Pettitt Test for Abrupt Changes in the Mean of a Time Series

Performs the nonparametric Pettitt test to detect a single abrupt change in the central tendency of a time series. Under the null hypothesis, there is no change.

Usage

eda_pettitt_test(data, years, alpha = 0.05)

Arguments

data: Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.
years: Numeric vector of observation years corresponding to data. Must be the same length as data and strictly increasing.
alpha: Numeric scalar in \([0.01, 0.1]\). The significance level for confidence intervals or hypothesis tests. Default is 0.05.

Value

A list containing the test results, including:

data: The data argument.
years: The years argument.
alpha: The significance level as specified in the alpha argument.
null_hypothesis: A string describing the null hypothesis.
alternative_hypothesis: A string describing the alternative hypothesis.
u_series: Numeric vector of absolute U-statistics for all years.
statistic: The test statistic and maximum absolute U-statistic.
bound: The critical value of the test statistic based on alpha.
change_points: A dataframe containing the potential change point.
p_value: An asymptotic approximation of the p-value for the test.
reject: Logical scalar. If TRUE, the null hypothesis was rejected.

change_points contains the years, test statistics, and p-values of each potential change point. If no change points were identified, change_points is empty.

References

Pettitt, A.N., 1979. A Non-parametric Approach to the Change-point Problem. J. Royal Statistics Society 28 (2), 126–135. http://www.jstor.org/stable/2346729

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
years <- seq(from = 1901, to = 2000)
eda_pettitt_test(data, years)
#> $data
#>   [1]  93.18624 103.82141 102.02935 112.10449  85.42835 107.26397  88.20753
#>   [8] 108.59298 100.01181  90.54158 111.24859 116.50599  99.71808  95.68262
#>  [15] 109.62970 101.42725  92.26551  98.38343 102.72831 111.78279  99.34285
#>  [22]  96.73675 106.16976 114.48573 104.01289 107.36656 106.75189 100.92422
#>  [29] 105.71910  95.62950 115.22793  90.09813 101.21090 105.45931 108.28352
#>  [36]  94.04016  97.61715 104.73747 103.40918  96.95804 107.33999 103.13770
#>  [43] 111.29980 103.81615 103.68654 108.84609 109.21164 117.78567  92.96911
#>  [50]  75.93637  99.68249  97.04275 106.00636 111.60364 100.56538  95.59872
#>  [57]  98.35395  90.02786  76.48258  97.01634  78.53935  97.08140  93.10026
#>  [64]  94.97523 106.05890  97.37607  96.90605 119.81818  94.51492  92.73484
#>  [71] 101.06323 114.59809  93.10381 114.15768 100.04895 101.07439  98.37847
#>  [78]  89.26774 100.03078 110.44615  98.93937 107.17062  87.33825  69.94219
#>  [85] 108.75675 106.93614 112.83858 109.99143  86.73613  81.15200 101.48586
#>  [92]  99.01536  91.65490 102.34030 104.16639  89.90877  92.40957  81.75752
#>  [99]  98.91953 104.97110
#> 
#> $years
#>   [1] 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915
#>  [16] 1916 1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930
#>  [31] 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945
#>  [46] 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960
#>  [61] 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
#>  [76] 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990
#>  [91] 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
#> 
#> $alpha
#> [1] 0.05
#> 
#> $null_hypothesis
#> [1] "There are no abrupt changes in the mean of the data."
#> 
#> $alternative_hypothesis
#> [1] "There is one abrupt change in the mean of the data."
#> 
#> $u_series
#>   [1]  55  28  15  68  19  34  47  14   7  64  11 106  97  54 123 132  65  44
#>  [19]  61 142 129  88 133 222 251 308 355 356 395 350 443 370 377 414 473 420
#>  [37] 393 426 447 410 465 484 561 586 609 674 741 838 777 680 669 636 677 756
#>  [55] 755 708 683 608 513 478 385 354 295 246 289 260 221 320 269 206 209 300
#>  [73] 243 330 327 332 309 230 225 298 281 332 249 150 213 262 347 418 333 242
#>  [91] 253 238 169 184 215 138  73  16  35  35
#> 
#> $statistic
#> [1] 838
#> 
#> $bound
#> [1] 710.1279
#> 
#> $p_value
#> [1] 0.015
#> 
#> $change_points
#>   index year    value statistic p_value
#> 1    48 1948 117.7857       838   0.015
#> 
#> $reject
#> [1] TRUE
#>