Nothing
R/xbooter.R
In extRemes: Extreme Value Analysis
Defines functions
rlvar
xbooter
xbooterPOT
xbooterBM
Documented in
rlvar
xbooter
xbooterBM
xbooterPOT
xbooterBM <- function( data, fevd.object, return.period, qcov, qcov.base, init, np, ... ) {
pm <- fevd.object$par.models
do.var <- fevd.object$method != "Lmoments"
do.rl <- length( return.period ) > 0
xdim <- dim( data )
if( !is.null( xdim ) ) {
fit <- try( fevd( x = data[, 1 ], data = data, location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} else {
fit <- try( fevd( x = data, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} # end of whether or not there is a 'data' argument stmt.
if( is( fit, "try-error" ) ) return( rep( NA, np ) )
nomen <- fevd.object$parnames
res <- c( distill( fit, cov = FALSE ) )[ 1:length( nomen ) ]
if( do.rl ) {
res2 <- return.level( fit, return.period = return.period, qcov = qcov, qcov.base = qcov.base )
if( !is.matrix( res2 ) ) {
res <- c( res, res2 )
nomen <- c( nomen, paste( return.period, "-", fevd.object$period.basis, " ret. lvl.", sep = "" ) )
} else {
rldim <- dim( res2 )
res <- c( res, c( res2 ) )
nomen <- c( nomen, paste( rep( paste( "erl", return.period, sep = "." ), each = rldim[ 1 ] ),
rep( paste( "t", 1:rldim[ 1 ], sep = "" ), rldim[ 2 ] ), sep = "." ) )
}
names( res ) <- nomen
} # end of if do return levels or not stmt.
if( do.var ) {
sumobj <- summary( fit, silent = TRUE )
varres <- diag( sumobj$cov.theta )
if( do.rl ) {
varres2 <- rlvar( fit, return.period = return.period, theta = sumobj,
qcov = qcov, qcov.base = qcov.base )
varres <- c( varres, varres2 )
} # end of if do return level estimates too stmt.
res <- c( res, varres )
nomen <- c( nomen, paste( "var(", nomen, ")", sep = "" ) )
names( res ) <- nomen
}
# TO DO: should scale be converted or not. If so, check variance to make sure it is correct.
# res[ nomen == "log.scale" ] <- exp( res[ nomen == "log.scale" ] )
# nomen[ nomen == "log.scale" ] <- "scale"
return( res )
} # end of 'xbooterBM' function.
xbooterPOT <- function( data, fevd.object, return.period, qcov, qcov.base, init, np, ... ) {
pm <- fevd.object$par.models
do.var <- fevd.object$method != "Lmoments"
do.rl <- length( return.period ) > 0
xdim <- dim( data )
if( is.data.frame( data ) && !is.null( data$threshold ) ) u <- data$threshold
else u <- fevd.object$threshold
if( !is.null( dim( data ) ) ) {
fit <- try( fevd( x = data[, 1 ], threshold = u, data = data, threshold.fun = pm$threshold,
location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} else {
fit <- try( fevd( x = data, threshold = u, threshold.fun = pm$threshold,
location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
}
if( is( fit, "try-error" ) ) return( rep( NA, np ) )
nomen <- fevd.object$parnames
res <- c( distill( fit, cov = FALSE ) )[ 1:length( nomen ) ]
if( do.rl ) {
res2 <- return.level( fit, return.period = return.period, qcov = qcov, qcov.base = qcov.base )
if( !is.matrix( res2 ) ) {
res <- c( res, res2 )
nomen <- c( nomen, paste( return.period, "-", fevd.object$period.basis, " ret. lvl.", sep = "" ) )
} else {
rldim <- dim( res2 )
res <- c( res, c( res2 ) )
nomen <- c( nomen, paste( rep( paste( "erl", return.period, sep = "." ), each = rldim[ 1 ] ),
rep( paste( "t", 1:rldim[ 1 ], sep = "" ), rldim[ 2 ] ), sep = "." ) )
}
names( res ) <- nomen
} # end of if do return levels or not stmt.
if( do.var ) {
sumobj <- summary( fit, silent = TRUE )
varres <- diag( sumobj$cov.theta )
if( do.rl ) {
varres2 <- rlvar( fit, return.period = return.period, theta = sumobj,
qcov = qcov, qcov.base = qcov.base )
varres <- c( varres, varres2 )
} # end of if do return level estimates too stmt.
