htsDegenerateR (version 0.1.0)

MinT: Using the method of Wickramasuriya et al. (2019), this function (based on Hyndman et al.'s hts library) combines the forecasts at all levels of a hierarchical time series and works for degenerate hierarchies.

Description

Using the method of Wickramasuriya et al. (2019), this function (based on Hyndman et al.'s hts library) combines the forecasts at all levels of a hierarchical time series and works for degenerate hierarchies.

Usage

MinT(
  fcasts,
  Smat,
  residual,
  covariance = c("shr", "sam", "custom"),
  nonnegative = FALSE,
  cov.type = "complete.obs",
  cov.matrix = NULL
)

Value

reconciled forecasts

Arguments

fcasts

a vector or a matrix (rows = horizon, columns = ts columns) of forecasts

Smat

a structure matrix detailing the hierarchical structure of the hts. Make sure that the order of the rows align with the order of the forecasts.

residual

a matrix of in-sample residuals (columns = ts columns)

covariance

should a shrinkage estimator or the sample estimator be used? alternatively, a custom covariance matrix can be passed (additionally requires the cov.matrix argument)

nonnegative

not implemented yet.

cov.type

specify how the covariance matrix should be computed (default = complete observations). Note that pairwise.complete.obs may not yield a positive definite matrix!

cov.matrix

specify in case a custom covariance matrix should be used

References

[hts: Hierarchical and Grouped Time Series]<https://cran.r-project.org/package=hts> [Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization]<doi:10.1080/01621459.2018.1448825> [Degenerate Hierarchical Time Series Reconciliation With The Minimum Trace Algorithm in R]<doi:10.15488/17729>

Examples

# Set the seed for reproducibility
set.seed(123)

# Create a sequence of 120 numbers
x <- seq(1, 120)

# Generate the columns
AA <- sin(x*pi/6) + rnorm(120, 0, 1) # Sine component with random noise
AB <- 0.05*x + rnorm(120, 0, 0.5) # Linear component
B <- cos(x*pi/6)+ rnorm(120, 0, 1) # Cosine component

# Combine the columns into a matrix
matrix <- cbind(AA, AB, B)
hts = ts(matrix, frequency = 12)

# Define S matrix
S <- rbind(c(1,1,1), c(1,1,0), diag(1,3))
rownames(S) <-c("Total", "A", "AA", "AB", "B")
colnames(S) <- c("AA", "AB", "B")

# Aggregate hts on all levels
hts.complete <- ts(t(S %*% t(hts)), frequency = 12)

# Fit a model to the time series
hts.models = lapply(hts.complete, function(c.ts) forecast::ets(c.ts))

# Fit a model to the time series
hts.models = lapply(hts.complete, function(c.ts) forecast::ets(c.ts))
# Generate predictions based on this model
hts.forecasts = sapply(hts.models, function(mdl) forecast::forecast(mdl, h = 1)$mean)
# Extract residuals
hts.residuals = sapply(hts.models, function(mdl) mdl$residuals)

# Compute reconciled forecasts
MinT(fcasts = hts.forecasts, Smat = S, residual = hts.residuals)