Question

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

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

Answer 1

x=c(9.8,9.0,10.5,20.6,28.1,28.3,36.4,51.0,51.1,46.9,50.5,58.5,53.4,66.6,70.6,76.4,88.4,98.6,99.2,90.4,91.2,94.9,94.2,104.1,105.3,116.7,113.2,120.5,124.2,130.2,141.3,151.8,151.1,156.4,155.9,160.0)

serialCorrelationTest(x, test = "rank.von.Neumann",
alternative = "two.sided", conf.level = 0.95)

ser i alcorrelationTest (y, "rank" von "Neumann", alternative = "two" sided", conf. Îeve1 test > = 0.95) Results of Hypothesis Test rho0 Null Hypothesis: Alternative Hypothesis: True rho is not equal to 0 Rank von Neumann Test for Test Name: Lag-1 Autocorrelation (Beta Approximation) Estimated Parameter (s): rho0. 8760415 Estimation Method: Yule-Wwalker Data: sample size: 36 RVN 0.04066924 Test Statistic: P-value: 0 Confidence Interval for: rho Confidence Interval Method: Normal Approximation Confidence Interval Type: two-sided Confidence Level: 95% Confidence Interval LCL = 0.718514 UCL 1.000000

Here from the serial correlation test the p value is 0.04<0.05. Hence we reject the null hypothesis that is rho =0.