# Module Reference¶

## Test of Superior Predictive Ability (SPA), Reality Check¶

The test of Superior Predictive Ability (Hansen 2005), or SPA, is an improved version of the Reality Check (White 2000). It tests whether the best forecasting performance from a set of models is better than that of the forecasts from a benchmark model. A model is "better" if its losses are smaller than those from the benchmark. Formally, it tests the null

$H_0: \max_i E[L_i] \geq E[L_{bm}]$

where $$L_i$$ is the loss from model i and $$L_{bm}$$ is the loss from the benchmark model. The alternative is

$H_1: \min_i E[L_i] < E[L_{bm}]$

This procedure accounts for dependence between the losses and the fact that there are potentially alternative models being considered.

Note: Also callable using RealityCheck

 SPA(benchmark, models[, block_size, reps, ...]) Test of Superior Predictive Ability (SPA) of White and Hansen.

## Stepwise Multiple Testing (StepM)¶

The Stepwise Multiple Testing procedure (Romano & Wolf (2005)) is closely related to the SPA, except that it returns a set of models that are superior to the benchmark model, rather than the p-value from the null. They are so closely related that StepM is essentially a wrapper around SPA with some small modifications to allow multiple calls.

 StepM(benchmark, models[, size, block_size, ...]) StepM multiple comparison procedure of Romano and Wolf.

## Model Confidence Set (MCS)¶

The Model Confidence Set (Hansen, Lunde & Nason (2011)) differs from other multiple comparison procedures in that there is no benchmark. The MCS attempts to identify the set of models which produce the same expected loss, while controlling the probability that a model that is worse than the best model is in the model confidence set. Like the other MCPs, it controls the Familywise Error Rate rather than the usual test size.

 MCS(losses, size[, reps, block_size, ...]) Model Confidence Set (MCS) of Hansen, Lunde and Nason.