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23507 Time Series Econometrics

Spring 2021

Problem Set 2

● Submit your solutions electronically via the Problem Set 1 link in the Assessments folder on Canvas by 10:00am on Monday, 16 August 2021.

● Your submission should take the form of a single PDF file that may contain scanned handwritten answers, answers typeset with Word, extracts of R code, and graphs and tables generated with R.

● All R code used to do the exercises should be submitted in a separate R file.

● The name of the PDF file should be 12345678.pdf and the name of the R file should be 12345678.R, where 12345678 is your student number.

● Ensure that your name and student ID appear in the title of the PDF file and as a comment at the top of the R file.

Exercise 1.

Consider the series determined by the AR(2) model

where is a white noise with . Calculate the conditional means and variances below, given that you have observed the following values for the series:

Exercise 2.

Consider the general AR(3) model given by

where is a white noise with variance . Derive expressions for the following conditional means and variances:

Exercise 3.

Write an R function testStat(arvec) that determines whether or not an AR(p) model whose autoregressive coefficients are given by the vector arvec of length p − 1 is stationary:

The function should return TRUE if the model is stationary and FALSE otherwise. For example, is.Stationary(c(0.9,-0.75)) should return TRUE, indicating that the AR(2) model

is stationary. Similarly is.Stationary(c(-0.75,0.75,-0.8,0.9,0.2)) should return FALSE, indicating that the AR(5) model

is not stationary.