A stationary autoregressive model of order one can be written as

[[math]] y_t = \beta_0 + \beta_1y_{t-1} + \epsilon_t, \, t = 1,2, \ldots [[/math]]

Determine which of the following statements about this model is false

• The parameter [math]\beta_0[/math] must not equal 1.
• The absolute value of the parameter [math]\beta_1[/math] must be less than 1.
• If the parameter [math]\beta_1 = 0[/math], then the model reduces to a white noise process.
• If the parameter [math]β_1 = 1,[/math] then the model is a random walk.
• Only the immediate past value, [math]y_{t−1}[/math], is used as a predictor for [math]y_t[/math].

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: A

The intercept term may be any value, hence (A) is false.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.