Kendall tau trend with continuity correction for time-series

Source: R/kendall.R

Calculates a nonparametric statistic for a monotonic trend based on the Kendall tau statistic and the Theil-Sen slope modification

kendall(
  y,
  tau = TRUE,
  p.value = TRUE,
  z.value = TRUE,
  confidence = TRUE,
  intercept = TRUE,
  prewhiten = FALSE,
  na.rm,
  ...
)

Arguments

y

A vector representing a timeseries with >= 8 obs
tau

(FALSE/TRUE) return tau values
p.value

(FALSE/TRUE) return p.values
z.value

(FALSE/TRUE) return z values
confidence

(FALSE/TRUE) return 95 pct confidence levels
intercept

(FALSE/TRUE) return intercept values
prewhiten

(FALSE/TRUE) Apply autocorrelation correction using pre-whitening
na.rm

(FALSE/TRUE) Remove NA values
...

Not used

Value

Depending on arguments, a vector containing:

  • value 1 Theil-Sen slope, always returned

  • value 2 Kendall's tau two-sided test, if tau TRUE

  • value 3 intercept for trend if intercept TRUE, not if prewhitened

  • value 4 p value for trend fit if p.value TRUE

  • value 5 Z value for trend fit if z.value TRUE

  • value 6 lower confidence level at 95-pct if confidence TRUE, not if prewhitened

  • value 7 upper confidence level at 95-pct if confidence TRUE, not if prewhitened

Details

This function implements Kendall's nonparametric test for a monotonic trend using the Theil-Sen (Theil 1950; Sen 1968; Siegel 1982) method to estimate the slope and related confidence intervals. Critical values are Z > 1.96 representing a significant increasing trend and a Z < -1.96 a significant decreasing trend (p < 0.05). The null hypothesis can be rejected if Tau = 0. There is also an option for autocorrelation correction using the method proposed in Yue & Wang (2002).

References

Theil, H. (1950) A rank invariant method for linear and polynomial regression analysis. Nederl. Akad. Wetensch. Proc. Ser. A 53:386-392 (Part I), 53:521-525 (Part II), 53:1397-1412 (Part III).

Sen, P.K. (1968) Estimates of Regression Coefficient Based on Kendall's tau. Journal of the American Statistical Association. 63(324):1379-1389.

Siegel, A.F. (1982) Robust Regression Using Repeated Medians. Biometrika, 69(1):242-244

Yue, S., & Wang, C. Y. (2002). Applicability of prewhitening to eliminate the influence of serial correlation on the Mann-Kendall test. Water Resources Research, 38(6):41-47.

Author

Jeffrey S. Evans <jeffrey_evans@tnc.org>