res <- c( res, varres )
nomen <- c( nomen, paste( "var(", nomen, ")", sep = "" ) )
names( res ) <- nomen
}
# TO DO: should scale be converted or not. If so, check variance to make sure it is correct.
# res[ nomen == "log.scale" ] <- exp( res[ nomen == "log.scale" ] )
# nomen[ nomen == "log.scale" ] <- "scale"
return( res )
} # end of 'xbooterPOT' function.
xbooter <- function( x, B, rsize, block.length = 1,
return.period = c( 10, 20, 50, 100, 200, 500 ), qcov = NULL, qcov.base = NULL,
shuffle = NULL, replace = TRUE, verbose = FALSE, ... ) {
if( verbose ) begin.tiid <- Sys.time()
if( x$method == "Bayesian" ) stop( "xbooter: invalid x argument." )
if( !is.fixedfevd( x ) && is.null( qcov ) ) {
if( !missing( return.period ) ) stop( "xbooter: Must use qcov argument for models with varying parameters." )
else return.period <- numeric( 0 )
}
theCall <- match.call()
if( !is.null( qcov.base ) ) warning( "xbooter: this function has not been tested with qcov.base!" )
if( missing( rsize ) ) rsize <- x$n
if( rsize > x$n || rsize < 1 ) stop( "xbooter: invalid rsize argument." )
# Obtain initial estimate information.
if( x$method == "Lmoments" ) {
theta.hat <- x$results
theta.names <- names( theta.hat )
} else {
theta.hat <- x$results$par
theta.names <- names( theta.hat )
}
ipar <- list()
if (any(is.element(c("location", "mu0"), theta.names))) {
if (is.element("location", theta.names))
ipar$location <- theta.hat["location"]
else {
id <- substring(theta.names, 1, 2) == "mu"
ipar$location <- theta.hat[id]
}
}
if (is.element("scale", theta.names))
ipar$scale <- theta.hat["scale"]
else {
if (!x$par.models$log.scale)
id <- substring(theta.names, 1, 3) == "sig"
else id <- substring(theta.names, 1, 3) == "phi"
ipar$scale <- theta.hat[id]
}
if (!is.element(x$type, c("Gumbel", "Exponential"))) {
if (is.element("shape", theta.names))
ipar$shape <- theta.hat["shape"]
else {
id <- substring(theta.names, 1, 2) == "xi"
ipar$shape <- theta.hat[id]
}
}
npar <- length( x$parnames )
if( is.fixedfevd( x ) ) {
npar <- npar + length( return.period )
bigD <- x$x
} else {
npar <- npar + length( return.period ) * nrow( qcov )
# dnames <- names( x$data )
bigD <- data.frame( x$x, x$cov.data )
# names( bigD ) <- c( "V1", dnames )
if( !is.null( x$threshold ) && length( x$threshold ) > 1 ) bigD <- data.frame( bigD, threshold = x$threshold )
}
if( is.element( x$type, c( "GP", "PP", "Exponential" ) ) ) {
sz <- rsize / block.length
ind <- matrix( rpois( sz * B, lambda = x$rate ), sz, B )
ind[ ind > 0 ] <- 1
exceeds <- x$x > x$threshold
id1 <- sample( (1:x$n)[ exceeds ], size = sz * B, replace = replace )
id2 <- sample( (1:x$n)[ !exceeds ], size = sz * B, replace = replace )
id <- id1 * ind + id2 * ( 1 - ind )
if( block.length > 1 ) {
bmaker <- function( x, b ) return( apply( cbind( x ), 1, function( x ) return( c( x:( x + b ) ) ) ) )
id <- apply( id, 2, bmaker, b = block.length )
if( any( id > x$n ) ) id[ id > x$n ] <- id[ id > x$n ] - x$n
} # end of if 'block.length' > 1 stmt.
shuffle.indices <- id
} # end of if method is POT stmt.
if( x$method != "Lmoments" ) {
vt <- (npar + 1):( 2 * npar )
npar <- npar * 2
if( is.element( x$type, c( "GEV", "Gumbel" ) ) ) {
out <- booter( x = bigD, statistic = xbooterBM, B = B, rsize = rsize,
block.length = block.length, v.terms = vt, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
if( !missing( block.length ) ) {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
block.length = block.length, v.terms = vt, shuffle = shuffle.indices,
replace = replace, fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
v.terms = vt, shuffle = shuffle.indices, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} # end of whether to use block.length argument or not stmt.
