Understanding AR(2) Model Implications

Hard Time-series Analysis Autoregressive Models

A financial analyst is examining a quarterly time series dataset of the revenue from a specific business unit of a company over the past five years. After fitting an autoregressive model to the data, the analyst specifies the model as AR(2), indicating that the current revenue ($R_t$) depends on the previous two periods' revenues ($R_{t-1}$ and $R_{t-2}$). The fitted model is represented as:

$$R_t = eta_0 + eta_1 R_{t-1} + eta_2 R_{t-2} + u_t$$

where $eta_0$ is the constant term, $eta_1$ and $eta_2$ are the coefficients for the lagged revenue terms, and $ u_t$ is the error term. The analyst notes that the coefficients $eta_1$ and $eta_2$ are significant at the 5% level. Given this context, which of the following statements about the AR(2) model is true?

The AR(2) model implies that the current revenue is solely determined by the immediate past revenue.

The presence of two autoregressive terms suggests that the series has a memory of at least two periods.

If the error term $ u_t$ is normally distributed, the model is invalid for forecasting future revenue.

Hint

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