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CFA Level 2
Quantitative Methods

Long-Term Behavior of AR(1) Process

Medium Time-series Analysis Autoregressive Models

Consider a time series model defined by an autoregressive process of order 1, denoted as AR(1). The model can be expressed as:

$$ Y_t = \phi Y_{t-1} + \epsilon_t $$

where $Y_t$ is the current value of the series, $\phi$ is the autoregressive coefficient, and $\epsilon_t$ is a white noise error term. It is known that the process is stationary if the absolute value of $\phi$ is less than 1.

Assume you have estimated the AR(1) model for a financial time series and found that $\phi = 0.8$. What can be inferred about the long-term behavior of the process?

Hint

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