#Stationary Processes

6 messages · Page 1 of 1 (latest)

junior wren
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For this problem, we're focusing on: "In each of the following cases, determine with justification whether or not the resulting
process indexed by t ∈ Z is weakly stationary. If so, compute its autocovariance and
autocorrelation functions, and give further conditions (if any) under which the process
is strongly stationary."

Now, I get to part f), and I'm a bit thrown off here. The previous parts were a lot less abstract, and I was easily able to check off the boxes to confirm stationarity. However, I get to the problem I've attached as an image below and have been lost on it for a bit now.

I'm understanding that it's normally distributed from 0 to 1 =, but I'm not really understanding the X_0 being uniformally distributed from -1 to 1, or at least not in this context. I think I recall the definition of autocorrelation involving this, but aside from that, I'm not sure what to do with these bits of information.

I appreciate any help that can be offered!

image.png
solemn knotBOT
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solemn knotBOT
little kindle
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Hi. So in this question you are having two cases. One for t \neq 0 and other one is t=0. You know for the first case that X_t follows a normal distribution with mean 0 and variance 1. You need to show that this is also the case for the X_0. Hence you need to calculate the mean and variance, since the definition of weakly stationarity requires the variance and mean to be constant across time. I will explain how to calculate the autocovariance function for you after you have calculated the mean and variance for X_0.

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@junior wren

solemn knotBOT
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@junior wren

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