} # end of if else do BM or POT method stmts.
} else {
if( is.element( x$type, c( "GEV", "Gumbel" ) ) ) {
out <- booter( x = bigD, statistic = xbooterBM, B = B, rsize = rsize,
block.length = block.length, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
if( !missing( block.length ) ) {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
block.length = block.length, shuffle = shuffle.indices,
replace = replace, fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
shuffle = shuffle.indices, replace = replace, fevd.object = x,
return.period = return.period, qcov = qcov, qcov.base = qcov.base,
init = ipar, np = npar, ... )
} # end of whether to use block.length argument or not stmt.
} # end of if else do BM or POT method stmts.
} # end of if else compute variance terms stmt.
if( verbose ) print( Sys.time() - begin.tiid )
out$call <- theCall
return( out )
} # end of 'xbooter' function.
rlvar <- function( x, return.period, theta = NULL, qcov = NULL, qcov.base = NULL ) {
if( is.null( theta ) ) theta <- summary( x, silent = TRUE )
grads <- t( rlgrad.fevd( x, period = return.period, qcov = qcov, qcov.base = qcov.base ) )
cov.theta <- theta$cov.theta
if ( is.element( x$type, c( "GP", "Beta", "Pareto", "Exponential" ) ) ) {
lam <- x$rate
var.theta <- diag( cov.theta )
if (x$type == "Exponential") cov.theta <- diag( c( lam * (1 - lam) / x$n, var.theta ) )
else cov.theta <- rbind( c( lam * ( 1 - lam ) / x$n, 0, 0 ), cbind( 0, cov.theta ) )
}
res <- diag( t(grads) %*% cov.theta %*% grads )
names( res ) <- paste( "var(", return.period, "-", x$period.basis, " return level)" )
return( res )
} # end of 'rlvar' function.
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Defines functions rlvar xbooter xbooterPOT xbooterBM
Documented in rlvar xbooter xbooterBM xbooterPOT
xbooterBM <- function( data, fevd.object, return.period, qcov, qcov.base, init, np, ... ) {
pm <- fevd.object$par.models
do.var <- fevd.object$method != "Lmoments"
do.rl <- length( return.period ) > 0
xdim <- dim( data )
if( !is.null( xdim ) ) {
fit <- try( fevd( x = data[, 1 ], data = data, location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} else {
fit <- try( fevd( x = data, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} # end of whether or not there is a 'data' argument stmt.
if( is( fit, "try-error" ) ) return( rep( NA, np ) )
nomen <- fevd.object$parnames
res <- c( distill( fit, cov = FALSE ) )[ 1:length( nomen ) ]
if( do.rl ) {
res2 <- return.level( fit, return.period = return.period, qcov = qcov, qcov.base = qcov.base )
if( !is.matrix( res2 ) ) {
res <- c( res, res2 )
nomen <- c( nomen, paste( return.period, "-", fevd.object$period.basis, " ret. lvl.", sep = "" ) )
} else {
rldim <- dim( res2 )
res <- c( res, c( res2 ) )
nomen <- c( nomen, paste( rep( paste( "erl", return.period, sep = "." ), each = rldim[ 1 ] ),
rep( paste( "t", 1:rldim[ 1 ], sep = "" ), rldim[ 2 ] ), sep = "." ) )
}
names( res ) <- nomen
} # end of if do return levels or not stmt.
if( do.var ) {
sumobj <- summary( fit, silent = TRUE )
varres <- diag( sumobj$cov.theta )
if( do.rl ) {
varres2 <- rlvar( fit, return.period = return.period, theta = sumobj,
qcov = qcov, qcov.base = qcov.base )
varres <- c( varres, varres2 )
} # end of if do return level estimates too stmt.
res <- c( res, varres )
nomen <- c( nomen, paste( "var(", nomen, ")", sep = "" ) )
names( res ) <- nomen
}
# TO DO: should scale be converted or not. If so, check variance to make sure it is correct.
# res[ nomen == "log.scale" ] <- exp( res[ nomen == "log.scale" ] )
# nomen[ nomen == "log.scale" ] <- "scale"
return( res )
} # end of 'xbooterBM' function.
