A currency trader is interested in converting between Brazilian Real and Canadian Dollars. She monitors the exchange rate over thirty consecutive trading days. Suppose the data are as plotted below:



The overall mean of the above series is . The first fifteen observations $x\left( 1\right) ,\dots ,x\left( t\right)$ in the series are



Part a)
Compared to a series of fifteen independent observations, the number of runs (above and below the mean ) in the fifteen observations given is

A. more than expected.
B. about the same as expected.
C. less than expected.


Part b)
Which of the following is a serial correlation plot for the first fifteen observations (that is, a plot of $x(t+1)$ against $x(t)$)? ??? A B C D



Part c)
Based on the serial correlation plot, what do you think is the correlation between consecutive values in the first fifteen observations?

A. 0
B.
C.
D.
E.


Part d)
The analyst decides to apply the runs test to the thirty observations. She counts the number of runs, then standardizes the count to give a test statistic value of . If testing at the 5% significance level, she should conclude:

A. there are fewer runs than would be expected in an independent series, the serial correlation being positive.
B. there are fewer runs than would be expected in an independent series, the serial correlation being negative.
C. there are more runs than would be expected in an independent series, the serial correlation being negative.
D. there are more runs than would be expected in an independent series, the serial correlation being positive.
E. there is no evidence to reject the hypothesis that the series are independent observations.


Part e)
Suppose the trader decides that a suitable model for the value $X\left( t\right)$ of a Canadian dollar in Brazilian Reals at time $t$ is



for $t=1,2,\dots$ where $\epsilon$ is an error term with mean zero. Given that the final value of the observed series is BRL, predict the next value to three decimal places.