Dear

The code I copied from http://faculty.chicagobooth.edu/ ... oTS/ch3Rscripts.txt  and output are as follows

Coulld you please help fix the issue such as[Error: could not find function 'backtest']. Thanks
================================================================================
### Chapter 3 ####
### Petro Price
da=read.table("C:/Downloads/ch3data/w-petroprice.txt",header=T)
da1=read.table("C:/Downloads/ch3data/w-gasoline.txt")
pgs=log(da1[,1])
pus=log(da$US)
tdx=c(1:717)/52+1997  # calendar time
par(mfcol=c(2,1))
plot(tdx,pgs,xlab='year',ylab='ln(price)',type='l')
title(main='(a) Gasoline')
plot(tdx,pus,xlab='year',ylab='ln(price)',type='l')
title(main='(b) Crude oil')
dpgs=diff(pgs)
acf(dpgs,lag=20)
pacf(dpgs,lag=20)
m1=ar(diff(pgs),method='mle')
m1$order
t.test(dpgs)
m1=arima(dpgs,order=c(5,0,0),include.mean=F)
m1
m1=arima(dpgs,order=c(5,0,0),include.mean=F,fixed=c(NA,NA,NA,0,NA))
m1
tsdiag(m1,gof=20)
dpus=diff(pus)
m3=lm(dpgs~-1+dpus)
summary(m3)
acf(m3$residuals,lag=20)
pacf(m3$residuals,lag=20)
m4=ar(m3$residuals,method='mle')
m4$order
m4=arima(dpgs,order=c(6,0,0),include.mean=F,xreg=dpus)
m4
m4=arima(dpgs,order=c(5,0,0),include.mean=F,xreg=dpus)
m4
m4=arima(dpgs,order=c(5,0,0),include.mean=F,xreg=dpus,fixed=c(NA,NA,NA,0,NA,NA))
m4
tsdiag(m4,gof=20)
c1=c(NA,NA,NA,0,NA)
pm1=backtest(m1,dpgs,316,1,fixed=c1,inc.mean=F)
c4=c(NA,NA,NA,0,NA,NA)
pm4=backtest(m4,dpgs,316,1,xre=dpus,inc.mean=F,fixed=c4)
tdx=tdx[2:717]
pm4fit=dpgs[317:716]-pm4$error
pm1fit=dpgs[317:716]-pm1$error
plot(tdx[317:716],dpgs[317:716],xlab='year',ylab='growth',type='l')
points(tdx[317:716],pm1fit,pch='*')
plot(tdx[317:716],dpgs[317:716],xlab='year',ylab='growth',type='l')
points(tdx[317:716],pm4fit,pch='*')
m6=lm(dpgs[2:716]~-1+dpus[1:715])
summary(m6)
acf(m6$residuals,lag=20)
pacf(m6$residuals,lag=20)
m7=ar(m6$residuals,method='mle')
m7$order
m7=arima(dpgs[2:716],order=c(9,0,0),include.mean=F,xreg=dpus[1:715])
m7
m7=arima(dpgs[2:716],order=c(9,0,0),include.mean=F,xreg=dpus[1:715],fixed=c(NA,NA,NA,0,NA,0,0,0,NA,NA))
m7
tsdiag(m7,gof=20)
c7=c(NA,NA,NA,0,NA,0,0,0,NA,NA)
pm7=backtest(m7,dpgs[2:716],315,1,xre=dpus[1:715],inc.mean=F,fixed=c7)

======================================================

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> ### Chapter 3 ####
> ### Petro Price
> da=read.table("C:/Downloads/ch3data/w-petroprice.txt",header=T)
> da1=read.table("C:/Downloads/ch3data/w-gasoline.txt")
> pgs=log(da1[,1])
> pus=log(da$US)
> tdx=c(1:717)/52+1997  # calendar time
> par(mfcol=c(2,1))
> plot(tdx,pgs,xlab='year',ylab='ln(price)',type='l')
> title(main='(a) Gasoline')
> plot(tdx,pus,xlab='year',ylab='ln(price)',type='l')
> title(main='(b) Crude oil')
> dpgs=diff(pgs)
> acf(dpgs,lag=20)
> pacf(dpgs,lag=20)
> m1=ar(diff(pgs),method='mle')
> m1$order
[1] 5
> t.test(dpgs)

