Understanding AR(2) Model Coefficients

Very Hard Time-series Analysis Autoregressive Models

A financial analyst is examining the quarterly returns of a stock over the past five years to develop an autoregressive model to forecast future returns. The analyst decides to fit an AR(2) model to the data, which is represented as follows:

$R_t = \alpha + \beta_1 R_{t-1} + \beta_2 R_{t-2} + \epsilon_t$

Where:

$R_t$: return at time $t$
$\alpha$: constant term
$\beta_1$: coefficient of the first lagged return
$\beta_2$: coefficient of the second lagged return
$\epsilon_t$: error term

After performing the estimation, the analyst obtains the estimates of the coefficients: $\hat{\beta_1} = 0.6$ and $\hat{\beta_2} = 0.3$. The analyst wants to evaluate the persistence and predictability of the model. Which of the following statements correctly describes the implications of these coefficient estimates?

The model suggests that returns are highly unpredictable as the sum of the coefficients is less than 1.

The model indicates a persistent return process since the sum of the coefficients exceeds 1.

The coefficients suggest that past returns have a diminishing effect on future returns, as the coefficients are less than 1.

Hint

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