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MATH38032 Time Series Analysis
Examples sheet 5
1. a) What is the large sample (asymptotic) distribution of the sample acf or pacfat fixed lag s or k?
b) The results in a) are based on what assumption on the time series?
c) What is the standard error to use when testing the significance of an estimated acf/pacf value?
d) How many times the standard error is allowed for (non)significance at 5%?
e) If a test result is nonsignificant, which type of error (I or II) can you make if you go along with it?
2. a) What is the Ljung-Box test?
b) Why is the test called a portmanteau test?
c) What do you get from Box.test in R with type=“Ljung-Box"?
d) How do you use the output from R?
3. Run the R code in notes. You will get a different set of simulated data unless you do set.seed(123) first.
4. (a) Simulate n = 100 observations from the AR(1) model with φ = 0.5 and σε(2) = 1.
n <- 100
x[1] <- rnorm(1, mean=0, sd=?) #work out the standard deviation of x_1 by hand for (i in 2:n)) x[i] <- 0.5*x[i-1] + rnorm(1)
(b) Repeat what we did with the MA(1) data.