Package {MCS}

Type:	Package
Title:	Model Confidence Set Procedure
Version:	0.2.1
Date:	2026-10-19
Maintainer:	Leopoldo Catania <leopoldo.catania@econ.au.dk>
Depends:	R (≥ 3.0.1)
Description:	Implements the Model Confidence Set procedure of Hansen, Lunde and Nason (2011) <doi:10.3982/ECTA5771> using bootstrap tests of equal predictive ability. Includes loss functions for level, volatility and quantile forecasts.
License:	GPL-2
Encoding:	UTF-8
Imports:	methods, stats
NeedsCompilation:	no
Packaged:	2026-10-19 08:12:52 UTC; au588008
Author:	Leopoldo Catania [aut, cre]
Config/roxygen2/version:	8.0.0
Repository:	CRAN
Date/Publication:	2026-10-19 12:30:02 UTC

Loss Function for Level Forecasts

Description

Calculate squared or absolute forecast errors for one or more models.

Usage

LossLevel(realized, evaluated, which = "SE")

Arguments

Details

Matrix columns are evaluated against the same realized series. Empty or non-finite inputs and non-finite calculated losses raise errors.

Value

A numeric matrix with the dimensions and dimnames of evaluated.

Author(s)

Leopoldo Catania

Loss Function for VaR Forecasts

Description

Calculate quantile losses for one or more forecast series.

Usage

LossVaR(realized, evaluated, which = "asymmetricLoss",
        type = "normal", delta = 25, tau)

Arguments

Details

With u=realized-evaluated, the normal loss is (tau-1{u<0})*u. The differentiable version replaces the indicator with plogis(-delta*u); it is an approximation for finite delta. Inputs must be finite and nonempty. Non-finite calculated losses raise an error rather than being passed silently to MCSprocedure.

Value

A numeric matrix with the dimensions and dimnames of evaluated.

Author(s)

Leopoldo Catania

References

Koenker R, Bassett G (1978). Regression quantiles. Econometrica, 46(1), 33-50.

Gonzalez-Rivera G, Lee TH, Mishra S (2004). Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood. International Journal of Forecasting, 20(4), 629-645. doi:10.1016/j.ijforecast.2003.10.003.

Loss Function for Volatility Forecasts

Description

Calculate forecast losses for standard deviations, not variances.

Usage

LossVol(realized, evaluated, which = "SE1")

Arguments

Details

For realized standard deviation s and forecast standard deviation f, the losses are (s-f)^2 (SE1), (s^2-f^2)^2 (SE2), log(f^2)+s^2/f^2 (QLIKE), [log(s^2/f^2)]^2 (R2LOG), abs(s-f) (AE1), and abs(s^2-f^2) (AE2). Zero realized volatility is allowed for QLIKE; R2LOG is undefined there and raises an error. Non-finite losses from arithmetic overflow raise an error. Matrix forecast columns are evaluated against the same realized series.

Value

A numeric matrix with the dimensions and dimnames of evaluated.

Author(s)

Leopoldo Catania

References

Hansen PR, Lunde A (2005). A forecast comparison of volatility models: does anything beat a GARCH(1,1)? Journal of Applied Econometrics, 20(7), 873-889. doi:10.1002/jae.800.

Bernardi M, Catania L (2018). The Model Confidence Set package for R. International Journal of Computational Economics and Econometrics, 8(2), 144-158. doi:10.1504/IJCEE.2018.091037.

Model Confidence Set Procedure

Description

Construct a model confidence set from competing loss series.

Usage

MCSprocedure(Loss, alpha = 0.15, B = 1000, statistic = "Tmax",
             k = NULL, min.k = 3, verbose = TRUE, seed = NULL)

Arguments

Details

The complete elimination path is computed. MCS p-values are running maxima of sequential p-values; models with MCS p-value >= alpha are included. Equality is retained, consistent with rejection when p < alpha. Bootstrap p-values use mean(T_boot >= T_observed), including ties.

Zero loss contrasts contribute zero statistics. Numerically constant nonzero contrasts contribute signed infinite observed statistics and zero centered bootstrap statistics. All-identical loss matrices return p-values of 1; constant strictly worse losses can be eliminated. Constancy is checked to a relative tolerance of 64*.Machine$double.eps when bootstrap errors are tiny. Zero bootstrap variance for a varying contrast raises an error. These are explicit degeneracy conventions, not additional asymptotic coverage claims. Inference for nondegenerate losses requires the stationarity, dependence and moment conditions of Hansen, Lunde and Nason (2011).

Bootstrap model means are computed once and reused. No B-by-m-by-m arrays are allocated. A single-model input returns that model with p-values 1; automatic block selection and resampling are skipped, and automatic k is reported as 0 in that case.

Value

An S4 object of class SSM. Slot show contains average losses, sequential test p-values and cumulative MCS p-values. Slot Info contains included/excluded model names, settings, elimination.order and timing.

Author(s)

Leopoldo Catania

References

Hansen PR, Lunde A, Nason JM (2011). The model confidence set. Econometrica, 79(2), 453-497. doi:10.3982/ECTA5771.

Bernardi M, Catania L (2018). The Model Confidence Set package for R. International Journal of Computational Economics and Econometrics, 8(2), 144-158. doi:10.1504/IJCEE.2018.091037.

Examples

set.seed(123)
y <- rnorm(500)
forecasts <- matrix(rep(seq(-0.5, 0.5, length.out=11), 500),
nrow=500, byrow=TRUE)
Loss <- LossLevel(y, forecasts, which="SE")
MCSprocedure(Loss, seed=123, verbose=FALSE)

Model Confidence Set Result

Description

An S4 container returned by MCSprocedure.

Slots

Info

A list containing model.names, included, excluded, n_elim, statistic, alpha, B, k, seed, elimination.order and elapsed.time.

show

A matrix containing average losses, sequential test p-values and cumulative MCS p-values. Membership is based on MCS p-value >= alpha.

Display a Model Confidence Set

Description

Display the result table and settings used for inference.

Usage

## S4 method for signature 'SSM'
show(object)

Arguments