plot_ordinal_cohens_kappa {otsfeatures}

Constructs a serial dependence plot based on the ordinal Cohen's kappa considering the block distance

Description

plot_ordinal_cohens_kappa constructs a serial dependence plot of an ordinal time series based on the ordinal Cohen's kappa considering the block distance

Usage

plot_ordinal_cohens_kappa(
  series,
  states,
  max_lag = 10,
  alpha = 0.05,
  plot = TRUE,
  title = "Serial dependence plot",
  bar_width = 0.12,
  ...
)

Arguments

series

An OTS.

states

A numerical vector containing the corresponding states.

max_lag

The maximum lag represented in the plot (default is 10).

alpha

The significance level for the corresponding hypothesis test (default is 0.05).

plot

Logical. If plot = TRUE (default), returns the serial dependence plot. Otherwise, returns a list with the values of the ordinal Cohens's kappa, the critical value and the corresponding p-values.

title

The title of the graph.

bar_width

The width of the corresponding bars.

...

Additional parameters for the function.

Details

Constructs a serial dependence plot based on the ordinal Cohens's kappa, \widehat{\kappa}_d(l), for several lags, where d is the block distance between ordinal states, that is, d(s_i, s_j)=|i-j| for two states s_i and s_j. A dashed lined is incorporated indicating the critical value of the test based on the following asymptotic approximation (under the i.i.d. assumption):

\sqrt{\frac{T\widehat{disp}_d^2}{4\sum_{k,l=0}^{n-1}(\widehat{f}_{min\{k,l\}}-\widehat{f}_k\widehat{f}_l)^2}}\bigg(\widehat{\kappa}_d(l)+\frac{1}{T}\bigg)\sim N\big(0, 1\big),

where T is the series length, \widehat{f_k} is the estimated cumulative probability for state s_k and \widehat{disp}_d is the DIVC estimate of the dispersion.

Value

If plot = TRUE (default), returns the serial dependence plot based on the ordinal Cohens's kappa. Otherwise, the function returns a list with the values of the ordinal Cohens's kappa, the critical value and the corresponding p-values.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Weiß CH (2019). “Distance-based analysis of ordinal data and ordinal time series.” Journal of the American Statistical Association.

Examples

plot_ock <- plot_ordinal_cohens_kappa(series = AustrianWages$data[[100]],
states = 0 : 5, max_lag = 3) # Representing
# the serial dependence plot
list_ck <- plot_ordinal_cohens_kappa(series = AustrianWages$data[[100]],
states = 0 : 5, max_lag = 3, plot = FALSE) # Obtaining
# the values of the ordinal Cohens's kappa, the critical value and the p-values