xbooterPOT <- function( data, fevd.object, return.period, qcov, qcov.base, init, np, ... ) {
pm <- fevd.object$par.models
do.var <- fevd.object$method != "Lmoments"
do.rl <- length( return.period ) > 0
xdim <- dim( data )
if( is.data.frame( data ) && !is.null( data$threshold ) ) u <- data$threshold
else u <- fevd.object$threshold
if( !is.null( dim( data ) ) ) {
fit <- try( fevd( x = data[, 1 ], threshold = u, data = data, threshold.fun = pm$threshold,
location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
} else {
fit <- try( fevd( x = data, threshold = u, threshold.fun = pm$threshold,
location.fun = pm$location, scale.fun = pm$scale,
shape.fun = pm$shape, use.phi = pm$log.scale, type = fevd.object$type,
method = fevd.object$method, initial = init, period.basis = fevd.object$period.basis,
optim.args = fevd.object$optim.args, priorFun = fevd.object$priorFun,
priorParams = fevd.object$priorParams ) )
}
if( is( fit, "try-error" ) ) return( rep( NA, np ) )
nomen <- fevd.object$parnames
res <- c( distill( fit, cov = FALSE ) )[ 1:length( nomen ) ]
if( do.rl ) {
res2 <- return.level( fit, return.period = return.period, qcov = qcov, qcov.base = qcov.base )
if( !is.matrix( res2 ) ) {
res <- c( res, res2 )
nomen <- c( nomen, paste( return.period, "-", fevd.object$period.basis, " ret. lvl.", sep = "" ) )
} else {
rldim <- dim( res2 )
res <- c( res, c( res2 ) )
nomen <- c( nomen, paste( rep( paste( "erl", return.period, sep = "." ), each = rldim[ 1 ] ),
rep( paste( "t", 1:rldim[ 1 ], sep = "" ), rldim[ 2 ] ), sep = "." ) )
}
names( res ) <- nomen
} # end of if do return levels or not stmt.
if( do.var ) {
sumobj <- summary( fit, silent = TRUE )
varres <- diag( sumobj$cov.theta )
if( do.rl ) {
varres2 <- rlvar( fit, return.period = return.period, theta = sumobj,
qcov = qcov, qcov.base = qcov.base )
varres <- c( varres, varres2 )
} # end of if do return level estimates too stmt.
res <- c( res, varres )
nomen <- c( nomen, paste( "var(", nomen, ")", sep = "" ) )
names( res ) <- nomen
}
# TO DO: should scale be converted or not. If so, check variance to make sure it is correct.
# res[ nomen == "log.scale" ] <- exp( res[ nomen == "log.scale" ] )
# nomen[ nomen == "log.scale" ] <- "scale"
return( res )
} # end of 'xbooterPOT' function.
xbooter <- function( x, B, rsize, block.length = 1,
return.period = c( 10, 20, 50, 100, 200, 500 ), qcov = NULL, qcov.base = NULL,
shuffle = NULL, replace = TRUE, verbose = FALSE, ... ) {
if( verbose ) begin.tiid <- Sys.time()
if( x$method == "Bayesian" ) stop( "xbooter: invalid x argument." )
if( !is.fixedfevd( x ) && is.null( qcov ) ) {
if( !missing( return.period ) ) stop( "xbooter: Must use qcov argument for models with varying parameters." )
else return.period <- numeric( 0 )
}
theCall <- match.call()
if( !is.null( qcov.base ) ) warning( "xbooter: this function has not been tested with qcov.base!" )
if( missing( rsize ) ) rsize <- x$n
if( rsize > x$n || rsize < 1 ) stop( "xbooter: invalid rsize argument." )
