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2017 CT4 April Q2ii

L

Laura

Very Active Member
Hi,
Why is the process stationary? The report mentions that this is as the increment depends on t the duration of the process.
But not too sure I understand this point.

Thanks in advance!
 
Hello

Let the process of interest be X_s (ie log(h(30 + s)). In this case, the question wants you to determine that the distribution of the increments of the process, ie X_(t+u) - X_u depend only on the duration t. So, for example, the distribution of the increment X_70 - X_50 is the same as the distribution as the increment X_40 - X_20, which is the same as the distribution as the increment X_35 - X_15 and so on.

This is an unusual question in that the process here is actually not really a stochastic process as all the values are known with certainty, given by the formula. So, in this case all the increments of the same duration take exactly the same value.

Hope this helps!

Andy
 
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