# Reference Request: Book on Unit Root Theory

In trying to do time series analysis, I almost regularly stumble upon unit root and cointegration tests. The design of most these tests is based on a null of unit root (for both linear and non-linear models) and the statistic's distribution is derived using concepts/properties of Brownian motion, Functional CLT, etc. See this for example, and this question for my motivation.

Since I do not have a strong background in Stochastic Processes, I am looking for resources (hopefully a book) which covers relevant topics from stochastic processes and asymptotics so that I can make sense of the derivations in papers on unit root tests.

I tried to check in books on Stochastic Processes but their coverage is wider than what I am looking for. I did found two interesting links: this and this, which have a rather focused use of stochastic process concepts for unit roots. I am looking for similar resources - preferably a book.

• 1/2 While you are learning about tests of unit root (i.e. $\text{H}_{0}\text{: time series has/have unit root}$) also take the time to learn about tests of stationarity (i.e. $\text{H}_{0}\text{: time series is/are stationary}$), such as the Kwiatkowski-Phillips-Schmidt-Shin test for single time series, and Hadri's test for multiple time series. Mar 1, 2021 at 19:11
• 2/2 Combining inference from tests of unit root with inference from tests of stationarity help guard against confirmation bias in modeling decisions around the stationarity, weak stationarity, or non-stationarity (unit rootness) of a time series. Mar 1, 2021 at 19:12
• @Alexis: Thanks for the references and I couldn't agree more. Also, i feel it's important to know about other stationarity tests becausr most unit root tests are designed to test for one type of non-stationarity and practitioners often miss other types. To share my experience, I have often seen that people use ADF on seasonal series and getting stationarity as output, which is clearly wrong. See this for example. Mar 2, 2021 at 0:24
• Thank you for that comment, I look forward to readingthe link! There is a good need for periodic review articles to lay out the considerations (e.g., size of $N$, $T$, and $N$ v $T$, seasonality, etc.), and present the current state of the art. Mar 2, 2021 at 17:17