estMCS: Estimation of a model confidence set (MCS) using an...

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

The function allows to estimate a model confidence set as described in Hansen, Lunde and Nason (2011), i.e. a set of models that contains the best models with a given probability. It is analogous to confidence intervals for parameters. A matrix is returned that contains the MCS p-values of all models.

Usage

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estMCS(loss, test = "t.range", B = 1000, l = 2)

Arguments

loss

A matrix of size (n x m). The columns contain the estimated losses for each of the m models.

test

A character string. It specifies the test statistic to be used. Available tests are "t.max", "t.range", and "t.min".

B

A scalar, the number of bootstrap samples.

l

A scalar, the block length used in the moving-block bootstrap.

Details

Any user defined loss criterion can be used to compute the matrix of losses. For forecasting exercises this would typically be squared or absolute forecast errors. The computation has to be done in advance and fed to the function via the loss argument. The models with the lowest expected loss are defined as the best models. To remove inferior models from the starting set, the null hypothesis that 'no inferior model is present' is tested in a sequential manner. If the null hypothesis is rejected, a model is removed and the null tested again. The decision which model to remove is based on elimination rules that are implied by the test statistic and cannot be changed by the user. When a test fails to reject the null at a pre-defined significance level, the procedure would in principle stop and deliver the remaining models as the estimated MCS. Here, however, all models will be returned with their associated MCS p-values. It is up to the user to decide on a significance level and then apply this to the outcome of this function (see the example section).

Note that the t.min test statistic is only included for legacy reasons and should not be used for empirical analysis as it violates a coherency condition in Hansen, Lunde and Nason (2011). It could therefore be heavily undersized in finite samples. See the corrigendum to Hansen, Lunde and Nason (2011) for details.

Value

A matrix of size (m x 3). The first column enumerates the models in the same order as they occurred in loss. The second column contains the p-value associated with the test that removed that particular model from the set. The third column contains the MCS p-values. These are useful for reading off which models would be included in the estimated MCS for any particular significance level. The matrix will have row names equal to the column names of loss.

Author(s)

Niels Aka

References

Hansen, P. R., Lunde, A., Nason, J. M. 2011. "The Model Confidence Set", Econometrica, 79(2), 453 - 497

See Also

See estMCS.reg for the MCS methodology applied to linear regression models and estMCS.quick for an implementation of this function which only returns the MCS (instead of all models). See np::b.star for choosing the block length l.

Examples

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### Reproducing the results in Hansen, Lunde and Nason (2011),
### p. 485, column 1.

data(SW_infl4cast)
data <- as.matrix(SW_infl4cast)
loss <- (data[, -1] - data[, 1])^2 # compute squared errors

# Estimate MCS same way that Hansen, Lunde, Nason (2011) did.
# Note: "t.min" should not be used in practice.

(my.MCS <- estMCS(loss, test = "t.min", B = 25000, l = 12))
my.MCS[my.MCS[, "MCS p-val"] > 0.1, ] # actual, estimated MCS at alpha = 0.1

nielsaka/modelconf documentation built on May 9, 2019, 7:35 p.m.