foster.plot {RecordTest}

Plots Based on Foster-Stuart and Diersen-Trenkler Statistics

Description

This function builds a ggplot object to display two-sided reference intervals based on Foster-Stuart and Diersen-Trenkler statistics to study the hypothesis of the classical record model (i.e., of IID continuous RVs).

Usage

foster.plot(
  X,
  weights = function(t) 1,
  statistic = c("D", "d", "S", "s", "U", "L", "W"),
  point.col = "black",
  point.shape = 19,
  conf.int = TRUE,
  conf.level = 0.9,
  conf.aes = c("ribbon", "errorbar"),
  conf.col = "grey69"
)

Arguments

X

A numeric vector, matrix (or data frame).

weights

A function indicating the weight given to the different records according to their position in the series, e.g., if function(t) t-1 then \omega_t = t-1.

statistic

A character string indicating the type of statistic to be calculated, i.e., one of "D", "d", "S", "s", "U", "L" or "W" (see foster.test).

point.col, point.shape

Value with the colour and shape of the points.

conf.int

Logical. Indicates if the RIs are also shown.

conf.level

(If conf.int == TRUE) Confidence level of the RIs.

conf.aes

(If conf.int == TRUE) A character string indicating the aesthetic to display for the RIs, "ribbon" (grey area) or "errorbar" (vertical lines).

conf.col

Colour used to plot the expected value and (if conf.int == TRUE) RIs.

Details

The function plots the observed values of the statistic selected with statistic, obtained with the series up to time t for t=1,\ldots,T. The plot also includes the expected values and reference intervals (RIs) based on the asymptotic normal distribution of the statistics under the null hypothesis.

This function implements the same ideas that N.plot, but with the statistics computed in foster.test.

These plots are useful to see the evolution in the record occurrence and to follow the evolution of the trend. The plot was proposed by Cebrián, Castillo-Mateo, Asín (2022) where its application is shown.

Value

A ggplot graph object.

Author(s)

Jorge Castillo-Mateo

References

Cebrián AC, Castillo-Mateo J, Asín J (2022). “Record Tests to Detect Non Stationarity in the Tails with an Application to Climate Change.” Stochastic Environmental Research and Risk Assessment, 36(2), 313-330. doi:10.1007/s00477-021-02122-w.

Diersen J, Trenkler G (1996). “Records Tests for Trend in Location.” Statistics, 28(1), 1-12. doi:10.1080/02331889708802543.

Diersen J, Trenkler G (2001). “Weighted Records Tests for Splitted Series of Observations.” In J Kunert, G Trenkler (eds.), Mathematical Statistics with Applications in Biometry: Festschrift in Honour of Prof. Dr. Siegfried Schach, pp. 163–178. Lohmar: Josef Eul Verlag.

Foster FG, Stuart A (1954). “Distribution-Free Tests in Time-Series Based on the Breaking of Records.” Journal of the Royal Statistical Society B, 16(1), 1-22. doi:10.1111/j.2517-6161.1954.tb00143.x.

See Also

foster.test, N.plot, N.test

Examples

# D-statistic
foster.plot(ZaragozaSeries)
# D-statistic with linear weights
foster.plot(ZaragozaSeries, weights = function(t) t-1)
# S-statistic with linear weights
foster.plot(ZaragozaSeries, statistic = "S", weights = function(t) t-1)
# U-statistic with weights (upper tail)
foster.plot(ZaragozaSeries, statistic = "U", weights = function(t) t-1)
# L-statistic with weights (lower tail)
foster.plot(ZaragozaSeries, statistic = "L", weights = function(t) t-1)