Time series : Autoregressive Models

Question 1

What is an autoregressive model of order 1 - AR(1)?

Answer 1

Time series where each term may be expressed in terms of the previous term plus white noise

Question 2

Give two examples of autoregressive time series and their characteristics.

Answer 2

1. White noise (B1 = 0)

2. Random walk (B1 = 1)

Question 3

How can we know if the process is stationary?

Answer 3

Absolute value of B1 is < 1

Question 4

How can we test that the time series is white noise (B1 = 0)

Answer 4

Check whether the sample autocorrelations (rk) are significant.
If absolute value of rk > 2 / sqrt(T) the autocorrelations are significant and the white noise model is rejected.

Question 5

What is the std error of rk?

Answer 5

1/sqrt(T)

Question 6

How can you estimate the coefficients and what are their estimations?

Answer 6

Conditional least square (regression of yt on y(t-1)).
b1 - > r1
b0 -> ybarre ( 1 - b1)

Question 7

True or false : the variance of yt is greater than the variance of the error terms?

Answer 7

True