Nested_Stats_S0 {pretest}

Predictive Accuracy Testing for Nested Environment S^0

Description

It calculates the S^0 statistics for nested models with null hypothesis being the two models having equal predictive power following Pitarakis (2023). There are in total four versions of S^0, based on the assumptions of variance (homo or hete) and residuals (original or adjusted). All S^0 statistics will be standarised to a standard N(0,1) normal distribution, and corresponding P values would be provided.

Usage

Nested_Stats_S0(Ehat1, Ehat2, lam10, lam20)

Arguments

Ehat1

Residual series from Model 1 (the smaller model). One dimension and numeric.

Ehat2

Residual series from Model 2 (the larger/nested model). One dimension and numeric.

lam10

Fraction of the sample used for Model 1, which should be within 0 and 1.

lam20

Fraction of the sample used for Model 2, which should be within 0 and 1. Note that lam10 cannot equal to lam20 (c.f. Pitarakis, 2023).

Value

A list of S^0 statistics and corresponding P values will be produced. "adj" means a Clark and West's (2007) reformulation of sample MSE has been applied , and "NW" means robust Newey-West type estimator (c.f. Deng and Perron, 2008) for heteroskedastic errors has been used.

Author(s)

Rong Peng, [e-mail]

References

Pitarakis, J. Y. (2023). A novel approach to predictive accuracy testing in nested environments. Econometric Theory, 1-44.

Deng, A., & Perron, P. (2008). The limit distribution of the CUSUM of squares test under general mixing conditions. Econometric Theory, 24(3), 809-822.

Clark, T. E., & West, K. D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of econometrics, 138(1), 291-311.

See Also

Nested_Stats_Sbar

Examples

e1<- rnorm(15);
e2<- rnorm(15);
temp1 <- Nested_Stats_S0(e1,e2,lam10=0.5,lam20=0.8)
temp1$S_lam10_lam20_adj_NW     #S^0_T(lam10, lam^20) with CW adjustment and NW correction
temp1$pv_S_lam10_lam20_adj_NW  #P value of it