| Title: | A Novel Approach to Predictive Accuracy Testing in Nested Environments |
|---|---|
| Description: | This repository contains the codes for using the predictive accuracy comparison tests developed in Pitarakis, J. (2023) <doi:10.1017/S0266466623000154>. |
| Authors: | Rong Peng [aut, cre] |
| Maintainer: | Rong Peng <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2 |
| Built: | 2024-11-16 06:37:21 UTC |
| Source: | CRAN |
It calculates the original DM statistics and the CW adjusted version of DM statistics, including the versions based on a Newey-West type estimator of the long run variance.
dm_cw(Ehat1, Ehat2)dm_cw(Ehat1, Ehat2)
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. |
A list of statistics and corresponding P values will be produced.
Clark, T. E., & West, K. D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of econometrics, 138(1), 291-311.
Diebold, F. X., & Mariano, R. S. (1995). Com paring predictive accu racy. Journal of Business and Economic Statistics, 13(3), 253-263.
e1<- rnorm(15); e2<- rnorm(15); temp1 <- dm_cw(e1,e2)e1<- rnorm(15); e2<- rnorm(15); temp1 <- dm_cw(e1,e2)
Long-run covariance estimation using Newey-West (Bartlett) weights
lr_var(u, nlag = NULL, demean = TRUE)lr_var(u, nlag = NULL, demean = TRUE)
u |
P by K vector of residual series, for which we recommend to use the recursive residuals from larger model. |
nlag |
Non-negative integer containing the lag length to use. If empty or not included, nleg = min(floor(1.2*T^(1/3)),T) will be used. |
demean |
Logical true of false (0 or 1) indicating whether the mean should be subtracted when computing. |
Copyright: Kevin Sheppard Kevin.sheppard\@economics.ox.ac.uk Revision: 3 Date: 5/1/2007
K by K vector of Long run variance using Newey-West (Bartlett) weights.
x<- rnorm(15); #Newey-West covariance with automatic BW selection lrcov = lr_var(x) #Newey-West covariance with 10 lags lrcov = lr_var(x, 10) #Newey-West covariance with 10 lags and no demeaning lrcov = lr_var(x, 10, 0)x<- rnorm(15); #Newey-West covariance with automatic BW selection lrcov = lr_var(x) #Newey-West covariance with 10 lags lrcov = lr_var(x, 10) #Newey-West covariance with 10 lags and no demeaning lrcov = lr_var(x, 10, 0)
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.
Nested_Stats_S0(Ehat1, Ehat2, lam10, lam20)Nested_Stats_S0(Ehat1, Ehat2, lam10, lam20)
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). |
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.
Rong Peng, [email protected]
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.
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 ite1<- 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
It calculates the SBar 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 SBar, based on the assumptions of variance (homo or hete) and residuals (original or adjusted). All SBar statistics will be standarised to a standard N(0,1) normal distribution, and corresponding P values would be provided.
Nested_Stats_Sbar(Ehat1, Ehat2, lam20, tau0)Nested_Stats_Sbar(Ehat1, Ehat2, lam20, tau0)
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. |
lam20 |
Fraction of the sample used for Model 2, which should be within 0 and 1. |
tau0 |
Fraction to determine the user-chosen range of lam10 over which the average is taken. |
A list of SBar 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.
Rong Peng, [email protected]
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.
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 ite1<- 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
Consider the following LS-fitted Model with intercept: y_(t+h) = beta_0 + x_t * beta + u_(t+h) which is used to generate out-of-sample forecasts of y, h-steps ahead (h=1,2,3,. . . ). It calculates the recursive residuals starting from the first (n * pi0) data points, where n is the total number of data points.
recursive_hstep_fast(y, x, pi0, h)recursive_hstep_fast(y, x, pi0, h)
y |
n x 1 Outcome series, which should be numeric and one dimensional. |
x |
n x p Predictor matrix (intercept would be added automatically). |
pi0 |
Fraction of the sample, which should be within 0 and 1. |
h |
Number of steps ahead to predict, which should be a positive integer. |
recursive_hstep_fast is the fast version that avoids the recursive calculation of inverse of the matrix using Sherman-Morrison formula. recursive_hstep_slow is the slow version that calculates the standard OLS recursively.
Series of residuals estimated
Rong Peng, [email protected]
x<- rnorm(15); y<- x+rnorm(15); temp1 <- recursive_hstep_fast(y,x,pi0=0.5,h=1);x<- rnorm(15); y<- x+rnorm(15); temp1 <- recursive_hstep_fast(y,x,pi0=0.5,h=1);
Consider the following LS-fitted Model with intercept: y_(t+h) = beta_0 + x_t * beta + u_(t+h) which is used to generate out-of-sample forecasts of y, h-steps ahead (h=1,2,3,. . . ). It calculates the recursive residuals starting from the first (n * pi0) data points, where n is the total number of data points.
recursive_hstep_slow(y, x, pi0, h)recursive_hstep_slow(y, x, pi0, h)
y |
n x 1 Outcome series, which should be numeric and one dimensional. |
x |
n x p Predictor matrix (intercept would be added automatically). |
pi0 |
Fraction of the sample, which should be within 0 and 1. |
h |
Number of steps ahead to predict, which should be a positive integer. |
recursive_hstep_fast is the fast version that avoids the recursive calculation of inverse of the matrix using Sherman-Morrison formula. recursive_hstep_slow is the slow version that calculates the standard OLS recursively.
Series of residuals estimated
Rong Peng, [email protected]
x<- rnorm(15); y<- x+rnorm(15); temp2 <- recursive_hstep_slow(y,x,pi0=0.5,h=1);x<- rnorm(15); y<- x+rnorm(15); temp2 <- recursive_hstep_slow(y,x,pi0=0.5,h=1);