Persistence in Predictive Regression and Dividend Yields

Summary

The document explains persistence in the context of regression models for forecasting returns, using the dividend-to-price ratio as an example. A variable is persistent when shocks to it have effects that fade slowly, so a one-time change can influence its level for an extended period. The question connects this property to the Stambaugh bias literature, where persistent predictors are used to model future returns.

The explanation is qualitative and offers no formal definition, equations, empirical results, or guidance for estimating persistence. Its “everlasting” phrasing is best understood as an illustration of long-lived influence, rather than a claim that a shock literally lasts forever. The note introduces a useful time-series concept but does not explain how persistence affects regression inference or how to correct for bias.

Key ideas

• Persistence describes how slowly a variable's response to a shock fades over time.
• Dividend-to-price ratios are cited as persistent predictors in return regressions.
• The explanation is intuitive and does not provide estimation methods or empirical evidence.

Tags

# What is a persistent variable?


# What is a persistent variable?












What is a persistent variable in the context of regression analysis? For example, dividend to price ratio (D/P) is considered to be persistent variable when used to model future returns (Stambaugh Bias literature).

## Answer by user40 (score 1, accepted)

https://quant.stackexchange.com/a/1014

In short, persistence is related to the long-term influence of a shock, e. g. that a one-off shock on the d/p would have an "everlasting" influence on the average return level.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.