x, = + 0.742,-1 where Z, is Normally distributed white noise with standard devia

Question

x, = + 0.742,-1 where Z, is Normally distributed white noise with standard deviation 2.2. Derive and sketch the actual spectral density function for X Part (a) Linked above is a realisation of X,, for 1,2,... , 500. Using the command spec.pgram, with log-" no " but otherwise taking default options, compute and plot the raw periodogram for the time series. Name your periodogram specl. The vector spec1l$freq gives the (approximate) Fourier frequencies at which the periodogram is computed, though these frequencies should be multiplied by 2? to be consistent with definations given for spectral densities. Moreover, the periodogram values given by R are ? times those given by the defination adopted. Compute the absolute difference between the raw periodogram from R (divided by ?) and the spectral density of X, at the pth frequency where p = 138, giving your answer to three decimal places. Part (b) The periodogram can be smoothed to give a consistent estimator of the spectral density function. A single (Daniell) smoother of span 14 can be implemented by adding the option spans = c(14) in spec. Pgram. Hence create a new periodo ram named spec2. Compute the absolute difference between the new periodogram and the spectral density of X, at the pth frequency where p=138, giving your answer to three decimal places. Part (c) In terms of the simple comparison above, which version of the periodogram gives a better estimate of the spectral density at the chosen frequency? A. The raw periodogram. B. The smoothed periodogram..

Explanation / Answer

given link is not opening plese attach a dataset for following answers.

Thank you

Related Questions

Navigate

• Browse (All)
• Browse X
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.