Consider a stock that exhibits linear growth over time. You wish to model the trend of its price using a linear trend model. You collect monthly price data over a 5-year period, which shows a consistent linear increase. To analyze the trend, you fit a linear regression model of the form: $$P_t = eta_0 + eta_1 t + eta_2 t^2 + eta_3 t^3 + ext{error}_t$$ where: $$P_t$$ = price of the stock at time $$t$$ $$t$$ = time in months since the start of the observation period $$eta_0$$ = intercept (initial price) $$eta_1, eta_2, eta_3$$ = coefficients representing the linear, quadratic, and cubic trend components, respectively When interpreting this model, which of the following statements regarding the trend components is correct?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Interpreting Trend Models

Medium Time-series Analysis Trend Models

Consider a stock that exhibits linear growth over time. You wish to model the trend of its price using a linear trend model. You collect monthly price data over a 5-year period, which shows a consistent linear increase. To analyze the trend, you fit a linear regression model of the form:

$$P_t = eta_0 + eta_1 t + eta_2 t^2 + eta_3 t^3 + ext{error}_t$$

where:

$$P_t$$ = price of the stock at time $$t$$
$$t$$ = time in months since the start of the observation period
$$eta_0$$ = intercept (initial price)
$$eta_1, eta_2, eta_3$$ = coefficients representing the linear, quadratic, and cubic trend components, respectively

When interpreting this model, which of the following statements regarding the trend components is correct?

Linear models assume constant growth rates, while a cubic component can account for accelerating growth.

The presence of a quadratic term guarantees that the price will increase at a decreasing rate.

If the cubic term coefficient is negative, it ensures the stock will decline in future periods.

Hint

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