# 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. ```r MinT( fcasts, Smat, residual, covariance = c("shr", "sam", "custom"), nonnegative = FALSE, cov.type = "complete.obs", cov.matrix = NULL ) ``` ## 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 ## Returns reconciled forecasts ## Examples ```r # 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) ``` ## References [hts: Hierarchical and Grouped Time Series] [Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization] [Degenerate Hierarchical Time Series Reconciliation With The Minimum Trace Algorithm in R]

MinT function