Question

1. What can we say about a time series given its sample autocorrelation function? An actuary produces the following sample ACF for vehicle accident severities over a 10-year period: 10 06 ACF 02 -52 0 5 10 15 20 25 30 30 You are also given the following three statements about this time series: I. There is a positive trend in accident severity; II. There is a negative trend in accident severity; III. The accident severity data shows a seasonal pattern. Determine which of the above statements can be concluded from the above graph. Note that you do not need to know the meaning of the term "accident severity" to answer this question. A. I only B. II only C. III only D. I, II and III E. The answer is not given by (A), (B), (C), or (D).

Please explain each choice in detail. Thank you very much.

Answer 1

In the sample ACF plot, we see that there are peaks and a wave-like pattern has been formed. These peaks indicate that there is a seasonal pattern in the data. Also, in the plot, the autocorrelations are positive and they are decreasing gradually, which tell us that there is a positive trend in the data. There is no negative trend, though.
Hence, statements I and III are correct. Our answer is - The answer is not given by (A), (B), (C), or (D).