Difference between lm function and arma function

Question

I have these two model in r. can i get an explanation for why i have different results when i use lm function and arma function on my time series data

fit1=arma(z,order=c(1,0))  
summary(fit1)

#Coefficient(s):  
#             Estimate    Std. Error    t value     Pr(>|t|)      
#  ar1        1.0001557      0.0001761   5678.00     <2e-16 ***  
#  intercept  1.8491535      0.1469061   12.59       <2e-16 ***  


fit2=lm(z~lag(z,1))  
summary(fit2)  

#Call:      
#lm(formula = z ~ lag(z, 1))       
#Coefficients:   
#            Estimate Std. Error   t value Pr(>|t|)          
#(Intercept) 8.699e-14  6.772e-15 1.285e+01   <2e-16 ***   
#lag(z, 1)   1.000e+00  8.109e-18 1.233e+17   <2e-16 ***

Answer 1

lag does not do what you think it does. It converts the object to ts and changes the index, not the actual vector values. The sign of the value for k is also opposite of what you'd expect.

set.seed(21)
z <- rnorm(6)
as.ts(z)
# Time Series:
# Start = 1 
# End = 8 
# Frequency = 1 
# [1]  0.7930132  0.5222513  1.7462222 -1.2713361  2.1973895  0.4331308
lag(as.ts(z),1)
# Time Series:
# Start = 0 
# End = 7 
# Frequency = 1 
# [1]  0.7930132  0.5222513  1.7462222 -1.2713361  2.1973895  0.4331308

xts::lag.xts provides the behavior you expect:

library(xts)
x <- .xts(z, 1:6)
xData <- merge(x=x, x1=lag(x,1))
fit3 <- lm(x ~ x1, data=xData)
summary(fit3)