1 30 130.2 36 160.0

(4.1) Does the time-series seem to follow a trend? If yes, which type of trend? Justify your answer. (2)

(4.2) Does the time-series show any evidence of seasonality? Justify your answer. (2)

(4.3) Is the time-series covariance-stationary? Justify your answer. (2)

(4.4) Assess the level of heteroskedasticity. Is there a reason for concern? Justify your answer. (3)

(4.5) Assess the level of serial correlation. Is there a reason for concern? Justify your answer. (3)

(4.6) Conduct an AR(1) process on a new time-series obtained after a carefully chosen transformation, and (5)

assess the level of serial correlation via an auto-correlation test.

(4.7) Provide an estimate of the value of the time-series at week 37. (3)