In a study analyzing monthly stock returns, an analyst develops an autoregressive model to forecast future returns based on previous observations. The analyst fits an AR(1) model represented as: $$ R_t = \alpha + \beta R_{t-1} + \epsilon_t $$ Where: $$ R_t $$ = the return at time t $$ \alpha $$ = the constant term $$ \beta $$ = the coefficient of the lagged return $$ \epsilon_t $$ = white noise error term The analyst finds the fitted equation to be: $$ R_t = 0.02 + 0.8 R_{t-1} + \epsilon_t $$ Which of the following statements correctly interprets the coefficient $$ \beta $$ in this model?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Interpreting the Coefficient in Autoregressive Model

Hard Time-series Analysis Autoregressive Models

In a study analyzing monthly stock returns, an analyst develops an autoregressive model to forecast future returns based on previous observations. The analyst fits an AR(1) model represented as:

$$ R_t = \alpha + \beta R_{t-1} + \epsilon_t $$

Where:

$$ R_t $$ = the return at time t
$$ \alpha $$ = the constant term
$$ \beta $$ = the coefficient of the lagged return
$$ \epsilon_t $$ = white noise error term

The analyst finds the fitted equation to be:

$$ R_t = 0.02 + 0.8 R_{t-1} + \epsilon_t $$

Which of the following statements correctly interprets the coefficient $$ \beta $$ in this model?

The coefficient $$ \beta = 0.8 $$ indicates that a 1% increase in the previous month's return is associated with a 0.8% increase in the current month's return.

The coefficient $$ \beta = 0.8 $$ implies that approximately 80% of the variation in the current month's return is explained by the previous month's return.

The coefficient $$ \beta = 0.8 $$ suggests that if the previous month's return was higher than the average, the current month's return will definitely also be higher.

Hint

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