Identifying Quadratic Trends

In the context of time-series analysis, trend models are used to identify and quantify the underlying patterns in data over time. One common trend model is the simple linear regression model, which can be used to forecast future values based on past trends. Consider the following regression equation:

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

where:

• $$ Y_t $$ is the value of the variable at time t,
• $$ T_t $$ represents time,
• $$ eta_0, eta_1, $$ and $$ eta_2 $$ are coefficients.

What type of trend is represented by the model if $$ eta_1 $$ is positive and $$ eta_2 $$ is positive?