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

    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

    TurningPoint – Teaching & Learning Support

    Results of turning point test | Download Table

    Results of turning point test | Download Table

    Turning Point Questions Flashcards | Quizlet

    Turning Point Questions Flashcards | Quizlet

    Turning Point - Elateminds

    Turning Point - Elateminds

    Turning point check mark Stock Photo - Alamy

    Turning point check mark Stock Photo - Alamy

    Solved The Turning Point Test If y1,dots,yn is a sequence | Chegg.com

    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 ...

    2: Results from the Turning Point test for testing the independence ...

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    turning point test

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    TIME SERIES - University of Cambridge

    1.7 The turning point test We may wish to test whether a series can be considered to be white noise, or whether a more complicated model is required. In later chapters we shall consider …

    Introduction to Time Series Analysis. Lecture 13.

    Testing i.i.d.: Turning point test Define T = |{t : Xt,Xt+1,Xt+2 is a turning point}|. ET = (n −2)2/3. Can show T ∼ AN(2n/3,8n/45). Reject (at 5% level) the hypothesis that the series is i.i.d. if T − …

    STATS – the Turning Point Test - datafireball

    Nov 5, 2013 · If you have three contiguous time points, assuming they are of different values. Then there are 6 permutations to order them. And four of them form a turning point (PEAK/PIT).

    time series - the turning point test - Cross Validated

    If $y_1, \ldots, y_n$ is a sequence of observations, we say that there is a turning point at time $i$, $1 < i < n$, if $y_{i−1} < y_i$ and $y_i > y_{i+1}$, or if $y_{i−1} > y_i$ and $y_i < y_{i+1}$.

    turningpoint.test function - RDocumentation

    Perform a test of statistical independence of a data series by comparing the number of turning points present in the series with the number of turning points expected to be present in an i.i.d. …

    The Turning Point Test of Statistical Independence - search.r …

    Perform a test of statistical independence of a data series by comparing the number of turning points present in the series with the number of turning points expected to be present in an i.i.d. …

    Turning Point Test for Randomness Equations taken loosely …

    Example: The turning point test for randomness is used to determine if points) of a serial data set (time-series) is independent of the order of the observations. In the data set to the right are …

    turningpoint.test: The Turning Point Test of Statistical …

    Oct 3, 2023 · Perform a test of statistical independence of a data series by comparing the number of turning points present in the series with the number of turning points expected to be present …