7.162
7.367
5.9
5.7
7
5.8
6.6
6.4
4.8
6
7
7.8
7.9
6.267
5.8
Turning point test GudangMovies21 Rebahinxxi LK21
In statistical hypothesis testing, a turning point test is a statistical test of the independence of a series of random variables. Maurice Kendall and Alan Stuart describe the test as "reasonable for a test against cyclicity but poor as a test against trend." The test was first published by Irénée-Jules Bienaymé in 1874.
Statement of test
The turning point test is a test of the null hypothesis
H0: X1, X2, ..., Xn are independent and identically distributed random variables (iid)
against
H1: X1, X2, ..., Xn are not iid.
This test assumes that the Xi have a continuous distribution (so adjacent values are almost surely never equal).
= Test statistic
=
We say i is a turning point if the vector X1, X2, ..., Xi, ..., Xn is not monotonic at index i. The number of turning points is the number of maxima and minima in the series.
Letting T be the number of turning points, then for large n, T is approximately normally distributed with mean (2n − 4)/3 and variance (16n − 29)/90. The test statistic
z
=
T
−
2
n
−
4
3
16
n
−
29
90
{\displaystyle z={\frac {T-{\frac {2n-4}{3}}}{\sqrt {\frac {16n-29}{90}}}}}
is approximately standard normal for large values of n.
Applications
The test can be used to verify the accuracy of a fitted time series model such as that describing irrigation requirements.
References
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Turning Point Test: An Easy Way To Check Randomness
Turning Point Test: An Easy Way To Check Randomness
Turning Point Test: An Easy Way To Check Randomness
Turning Point Test: An Easy Way To Check Randomness
Turning Point Test: An Easy Way To Check Randomness
TurningPoint – Teaching & Learning Support
Results of turning point test | Download Table
Turning Point Questions Flashcards | Quizlet
Turning Point - Elateminds
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Solved The Turning Point Test If y1,dots,yn is a sequence | Chegg.com
2: Results from the Turning Point test for testing the independence ...