        One Sample t-test

data:  dpgs
t = 1.3062, df = 715, p-value = 0.1919
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
-0.0005536374  0.0027549956
sample estimates:
  mean of x
0.001100679

> m1=arima(dpgs,order=c(5,0,0),include.mean=F)
> m1

Call:
arima(x = dpgs, order = c(5, 0, 0), include.mean = F)

Coefficients:
         ar1     ar2     ar3      ar4      ar5
      0.5073  0.0788  0.1355  -0.0360  -0.0862
s.e.  0.0372  0.0417  0.0415   0.0417   0.0372

sigma^2 estimated as 0.0003262:  log likelihood = 1857.85,  aic = -3703.71
> m1=arima(dpgs,order=c(5,0,0),include.mean=F,fixed=c(NA,NA,NA,0,NA))
Warning message:
In arima(dpgs, order = c(5, 0, 0), include.mean = F, fixed = c(NA,  :
  some AR parameters were fixed: setting transform.pars = FALSE
> m1

Call:
arima(x = dpgs, order = c(5, 0, 0), include.mean = F, fixed = c(NA, NA, NA,
    0, NA))

Coefficients:
         ar1     ar2     ar3  ar4      ar5
      0.5036  0.0789  0.1220    0  -0.1009
s.e.  0.0370  0.0418  0.0385    0   0.0330

sigma^2 estimated as 0.0003265:  log likelihood = 1857.48,  aic = -3704.96
> tsdiag(m1,gof=20)
> dpus=diff(pus)
> m3=lm(dpgs~-1+dpus)
> summary(m3)

Call:
lm(formula = dpgs ~ -1 + dpus)

Residuals:
      Min        1Q    Median        3Q       Max
-0.076149 -0.008834  0.000365  0.009441  0.151350

Coefficients:
     Estimate Std. Error t value Pr(>|t|)   
dpus  0.28703    0.01507   19.05   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.01839 on 715 degrees of freedom
Multiple R-squared:  0.3366,    Adjusted R-squared:  0.3357
F-statistic: 362.8 on 1 and 715 DF,  p-value: < 2.2e-16

> acf(m3$residuals,lag=20)
> pacf(m3$residuals,lag=20)
> m4=ar(m3$residuals,method='mle')
> m4$order
[1] 6
> m4=arima(dpgs,order=c(6,0,0),include.mean=F,xreg=dpus)
> m4

Call:
arima(x = dpgs, order = c(6, 0, 0), xreg = dpus, include.mean = F)

Coefficients:
         ar1     ar2     ar3     ar4      ar5      ar6    dpus
      0.3953  0.1634  0.0946  0.0297  -0.0873  -0.0525  0.1927
s.e.  0.0389  0.0400  0.0404  0.0405   0.0400   0.0373  0.0136

sigma^2 estimated as 0.0002524:  log likelihood = 1949.61,  aic = -3883.21
> m4=arima(dpgs,order=c(5,0,0),include.mean=F,xreg=dpus)
> m4

Call:
arima(x = dpgs, order = c(5, 0, 0), xreg = dpus, include.mean = F)

Coefficients:
         ar1     ar2     ar3     ar4      ar5    dpus
      0.4022  0.1621  0.0899  0.0209  -0.1086  0.1914
s.e.  0.0387  0.0401  0.0403  0.0400   0.0371  0.0136

sigma^2 estimated as 0.0002531:  log likelihood = 1948.62,  aic = -3883.23
> m4=arima(dpgs,order=c(5,0,0),include.mean=F,xreg=dpus,fixed=c(NA,NA,NA,0,NA,NA))
Warning message:
In arima(dpgs, order = c(5, 0, 0), include.mean = F, xreg = dpus,  :
  some AR parameters were fixed: setting transform.pars = FALSE
> m4

Call:
arima(x = dpgs, order = c(5, 0, 0), xreg = dpus, include.mean = F, fixed = c(NA,
    NA, NA, 0, NA, NA))

