A stationary autoregressive model of order one can be written as

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].

You are given the following six observed values of the autoregressive model of order one time series

with [math]\operatorname{Var}(\epsilon_t) = \sigma^2 [/math].

The approximation to the conditional least squares method is used to estimate [math]β_0[/math] and [math]β_1[/math] .

Calculate the mean squared error [math]s^2[/math] that estimates [math]σ^2.[/math]

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You are given a stationary AR(1) model,

Determine which or the following is always true.

• [math]\beta_0 \neq 0 [/math]
• [math]\beta_0 = 1[/math]
• [math]\beta_1 = 0[/math]
• [math]\beta_1 = 1[/math]
• [math]|\beta_1| \lt 1[/math]