Include output and graphics in your discussions in the appropriate places, do not attach output separately.
statistics
Description
Include output and graphics in your discussions in
the appropriate places, do not attach output separately. Do not display output
or graphics without comments. You will be graded on the thoroughness of your
analysis and your discussions.
All data sets can be found in asta.
1. Let St represent the monthly sales data in sales (n = 150), and
let Lt be the leading
indicator in lead.
. (a) Fit
an ARIMA model to St, the monthly
sales data. Discuss your model fitting in a step-by-step fashion, presenting
your: (A) initial examination of the data, (B) transformations and differencing
orders, if necessary, (C) initial identification of the dependence orders, (D)
parameter estimation, (E) residual diagnostics and model choice.
. (b) Use
the CCF and lag plots between ∇St and ∇Lt to argue that a regression of ∇St on ∇Lt−3 is reasonable.
[Note: In lag2.plot(), the first named series is the one that gets
lagged.]
. (c) Fit
the regression model ∇St = β0 + β1∇Lt−3 + xt, where xt is an ARMA
process (explain how you decided on your model for xt). Discuss your results.
.
If you have to work with
various transformations of series in x and
y, you have to align the data: x = ts(rnorm(100), start= 2001, freq=4)
y = ts(rnorm(100), start= 2002, freq=4)
dog = ts.intersect( lag(x,-1), diff(y,2) )
xnew = dog[,1] # dog has 2
columns, the first is lag(x,-1) ... ynew = dog[,2] # ... and
the second column is diff(y,2)
plot(dog) # now you
can manipulate xnew and ynew simultaneously
2. Fit an ARIMA
model of your choice to the unemployment data, UnempRate following (A)
– (E) of Problem 1a. Then use the estimated model to forecast the next 12
months.
3. Investigate
whether the quarterly growth rate of US GDP (gdp) exhibits
GARCH behavior. If so, fit an appropriate model to the growth rate.
4. Fit a state
space model to the Johnson & Johnson earnings in jj. Plot the
data with (a) the smoothers, and (b) the filters, superimposed each with error
bounds (two separate graphs). Compare the results of (a) and (b). In addition,
what does the estimated value of φ tell you about the growth rate in the
earnings?
5. x Crude oil prices in dollars per barrel
are in oil. Fit an ARIMA(p,d,q) model to the growth rate following (A) – (E)
of Problem 1a.