# Obtain initial estimate information.
if( x$method == "Lmoments" ) {
theta.hat <- x$results
theta.names <- names( theta.hat )
} else {
theta.hat <- x$results$par
theta.names <- names( theta.hat )
}
ipar <- list()
if (any(is.element(c("location", "mu0"), theta.names))) {
if (is.element("location", theta.names))
ipar$location <- theta.hat["location"]
else {
id <- substring(theta.names, 1, 2) == "mu"
ipar$location <- theta.hat[id]
}
}
if (is.element("scale", theta.names))
ipar$scale <- theta.hat["scale"]
else {
if (!x$par.models$log.scale)
id <- substring(theta.names, 1, 3) == "sig"
else id <- substring(theta.names, 1, 3) == "phi"
ipar$scale <- theta.hat[id]
}
if (!is.element(x$type, c("Gumbel", "Exponential"))) {
if (is.element("shape", theta.names))
ipar$shape <- theta.hat["shape"]
else {
id <- substring(theta.names, 1, 2) == "xi"
ipar$shape <- theta.hat[id]
}
}
npar <- length( x$parnames )
if( is.fixedfevd( x ) ) {
npar <- npar + length( return.period )
bigD <- x$x
} else {
npar <- npar + length( return.period ) * nrow( qcov )
# dnames <- names( x$data )
bigD <- data.frame( x$x, x$cov.data )
# names( bigD ) <- c( "V1", dnames )
if( !is.null( x$threshold ) && length( x$threshold ) > 1 ) bigD <- data.frame( bigD, threshold = x$threshold )
}
if( is.element( x$type, c( "GP", "PP", "Exponential" ) ) ) {
sz <- rsize / block.length
ind <- matrix( rpois( sz * B, lambda = x$rate ), sz, B )
ind[ ind > 0 ] <- 1
exceeds <- x$x > x$threshold
id1 <- sample( (1:x$n)[ exceeds ], size = sz * B, replace = replace )
id2 <- sample( (1:x$n)[ !exceeds ], size = sz * B, replace = replace )
id <- id1 * ind + id2 * ( 1 - ind )
if( block.length > 1 ) {
bmaker <- function( x, b ) return( apply( cbind( x ), 1, function( x ) return( c( x:( x + b ) ) ) ) )
id <- apply( id, 2, bmaker, b = block.length )
if( any( id > x$n ) ) id[ id > x$n ] <- id[ id > x$n ] - x$n
} # end of if 'block.length' > 1 stmt.
shuffle.indices <- id
} # end of if method is POT stmt.
if( x$method != "Lmoments" ) {
vt <- (npar + 1):( 2 * npar )
npar <- npar * 2
if( is.element( x$type, c( "GEV", "Gumbel" ) ) ) {
out <- booter( x = bigD, statistic = xbooterBM, B = B, rsize = rsize,
block.length = block.length, v.terms = vt, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
if( !missing( block.length ) ) {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
block.length = block.length, v.terms = vt, shuffle = shuffle.indices,
replace = replace, fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
v.terms = vt, shuffle = shuffle.indices, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} # end of whether to use block.length argument or not stmt.
} # end of if else do BM or POT method stmts.
} else {
if( is.element( x$type, c( "GEV", "Gumbel" ) ) ) {
out <- booter( x = bigD, statistic = xbooterBM, B = B, rsize = rsize,
block.length = block.length, replace = replace,
fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
if( !missing( block.length ) ) {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
block.length = block.length, shuffle = shuffle.indices,
replace = replace, fevd.object = x, return.period = return.period,
qcov = qcov, qcov.base = qcov.base, init = ipar, np = npar, ... )
} else {
out <- booter( x = bigD, statistic = xbooterPOT, B = B, rsize = rsize,
shuffle = shuffle.indices, replace = replace, fevd.object = x,
return.period = return.period, qcov = qcov, qcov.base = qcov.base,
init = ipar, np = npar, ... )
} # end of whether to use block.length argument or not stmt.
} # end of if else do BM or POT method stmts.
} # end of if else compute variance terms stmt.
if( verbose ) print( Sys.time() - begin.tiid )
out$call <- theCall
return( out )
} # end of 'xbooter' function.
rlvar <- function( x, return.period, theta = NULL, qcov = NULL, qcov.base = NULL ) {
if( is.null( theta ) ) theta <- summary( x, silent = TRUE )
grads <- t( rlgrad.fevd( x, period = return.period, qcov = qcov, qcov.base = qcov.base ) )
cov.theta <- theta$cov.theta
if ( is.element( x$type, c( "GP", "Beta", "Pareto", "Exponential" ) ) ) {
lam <- x$rate
var.theta <- diag( cov.theta )
if (x$type == "Exponential") cov.theta <- diag( c( lam * (1 - lam) / x$n, var.theta ) )
else cov.theta <- rbind( c( lam * ( 1 - lam ) / x$n, 0, 0 ), cbind( 0, cov.theta ) )
}
res <- diag( t(grads) %*% cov.theta %*% grads )
names( res ) <- paste( "var(", return.period, "-", x$period.basis, " return level)" )
return( res )
} # end of 'rlvar' function.
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