Chartered Financial Analyst (CFA) Practice Exam Level 2

In which model do residuals that show long-term trends indicate serial correlation?

1. Linear Trend Model

2. Log Linear Model

3. Exponential Trend Model

4. Quadratic Trend Model

The correct answer is: Log Linear Model

In a Log Linear Model, the analysis involves transforming the data using the logarithm of the dependent variable, which allows for multiplicative relationships to be linearized. This model is often used when the data is expected to grow at a constant relative rate, making it particularly useful for economic data that increases over time. When residuals from a Log Linear Model display long-term trends, it suggests that there is a systematic pattern rather than a random distribution of errors. Such patterns in the residuals imply the presence of serial correlation, meaning that current residuals are correlated with past residuals. This indicates that the model may not adequately capture all relevant information and dynamics in the data, leading to biased estimates and invalid inferences. In contrast, other models such as the Linear Trend Model, Exponential Trend Model, and Quadratic Trend Model can also exhibit serial correlation under certain conditions, but the context provided here specifically addresses how long-term trends in residuals signal serial correlation particularly in a Log Linear Framework where the transformations of dependent variables help in illuminating such trends. Therefore, the presence of long-term trends in residuals is primarily indicative of serial correlation, making the Log Linear Model particularly relevant in this context.