title: R language: What does the result of the augmented Dickey Fuller test mean?
body: <p>I've seen <a href="https://stats.stackexchange.com/questions/55805/how-do-you-interpret-results-from-unit-root-tests">this</a>, <a href="https://stats.stackexchange.com/questions/57807/confusion-with-augmented-dickey-fuller-test">this</a> and <a href="https://stats.stackexchange.com/questions/213551/how-is-the-augmented-dickey-fuller-test-adf-table-of-critical-values-calculate">this</a>, but none explain properly, the interpretation of the basic output that R shows. Also, some of the other questions about Dickey Fuller test didn't even receive answers, so I'm asking here.  </p>
  
  <p>Eg: From <a href="https://www.datascience.com/blog/introduction-to-forecasting-with-arima-in-r-learn-data-science-tutorials" rel="nofollow noreferrer">this tutorial</a>, it says the null hypothesis is rejected, but I don't see anything in the output that indicates that. If I'm supposed to take a hint from the p value, then how do I know what is the cutoff limit considered for p?  </p>
  
  <pre><code>count_d1 = diff(deseasonal_cnt, differences = 1) 
  plot(count_d1)
  adf.test(count_d1, alternative = "stationary")
  </code></pre>
  
  <blockquote>
    <p>Augmented Dickey-Fuller Test</p>
    
    <p>data:  count_d1 Dickey-Fuller = -9.9255, Lag order = 8, p-value = 0.01
    alternative hypothesis: stationary</p>
  </blockquote>
  
  <p>In other tutorials I've seen such outputs where they conclude that the time series is stationary or non-stationary by looking at the <code>adt.test</code> output, but they mention nothing about how they came to that conclusion.  </p>
  
  <p>So how do I know if the null hypothesis was rejected or not? Isn't it possible to have an if statement like:<br>
  <code>if adf.test(count_d1, alternative = "stationary")==TRUE, 
  print("null hypo true"); else print("null hypo rejected");</code>?</p>