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Convert between vector and season-lag representations

sl2acfbase.Rd

Convert between vector and season-lag representations of autocovariances of multivariate and periodically correlated time series.

Usage

sl2acfbase(mat, maxlag, fullblocks = FALSE)

acfbase2sl(acf)

sl2vecacf(mat, maxlag, fullblocks = FALSE)

Arguments

acf

an acf as returned by base R acf.

mat

a matrix containing autocovariances in season-lag arrangement.

maxlag

maximal lag, a positive integer.

fullblocks

if TRUE, keep full blocks only.

Details

These functions rearrange autocovariances and autocorrelations between the native season-lag arrangement in package “pcts” and the vector representations of the corresponding mutivariate models (vector of seasons representation of periodic models). Variable \(s\) is taken be season \(s\) and vice versa in the opposite direction.

“acfbase” in the names of the functions refers to the representation returned by base function acf.

acfbase2sl rearranges a multivariate acf in season-lag form.

sl2acfbase rearranges a season-lag form into the multivariate form used by base function acf.

sl2vecacf is similar to sl2acfbase but the result is such that the lag is in the third dimension and r[ , , k] is \(Cov(X_{t}, X_{t-k})\) (not its transpose). See also the examples below and in acf2Lagged.

Value

for acfbase2sl, a matrix.

for sl2acfbase and sl2vecacf, an array.

Author

Georgi N. Boshnakov

Examples

## use a character matrix to illustrate the positions of the elements
matsl <- rbind(paste0("Ra", 0:3), paste0("Rb", 0:3))
matsl
#>      [,1]  [,2]  [,3]  [,4] 
#> [1,] "Ra0" "Ra1" "Ra2" "Ra3"
#> [2,] "Rb0" "Rb1" "Rb2" "Rb3"
## convert to what I consider "standard" vec format R(k)=EX_tX_{t-k}'
sl2vecacf(matsl)
#> , , 1
#> 
#>      [,1]  [,2] 
#> [1,] "Ra0" "Rb1"
#> [2,] "Rb1" "Rb0"
#> 
#> , , 2
#> 
#>      [,1]  [,2] 
#> [1,] "Ra2" "Ra1"
#> [2,] "Rb3" "Rb2"
#> 
#> , , 3
#> 
#>      [,1] [,2] 
#> [1,] NA   "Ra3"
#> [2,] NA   NA   
#> 
## convert to the format from acf() (R(k) is the transposed from mine).
sl2acfbase(matsl)
#> , , 1
#> 
#>      [,1]  [,2] 
#> [1,] "Ra0" "Rb1"
#> [2,] "Ra2" "Ra1"
#> [3,] NA    "Ra3"
#> 
#> , , 2
#> 
#>      [,1]  [,2] 
#> [1,] "Rb1" "Rb0"
#> [2,] "Rb3" "Rb2"
#> [3,] NA    NA   
#> 
identical(sl2vecacf(matsl), aperm(sl2acfbase(matsl), c(3, 2, 1))) # TRUE
#> [1] TRUE

## by default the conversion is lossles;
## so this contains all values from the original and some NA's:
sl2acfbase(matsl)
#> , , 1
#> 
#>      [,1]  [,2] 
#> [1,] "Ra0" "Rb1"
#> [2,] "Ra2" "Ra1"
#> [3,] NA    "Ra3"
#> 
#> , , 2
#> 
#>      [,1]  [,2] 
#> [1,] "Rb1" "Rb0"
#> [2,] "Rb3" "Rb2"
#> [3,] NA    NA   
#> 
## the orignal, matsl, can be restored:
acfbase2sl(sl2acfbase(matsl))
#>      [,1]  [,2]  [,3]  [,4] 
#> [1,] "Ra0" "Ra1" "Ra2" "Ra3"
#> [2,] "Rb0" "Rb1" "Rb2" "Rb3"
identical(acfbase2sl(sl2acfbase(matsl)), matsl)  # TRUE
#> [1] TRUE

## this drops some values (if necessary) to keep complete block only
sl2acfbase(matsl, fullblocks = TRUE)
#> , , 1
#> 
#>      [,1]  [,2] 
#> [1,] "Ra0" "Rb1"
#> [2,] "Ra2" "Ra1"
#> 
#> , , 2
#> 
#>      [,1]  [,2] 
#> [1,] "Rb1" "Rb0"
#> [2,] "Rb3" "Rb2"
#>