SOA Exam SRM Sample Question 22

Study guide: Exam SRM

A stationary autoregressive model of order one can be written as

$y_t = \beta_0 + \beta_1 y_{t-1} + \varepsilon_t, \quad t = 1, 2, \ldots.$

Determine which of the following statements about this model is NOT true.

A) The parameter $\beta_0$ must not equal 1.
B) The absolute value of the parameter $\beta_1$ must be less than 1.
C) If the parameter $\beta_1 = 0$ , then the model reduces to a white noise process.
D) If the parameter $\beta_1 = 1$ , then the model is a random walk.
E) Only the immediate past value, $y_{t-1}$ , is used as a predictor for $y_t$ .

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