Consider a time-series dataset that is suspected to exhibit autoregressive behavior. You fit an Autoregressive model of order 2 (AR(2)) to the data, represented by the equation: $$Y_t = \beta_0 + \beta_1 Y_{t-1} + \beta_2 Y_{t-2} + \epsilon_t$$ Where: $$Y_t$$ is the value of the time series at time $$t$$. $$\epsilon_t$$ is a white noise error term. After analyzing the model output, you find that $$\beta_1 = 0.5$$ and $$\beta_2 = 0.3$$, with an intercept $$\beta_0 = 2$$. You also observe that the coefficient of determination $$R^2$$ is 0.64. Considering the implications of these results, which of the following statements is true regarding the behavior of the time series?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Autoregressive Model Stationarity Diagnosis

Very Hard Time-series Analysis Autoregressive Models

Consider a time-series dataset that is suspected to exhibit autoregressive behavior. You fit an Autoregressive model of order 2 (AR(2)) to the data, represented by the equation:

$$Y_t = \beta_0 + \beta_1 Y_{t-1} + \beta_2 Y_{t-2} + \epsilon_t$$

Where:

$$Y_t$$ is the value of the time series at time $$t$$.
$$\epsilon_t$$ is a white noise error term.

After analyzing the model output, you find that $$\beta_1 = 0.5$$ and $$\beta_2 = 0.3$$, with an intercept $$\beta_0 = 2$$. You also observe that the coefficient of determination $$R^2$$ is 0.64. Considering the implications of these results, which of the following statements is true regarding the behavior of the time series?

The series is stationary because both autoregressive coefficients are less than 1.

The series is non-stationary due to the presence of a unit root.

The series is stationary but has a deterministic trend.

Hint

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