Determine which of the following indicates that a nonstationary time series can be represented as a random walk

• A control chart of the series detects a linear trend in time and increasing variability.
• The differenced series follows a white noise model.
• The standard deviation of the original series is greater than the standard deviation of the differenced series.

• I only
• II only
• III only
• I, II and III
• The correct answer is not given by (A), (B), (C), or (D).

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: D

See Page 242 of Regression Modeling with Actuarial and Financial Applications.

I is true because a random walk is characterized by a linear trend and increasing variability.

II is true because differencing removes the linear trend and stabilizes the variance.

III is true as both the linear trend and the increasing variability contribute to a higher standard deviation.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.