CFA CFA Level 2 T-stat and Dickey-Fuller test – QUANTS help!

T-stat and Dickey-Fuller test – QUANTS help!

  • This topic has 12 replies, 2 voices, and was last updated Oct-18 by googs1484.
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    • jstarrie
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      See the images below….anyone please explain to me why the DF test is rejected for ‘outline air temperate and ‘assembly line speed’… when test statistic values are NOT < -t critical? am i reading it wrong? DF test fails to reject 'defective assembly per hour', i could understand that because test statistics > t-critical.

    • googs1484
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      hmmmm I am not 100% confident in this answer but the DF test is to test for a unit root and that the slope coefficient is equal to 1. Clearly outline air temp and assembly line speed can be rejected if they are approximately 5 and 13 standard deviations away from 1. Defects, however, we cannot say that they are statistically different from one. 

    • jstarrie
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      I am not entirely following.. 🙁 the rule is reject null when t > + t critical, or t < - t critical. (see the 2nd image) for example on air temp, t-critical is -5.8, and test stat is -0.4, it doesnt satisfy this reject if 't < - t critical'.... i dont understand why it rejected. pls pls help!!!

    • jstarrie
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      i understand this ‘if the absolute T-value is bigger than the critical T-value of reference, one must reject the null hypothesis.’ 

      so taking the air temp example, 0.4 is not greater than 5.8… how come the answer is reject the null???  i am so confused!! please help me understand this!!  thank you!!

    • googs1484
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      I think your not understanding the table.  The first column is the absolute distance each coefficient/beta is from 1 in the regession. Dickey Fuller test is b1-1=0 and we want to reject the null being =0 becaue if b1 (slope/beta) is 1 then 1-1 is 0 and we will have a unit root bease the null bring 0 is how dicky fuller defines it for this test. To clarify look at outside air temp with a test statistic of -.423. That is how far b1 is from 1 or b1-1= -.423. So the slope coefficient must be .577…. to check my work( .577-1=-.423).  Second column has the standard errors. So dividing column 1 by column 2 gives us the t-stat, or the number of deviations we are from zero, which is column 3.  If this number is more than our critical t stat, that we need to look up on a t table but is close to 1.96 @ a 5% significance,  then we can say it’s not equal to 0 or that b1 does not = 1 which is the definition of a unit root. When you say outside air temp .4 is less than 5.8 your using wrong numbers. 5.8 is the t stat, numbers deviations from 0, and u need to compare that to the critical t stat that is about 1.96 that you need to look up. 

    • googs1484
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      I have no damn clue what column 4 is haha

    • jstarrie
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      yes i read it as ‘col 1’ is the T-stat value and ‘col 3’ is the T-critical.  i’ve seen on other questions that provide both value of test statistics and the t-critical @ 5% significance.  i think the wording is just confusing… 

    • jstarrie
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      thank you for your help!

    • googs1484
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      I actually like how that table is presented. Something you’d CFAI do on the real exam. Everyone is SO accustomed to seeing the table the same way. Coefficient first, then standard error then t stat. They just changed one column and used different terminology to show you understand the concepts and didn’t just memorize tables.

    • jstarrie
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      the first column is more appropriately named ‘coefficient estimate” as there are examples in the text and sample exams that have ‘test statistics’ referred to the calculated t-stat..like this one 

      what do you think?

    • googs1484
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      Just to make sure we are on the same page, that image is not a dickey fuller test. That’s just a general t-test for a slope coefficient from the regression. To run the DF test on that slope coefficient you would take .64-1= -.36. Then -.36/.26= -1.385 is your t-stat which is not significant so you could say it has a unit root. This is if the regression is an AR model of course.

    • jstarrie
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      that makes sense..

      can you confirm if DF is a two tailed T-test with df (n-k-1)?

    • googs1484
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      1 tailed with null being equal to or less than 0 that there is a unit root.  So you reject the null if tstat is higher than critical to value on the positive end.  DF you have right.  

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