Understanding Autoregressive Models - AR(1) Implications

A financial analyst is studying the monthly returns of a stock over the past five years. The analyst suspects that the current month's return is influenced by the return of the previous month. To test this hypothesis, the analyst decides to use an autoregressive model of order 1, denoted as AR(1).

The general form of an AR(1) model can be expressed as:

$$ R_t = c + \phi R_{t-1} + \epsilon_t $$

where:

• $$ R_t $$ is the return in month t,
• $$ c $$ is a constant,
• $$ \phi $$ is the autoregressive parameter,
• $$ R_{t-1} $$ is the return in the previous month, and
• $$ \epsilon_t $$ is a white noise error term.

The analyst obtains an estimate of $$ \phi = 0.75 $$. What does this imply about the relationship between the current month's return and the previous month's return?