hts (version 5.1.5)

MinT: Trace minimization for hierarchical or grouped time series

Description

Using the method of Wickramasuriya et al. (2015), this function combines the forecasts at all levels of a hierarchical or grouped time series. The forecast.gts calls this function when the MinT method is selected.

Usage

MinT(fcasts, nodes, groups, residual, covariance = c("shr", "sam"),
  algorithms = c("lu", "cg", "chol"), keep = c("gts", "all", "bottom"))

Arguments

fcasts

Matrix of forecasts for all levels of a hierarchical or grouped time series. Each row represents one forecast horizon and each column represents one time series of aggregated or disaggregated forecasts.

nodes

If the object class is hts, a list contains the number of child nodes referring to hts.

groups

If the object is gts, a gmatrix is required, which is the same as groups in the function gts.

residual

Matrix of insample residuals for all the aggregated and disaggregated time series. The columns must be in the same order as fcasts.

covariance

Type of the covariance matrix to be used. Shrinking towards a diagonal unequal variances ("shr") or sample covariance matrix ("sam").

algorithms

Algorithm used to compute inverse of the matrices.

keep

Return a gts object or the reconciled forecasts at the bottom level.

Value

Return the reconciled gts object or forecasts at the bottom level.

References

Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2015). Forecasting hierarchical and grouped time series through trace minimization. Working paper 15/15, Department of Econometrics & Business Statistics, Monash University. http://robjhyndman.com/working-papers/mint/

Hyndman, R. J., Lee, A., & Wang, E. (2015). Fast computation of reconciled forecasts for hierarchical and grouped time series. Computational Statistics and Data Analysis, 97, 16--32. http://robjhyndman.com/papers/hgts/

See Also

hts, gts, forecast.gts, combinef

Examples

# NOT RUN {
# hts example
# }
# NOT RUN {
h <- 12 
ally <- aggts(htseg1)
n <- nrow(ally)
p <- ncol(ally)
allf <- matrix(NA, nrow = h, ncol = p)
res <- matrix(NA, nrow = n, ncol = p)
for(i in 1:p)
{
  fit <- auto.arima(ally[, i])
  allf[, i] <- forecast(fit, h = h)$mean
  res[, i] <- na.omit(ally[, i] - fitted(fit))
}
allf <- ts(allf, start = 51)
y.f <- MinT(allf, get_nodes(htseg1), residual = res, covariance = "shr", 
  keep = "gts", algorithms = "lu")
plot(y.f)
y.f_cg <- MinT(allf, get_nodes(htseg1), residual = res, covariance = "shr", 
  keep = "all", algorithms = "cg")
# }
# NOT RUN {
  
# gts example
# }
# NOT RUN {
abc <- ts(5 + matrix(sort(rnorm(200)), ncol = 4, nrow = 50))
g <- rbind(c(1,1,2,2), c(1,2,1,2))
y <- gts(abc, groups = g)
h <- 12
ally <- aggts(y)
n <- nrow(ally)
p <- ncol(ally)
allf <- matrix(NA,nrow = h,ncol = ncol(ally))
res <- matrix(NA, nrow = n, ncol = p)
for(i in 1:p)
{
  fit <- auto.arima(ally[, i])
  allf[, i] <- forecast(fit, h = h)$mean
  res[, i] <- na.omit(ally[, i] - fitted(fit))
}
allf <- ts(allf, start = 51)
y.f <- MinT(allf, groups = get_groups(y), residual = res, covariance = "shr", 
  keep = "gts", algorithms = "lu")
plot(y.f)
# }
# NOT RUN {
# }