[AR1] Editorial Suggestions

[pgrosser1]

Suggestions by @mbek0605 and @Jiarui-ZH

Content

• Under 31.1, refer to the equation as a "stochastic recurrence relations"
• Before 31.2, include one more iteration backwards in the preceding equation
• In 31.2.2, link to Lecture 16
• Before 31.3.1, mention the importance of stationarity in being able to predict the long-term dynamics of a system, and the fact that stationary distributions gives us testable implications for the model
• In 31.4, include an example of how ergodicity can be used to understand real-life phenomena (ie. if the AR(1) process is used to model how the wealth of households evolve with independent shocks, then ergodicity can be used to understand the mean wealth of all households after many iterations --> can be modelled by studying a single, independent household)
• Clarify the use of the terms "moments" to make it clear it is not referring to iterations
• In the plot before 31.3, adjust to show fewer iterations (to make it more distinct from the next plot)
• When plotting the alternative density distribution, use a \mu_0 and \sigma_0 that is more dissimilar than the previous choices to make it clear that the choices are arbitrary, ie. that all initial conditions converge to the same stationary sequence

[HumphreyYang]

Comments by @SylviaZhaooo

Content

• Change 'AR1' to 'AR(1)' in title.
• Add a sentence about why AR(1) is useful (@SylviaZhaooo).
• Add a link to 'IID' in probability distribution lectures.
• Link 'moments' to probability distribution lectures.
• Explain why stationarity and asymptotic stability are important -- single prediction over the long run.
• Give examples of ergodicity (wealth distribution?) and when it fails.
• Add a Wikipedia link to double factorial.
• Change the capitalization for titles in this lecture.
• Law of Large Numbers -> law of large numbers.

[mmcky]

@SylviaZhaooo would you be able to review the first comment block feedback and open a second update PR?

[mmcky]

@SylviaZhaooo can this issue be closed?

[mmcky]

thanks for all the comments @mbek0605, @Jiarui-ZH, @pgrosser1, and @HumphreyYang.

Thanks @SylviaZhaooo for working on the associated PRs.