A financial analyst is studying the monthly sales data of a retail company over the past five years. The data exhibit a clear upward trend due to factors such as increasing brand recognition and expanding product lines. To model this trend over time, the analyst decides to use a linear trend model. The linear trend model can be represented by the equation: $$Y_t = eta_0 + eta_1 t + ho_t$$ where: $$Y_t$$ = sales at time t $$eta_0$$ = intercept (sales when t = 0) $$eta_1$$ = slope (change in sales per unit increase in time) $$ ho_t$$ = random error term At the end of the analysis, the analyst discovers that the slope, $$eta_1$$, has a statistically significant positive value. Based on this information, which of the following interpretations about the trend does this imply?

Exam

CFA Level 2

Section

Difficulty

Quantitative Methods

Interpreting Trend Model Results in Time Series Analysis

Hard Time-series Analysis Trend Models

A financial analyst is studying the monthly sales data of a retail company over the past five years. The data exhibit a clear upward trend due to factors such as increasing brand recognition and expanding product lines. To model this trend over time, the analyst decides to use a linear trend model.

The linear trend model can be represented by the equation:

$$Y_t = eta_0 + eta_1 t + ho_t$$

where:

$$Y_t$$ = sales at time t
$$eta_0$$ = intercept (sales when t = 0)
$$eta_1$$ = slope (change in sales per unit increase in time)
$$ ho_t$$ = random error term

At the end of the analysis, the analyst discovers that the slope, $$eta_1$$, has a statistically significant positive value. Based on this information, which of the following interpretations about the trend does this imply?

Sales are decreasing over time due to external market pressures.

Sales are increasing over time, indicating a positive growth trend.

Sales remain constant over time, showing no significant trend.

Hint

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