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CFA Level 2
Quantitative Methods

Interpreting Trends in Time-Series Analysis

Hard Time-series Analysis Trend Models

A financial analyst is examining a time series dataset of quarterly sales revenue for a company over the last five years. The analyst decides to apply a linear trend model to better understand the long-term growth trajectory of the sales.

In constructing the model, the quarterly sales revenue ($Y_t$) can be expressed as:

$$Y_t = eta_0 + eta_1 t + eta_2 t^2 + ext{error}$$

where:

  • $Y_t$ = Sales revenue at time $t$
  • $t$ = Time period (in quarters)
  • $$eta_0, eta_1, eta_2$$ = Coefficients to be estimated

After running the regression, the analyst finds that the quadratic term ($eta_2$) is statistically significant while the linear term ($eta_1$) is not. The analyst wonders what implications this has for the trend in sales revenue.

What can be inferred about the sales revenue trend based on these regression results?

Hint

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