代做STAT463、代写R设计、代做R编程、代写data留学生

日期：2019-02-12 11:37

STAT463 Homework #4

due Monday, 2/11

1. (data from Shumway & Stoffer, 2e) The data in “varve.dat” contains sedimentary deposit

(sand and silt from melting glaciers) thicknesses for n = 634 consecutive years in Massachusetts.

It can be read into R with y=ts(scan(file.choose())).

(a) Plot the data and comment on violations of stationarity.

(b) Argue that the (natural) log of the data stabilizes the variance over time. Is the transformed

data now stationary? Why or why not?

(c) Define the differences dt = log yt log yt1. Plot, and argue in favor of stationary now.

Hint: use the R function diff(log(y)).

(d) Plot and interpret the estimated ACF (autocorrelation function) for the differenced data.

What significant spike(s) do you see?

(e) Recall the moving average model dt = et θet1, where et are independent with mean

0 and variance σ

2

. Find its autocorrelation function ρk = Cor(dt, dtk).

(f) Comparing ρk with the estimated ACF in (d) above, comment on whether this model is

reasonable for dt

.

2. Load the deere2 data set that is included in the TSA package. (use data(deere2) to make

the data available). The data contains deviations from a specified target, in units of length,

for an industrial process at Deere&Co.

(a) Display the time series plot for these data, and comment on the appearance. Is a

stationary model reasonable?

(b) Plot the sample ACF and sample PACF, and select, with justification, tentative orders

for an ARMA model for this time series.

3. For each of the following, find the values of p, d, and q such that Yt ～ ARIMA(p, d, q), and

state whether Yt

is stationary and whether dYt

is stationary.

(a) Yt = Yt1 0.25Yt2 + et 0.1et1

(b) Yt = 0.5Yt1 0.5Yt2 + et 0.5et1 + 0.25et2

(c) Yt = 0.9Yt1 + 0.09Yt2 + et