Sliding and disjoint block maxima

Calculates the (sliding) maxima of all blocks of b contiguous values and all sets of the maxima of disjoint blocks of b contiguous values in the vector x. This provides the first step of computations in spm.

Usage

all_max_rcpp(x, b = 1, which_dj = c("all", "first", "last"), ...)

Arguments

x

A numeric vector of raw observations.

b

A numeric scalar. The block size.

which_dj

A character scalar. Determines Which sets of disjoint maxima are calculated: "all", all sets; "first", only the set whose first block starts on the first observation in x; "last", only the set whose last block end on the last observation in x.

...

Further arguments to be passed to roll_max.

Value

A list containing

ys

a numeric vector containing one set of sliding block maxima.

xs

a numeric vector containing the values that contribute to ys, that is, the whole input vector x.

yd

if which_dj = "all" a floor(n / b) by n - floor(n / b) * b + 1 numeric matrix. Each column contains a set of disjoint maxima. Otherwise, a floor(n / b) by 1 numeric matrix containing one set of block maxima.

xd

if which_dj = "all" a floor(n / b) * b by n - floor(n / b) * b + 1 numeric matrix. Each column contains the values in x that contribute to the corresponding column in yd. Otherwise, a floor(n / b) by 1 numeric matrix containing one the one set of the values in x that contribute to yd.

Details

Sliding maxima. The function roll_max in the RcppRoll package is used.

Disjoint maxima. If n = length(x) is an integer multiple of b, or if which_dj = "first" or which_dj = "last" then only one set of n / b disjoint block maxima are returned. Otherwise, n - floor(n / b) * b + 1 sets of floor(n / b) disjoint block maxima are returned. Set i are the disjoint maxima of x[i:(i + floor(n / b) * b - 1)]. That is, all possible sets of contiguous disjoint maxima achieving the maxima length of floor(n / b) are calculated.

In both instances na.rm = TRUE is passed to max so that blocks containing missing values produce a non-missing result.

Also returned are the values in x that contribute to each set of block maxima.

See also

spm for semiparametric estimation of the extremal index based on block maxima.

Examples

x <- 1:11
all_max_rcpp(x, 3)
#> $ys
#> [1]  3  4  5  6  7  8  9 10 11
#> 
#> $xs
#>  [1]  1  2  3  4  5  6  7  8  9 10 11
#> 
#> $yd
#>      [,1] [,2] [,3]
#> [1,]    3    4    5
#> [2,]    6    7    8
#> [3,]    9   10   11
#> 
#> $xd
#>       [,1] [,2] [,3]
#>  [1,]    1    2    3
#>  [2,]    2    3    4
#>  [3,]    3    4    5
#>  [4,]    4    5    6
#>  [5,]    5    6    7
#>  [6,]    6    7    8
#>  [7,]    7    8    9
#>  [8,]    8    9   10
#>  [9,]    9   10   11
#> 
all_max_rcpp(x, 3, which_dj = "first")
#> $ys
#> [1]  3  4  5  6  7  8  9 10 11
#> 
#> $xs
#>  [1]  1  2  3  4  5  6  7  8  9 10 11
#> 
#> $yd
#>      [,1]
#> [1,]    3
#> [2,]    6
#> [3,]    9
#> 
#> $xd
#>       [,1]
#>  [1,]    1
#>  [2,]    2
#>  [3,]    3
#>  [4,]    4
#>  [5,]    5
#>  [6,]    6
#>  [7,]    7
#>  [8,]    8
#>  [9,]    9
#> 
all_max_rcpp(x, 3, which_dj = "last")
#> $ys
#> [1]  3  4  5  6  7  8  9 10 11
#> 
#> $xs
#>  [1]  1  2  3  4  5  6  7  8  9 10 11
#> 
#> $yd
#>      [,1]
#> [1,]    5
#> [2,]    8
#> [3,]   11
#> 
#> $xd
#>       [,1]
#>  [1,]    3
#>  [2,]    4
#>  [3,]    5
#>  [4,]    6
#>  [5,]    7
#>  [6,]    8
#>  [7,]    9
#>  [8,]   10
#>  [9,]   11
#>