Coefficients:
         ar1     ar2     ar3  ar4      ar5    dpus
      0.4037  0.1642  0.0961    0  -0.1014  0.1911
s.e.  0.0386  0.0399  0.0386    0   0.0345  0.0136

sigma^2 estimated as 0.0002532:  log likelihood = 1948.48,  aic = -3884.95
> tsdiag(m4,gof=20)
> c1=c(NA,NA,NA,0,NA)
> pm1=backtest(m1,dpgs,316,1,fixed=c1,inc.mean=F)
Error: could not find function "backtest"
> c4=c(NA,NA,NA,0,NA,NA)
> pm4=backtest(m4,dpgs,316,1,xre=dpus,inc.mean=F,fixed=c4)
Error: could not find function "backtest"
> tdx=tdx[2:717]
> pm4fit=dpgs[317:716]-pm4$error
Error: object 'pm4' not found
> pm1fit=dpgs[317:716]-pm1$error
Error: object 'pm1' not found
> plot(tdx[317:716],dpgs[317:716],xlab='year',ylab='growth',type='l')
> points(tdx[317:716],pm1fit,pch='*')
Error in xy.coords(x, y) : object 'pm1fit' not found
> plot(tdx[317:716],dpgs[317:716],xlab='year',ylab='growth',type='l')
> points(tdx[317:716],pm4fit,pch='*')
Error in xy.coords(x, y) : object 'pm4fit' not found
> m6=lm(dpgs[2:716]~-1+dpus[1:715])
> summary(m6)

Call:
lm(formula = dpgs[2:716] ~ -1 + dpus[1:715])

Residuals:
      Min        1Q    Median        3Q       Max
-0.088318 -0.011145 -0.000011  0.011391  0.161679

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
dpus[1:715]  0.18560    0.01716   10.81   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.02093 on 714 degrees of freedom
Multiple R-squared:  0.1408,    Adjusted R-squared:  0.1395
F-statistic:   117 on 1 and 714 DF,  p-value: < 2.2e-16

> acf(m6$residuals,lag=20)
> pacf(m6$residuals,lag=20)
> m7=ar(m6$residuals,method='mle')
> m7$order
[1] 9
> m7=arima(dpgs[2:716],order=c(9,0,0),include.mean=F,xreg=dpus[1:715])
> m7

Call:
arima(x = dpgs[2:716], order = c(9, 0, 0), xreg = dpus[1:715], include.mean = F)

Coefficients:
         ar1     ar2     ar3      ar4      ar5      ar6      ar7     ar8
      0.4559  0.0888  0.1679  -0.0468  -0.0653  -0.0195  -0.0362  0.0797
s.e.  0.0425  0.0410  0.0423   0.0415   0.0416   0.0414   0.0410  0.0408
          ar9  dpus[1:715]
      -0.0882       0.0454
s.e.   0.0373       0.0174

sigma^2 estimated as 0.0003204:  log likelihood = 1861.55,  aic = -3701.1
> m7=arima(dpgs[2:716],order=c(9,0,0),include.mean=F,xreg=dpus[1:715],fixed=c(NA,NA,NA,0,NA,0,0,0,NA,NA))
Warning message:
In arima(dpgs[2:716], order = c(9, 0, 0), include.mean = F, xreg = dpus[1:715],  :
  some AR parameters were fixed: setting transform.pars = FALSE
> m7

Call:
arima(x = dpgs[2:716], order = c(9, 0, 0), xreg = dpus[1:715], include.mean = F,
    fixed = c(NA, NA, NA, 0, NA, 0, 0, 0, NA, NA))

Coefficients:
         ar1     ar2     ar3  ar4      ar5  ar6  ar7  ar8      ar9  dpus[1:715]
      0.4544  0.0877  0.1415    0  -0.0830    0    0    0  -0.0640       0.0406
s.e.  0.0427  0.0413  0.0393    0   0.0345    0    0    0   0.0318       0.0176

sigma^2 estimated as 0.000323:  log likelihood = 1858.7,  aic = -3703.4
> tsdiag(m7,gof=20)
> c7=c(NA,NA,NA,0,NA,0,0,0,NA,NA)
> pm7=backtest(m7,dpgs[2:716],315,1,xre=dpus[1:715],inc.mean=F,fixed=c7)
Error: could not find function "backtest"
>