regres_36_anual <- lm(backtest_36_anual  ~ IBRX_Rf)

bptest(regres_36_anual)

## 
##  studentized Breusch-Pagan test
## 
## data:  regres_36_anual
## BP = 4.0176, df = 1, p-value = 0.04503

bgtest(regres_36_anual)

## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  regres_36_anual
## LM test = 10.284, df = 1, p-value = 0.001342

regres_12_anual <- lm(backtest_12_anual  ~ IBRX_Rf)

bptest(regres_12_anual)

## 
##  studentized Breusch-Pagan test
## 
## data:  regres_12_anual
## BP = 3.4086, df = 1, p-value = 0.06486

bgtest(regres_12_anual)

## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  regres_12_anual
## LM test = 9.6707, df = 1, p-value = 0.001872

regres_36_tri <- lm(backtest_36_tri  ~ IBRX_Rf)

bptest(regres_36_tri)

## 
##  studentized Breusch-Pagan test
## 
## data:  regres_36_tri
## BP = 1.6156, df = 1, p-value = 0.2037

bgtest(regres_36_tri)

## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  regres_36_tri
## LM test = 13.093, df = 1, p-value = 0.0002963

regres_12_tri <- lm(backtest_12_tri  ~ IBRX_Rf)

bptest(regres_12_tri)

## 
##  studentized Breusch-Pagan test
## 
## data:  regres_12_tri
## BP = 13.306, df = 1, p-value = 0.0002645

bgtest(regres_12_tri)

## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  regres_12_tri
## LM test = 23.473, df = 1, p-value = 1.267e-06

coeftest(regres_36_anual, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value  Pr(>|t|)    
## (Intercept)  0.00040998  0.00018256  2.2457   0.02481 *  
## IBRX_Rf     -0.13346059  0.01938991 -6.8830 7.403e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_12_anual, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value  Pr(>|t|)    
## (Intercept)  0.00026413  0.00018230  1.4489    0.1475    
## IBRX_Rf     -0.10417139  0.02406612 -4.3285 1.561e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_36_tri, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value  Pr(>|t|)    
## (Intercept)  0.00067127  0.00019846  3.3824 0.0007298 ***
## IBRX_Rf     -0.14020544  0.02204435 -6.3602 2.393e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_12_tri, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##                Estimate  Std. Error t value  Pr(>|t|)    
## (Intercept)  0.00061113  0.00019604  3.1174  0.001845 ** 
## IBRX_Rf     -0.14181798  0.02960408 -4.7905 1.762e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Signif. codes: *** < 0.001; ** < 0.01; * < 0.05; . < 0.1; "" < 1

Signif. codes: *** < 0.001; ** < 0.01; * < 0.05; . < 0.1; "" < 1

coeftest(regres_36_anual, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.00026513 0.00012797  2.0719  0.03838 *  
## IBRX_Rf     0.87460173 0.02137962 40.9082  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_12_anual, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 0.00012787 0.00012193  1.0487   0.2944    
## IBRX_Rf     0.89480235 0.02809849 31.8452   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_36_tri, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##               Estimate Std. Error t value  Pr(>|t|)    
## (Intercept) 0.00038765 0.00013075  2.9649  0.003057 ** 
## IBRX_Rf     0.88241764 0.01892254 46.6331 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

coeftest(regres_12_tri, vcov = vcovHAC)

## 
## t test of coefficients:
## 
##               Estimate Std. Error t value  Pr(>|t|)    
## (Intercept) 0.00036558 0.00011907  3.0704  0.002161 ** 
## IBRX_Rf     0.87890713 0.03118834 28.1806 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Signif. codes: *** < 0.001; ** < 0.01; * < 0.05; . < 0.1; "" < 1

Signif. codes: *** < 0.001; ** < 0.01; * < 0.05; . < 0.1; "" < 1