5. Load the data in “dailyibm.dat” using the command ibm<-scan("dailyibm.dat", skip=1). This series is the daily closing price of IBM stock from Jan 1, 1980 to Oct 8, 1992. (a) Make a plot of the data and an ACF plot of the data. Does the time series appear to be stationary? Explain. Interpret the ACF plot in this situation. (b) Difference the data. Plot this differenced data, and make an ACF plot. What is your opinion of whether the series is stationary after differencing? (c) Another option for attempting to obtain stationary data when there is something similar to an exponential trend is to take the logarithm. Use the R command log() to take the logarithm of the data. Plot this transformed data. Does the transformed data appear stationary? Explain. (d) Perhaps some combination of differencing and the logarithmic transform will give us stationary data. Why would log(diff(ibm)) not be a very good idea? Try the opposite, difference the log transformed data difflogibm<-diff(log(ibm)). Except for a few extreme outliers, does this transformation succeed in creating stationary data? (e) Delete the extreme outliers using the following command: difflogibm<-difflogibm[difflogibm> -0.1] Plot this data and the ACF for this data. Sometimes with very long time series like this one, portions of the series exhibit different behavior than other portions. Break the series into two parts using the following commands: difflogibm1<-difflogibm[1:500] difflogibm2<-difflogibm[501:length(difflogibm)] Plot both of these and create ACF plots of each. Do you notice a difference between these two sections of the larger time series? (f) Assume the model for the data that we have called difflogibm2 is of the following form: dt = δ + wt 4 where wt , t = 1, ..., T is Gaussian white noise with variance σ 2 w. Is this reasonable from what you now know of this time series? How would you estimate δ and σw? What are the numerical values of these estimates?
Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.
You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.Read more
Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.Read more
Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.Read more
Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.Read more
By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.Read more