Question

3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Y% (a) Using R generate 300 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 300 observations of the series Y -Z. Plot its acf. c) Analyze graphs from (a) and (b). Can you see a difference between the plots of graphs of time series Z and Y? From the graphs, would you conclude that both series are stationary (or not)? Is there a noticeable difference in the plots of acf functions ρz and PY? Would you describe as a non-Gaussian white noise sequence based on your plots? Provide full analysis of your conclusions. (d) Calculate the second-order moments of Y: μΥ(t-EĢ), σ3(t)-VarĢ), and py (t,t+h) Cor(Y, Yi+h). Do your calculations support your observations in (c)? (Hint: For X ~ Ņ(0, σ2), E(X*)--3(o2)2.)

Answer 1

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