Methods for forecasting hierarchical or grouped time series.
# S3 method for gts
forecast(object, h = ifelse(frequency(object$bts) > 1L,
2L * frequency(object$bts), 10L),
method = c("comb", "bu", "mo","tdgsa", "tdgsf", "tdfp"),
weights = c("wls", "ols", "mint", "nseries"),
fmethod = c("ets", "arima", "rw"),
algorithms = c("lu", "cg", "chol", "recursive", "slm"),
covariance = c("shr", "sam"),
keep.fitted = FALSE, keep.resid = FALSE,
positive = FALSE, lambda = NULL, level,
parallel = FALSE, num.cores = 2, FUN = NULL,
xreg = NULL, newxreg = NULL, ...)Hierarchical or grouped time series object of class {gts}
Forecast horizon
Method for distributing forecasts within the hierarchy. See details
Weights used for "optimal combination" method:
weights="ols" uses an unweighted combination (as described in Hyndman et al 2011);
weights="wls" uses weights based on forecast variances (as described in Hyndman et al 2015);
weights="mint" uses a full covariance estimate to determine the weights (as described in Hyndman et al 2016);
weights="nseries" uses weights based on the number of series aggregated at each node.
Forecasting method to use for each series.
An algorithm to be used for computing the combination forecasts (when method=="comb"). The combination forecasts are based on an ill-conditioned regression model. "lu" indicates LU decomposition is used; "cg" indicates a conjugate gradient method; "chol" corresponds to a Cholesky decomposition; "recursive" indicates the recursive hierarchical algorithm of Hyndman et al (2015); "slm" uses sparse linear regression. Note that algorithms = "recursive" and algorithms = "slm" cannot be used if weights="mint".
Type of the covariance matrix to be used with weights="mint": either a shrinkage estimator ("shr") with shrinkage towards the diagonal; or a sample covariance matrix ("sam").
If TRUE, keep fitted values at the bottom level.
If TRUE, keep residuals at the bottom level.
If TRUE, forecasts are forced to be strictly positive (by setting lambda=0).
Box-Cox transformation parameter.
Level used for "middle-out" method (only used when method = "mo").
If TRUE, import parallel package to allow parallel processing.
If parallel = TRUE, specify how many cores are going to be used.
When fmethod = "arima", a vector or matrix of external regressors used for modelling, which must have the same number of rows as the original univariate time series
When fmethod = "arima", a vector or matrix of external regressors used for forecasting, which must have the same number of rows as the h forecast horizon
Other arguments passed to ets,
auto.arima or FUN.
A forecasted hierarchical/grouped time series of class gts.
Base methods implemented include ETS, ARIMA and the naive (random walk) models. Forecasts are distributed in the hierarchy using bottom-up, top-down, middle-out and optimal combination methods.
Three top-down methods are available: the two Gross-Sohl
methods and the forecast-proportion approach of Hyndman, Ahmed, and Athanasopoulos (2011).
The "middle-out" method "mo" uses bottom-up ("bu") for levels higher than
level and top-down forecast proportions ("tdfp") for levels lower than level.
For non-hierarchical grouped data, only bottom-up and combination methods are possible, as any method involving top-down disaggregation requires a hierarchical ordering of groups.
When xreg and newxreg are passed, the same covariates are applied to every series in the hierarchy.
G. Athanasopoulos, R. A. Ahmed and R. J. Hyndman (2009) Hierarchical forecasts for Australian domestic tourism, International Journal of Forecasting, 25, 146-166.
R. J. Hyndman, R. A. Ahmed, G. Athanasopoulos and H.L. Shang (2011) Optimal combination forecasts for hierarchical time series. Computational Statistics and Data Analysis, 55(9), 2579--2589. http://robjhyndman.com/papers/hierarchical/
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/
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/
Gross, C. and Sohl, J. (1990) Dissagregation methods to expedite product line forecasting, Journal of Forecasting, 9, 233-254.
forecast(htseg1, h = 10, method = "bu", fmethod = "arima")
forecast(htseg2, h = 10, method = "comb", algorithms = "lu",
FUN = function(x) tbats(x, use.parallel = FALSE))
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