Consider a time-series data set representing the quarterly sales of a company over the past ten years. One of the methods used to forecast future sales based on this historical data is the Autoregressive (AR) model. If the AR model is formulated as follows: $$Y_t = \phi_1 Y_{t-1} + \phi_2 Y_{t-2} + \ldots + \phi_p Y_{t-p} + \epsilon_t$$ where: $$Y_t$$ is the value of the time series at time $t$. $$\phi_i$$ represents the autoregressive coefficients. $$\epsilon_t$$ is the error term, assumed to be white noise. Assuming that this model has been fitted on your data and returns an $R^2$ value of 0.70. Which of the following statements about the model's performance and characteristics is true?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Understanding Autoregressive Models and R-squared

Medium Time-series Analysis Autoregressive Models

Consider a time-series data set representing the quarterly sales of a company over the past ten years. One of the methods used to forecast future sales based on this historical data is the Autoregressive (AR) model. If the AR model is formulated as follows:

$$Y_t = \phi_1 Y_{t-1} + \phi_2 Y_{t-2} + \ldots + \phi_p Y_{t-p} + \epsilon_t$$

where:

$$Y_t$$ is the value of the time series at time $t$.
$$\phi_i$$ represents the autoregressive coefficients.
$$\epsilon_t$$ is the error term, assumed to be white noise.

Assuming that this model has been fitted on your data and returns an $R^2$ value of 0.70. Which of the following statements about the model's performance and characteristics is true?

The model explains 70% of the variance in the dependent variable.

The model's coefficient of determination indicates a strong positive correlation.

The residuals of the model are likely to be normally distributed.

Hint

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