Consider the random walk with drift model xt = d + + wt, for t = 1, 2, . . , with x0 = 0, where wt is white noise with variance s2w . (a) show that the model can be written as xt = dt + åt k=1 wk. (b) find the mean function and the autocovariance function of xt. (c) argue that xt is not stationary. (d) show rx(t 1, t) = q t ! 1 as t ! ¥. what is the implication of this result? (e) suggest a transformation to make the series stationary, and prove that the transformed series is stationary.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!