Understanding Trend Models in Time-Series Analysis

Easy Time-series Analysis Trend Models

A financial analyst is studying a stock that has shown consistent upward growth over the past several years. The analyst decides to implement a trend model to forecast future stock returns based on historical data. The trend model can be expressed as:

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

where:

- $Y_t$ is the value of the stock at time $t$,

- $eta_0$ is the intercept,

- $eta_1$ is the coefficient for the linear trend,

- $eta_2$ is the coefficient for the quadratic trend, and

- Error is the random error term.

Given this trend model, which of the following statements regarding the trend model is correct?

The model indicates that stock returns will increase at a decreasing rate over time if $eta_2 < 0$.

The presence of the $t^2$ term means that the relationship can only capture linear trends and not quadratic trends.

The intercept $eta_0$ represents the expected value of the stock when time $t$ is zero.

Hint

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