How can I get the t-statistics for the results of an AR(1) model in R

Question

I have a Time-series data and I ran an AR(1) model using my data. What I want to do is do a test for significance of a policy intervention. So my ts data is estimated treatment effect over 10 years(1984 to 1994). My results from R looks like this:

>Call:
arima(x = data, order = c(1, 0, 0))

Coefficients:
        ar1  intercept
     0.7063    -0.7838
 s.e.  0.0732     1.5316

sigma^2 estimated as 18.97:  log likelihood = -257.6,  aic = 521.19

From the results I can get an equation and then find the implied long run effect which I found to be -2.67. My question is how can I get the t-statistics from the current information that I have? and how can I get it in R. Also, since I couldn't get the t-statistics, what I did was use the coeftest function in the lmtest package and found the z score:

> coeftest(ar)

z test of coefficients:

           Estimate Std. Error z value Pr(>|z|)    
ar1        0.706265   0.073248  9.6422   <2e-16 ***
intercept -0.783839   1.531599 -0.5118   0.6088    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Could I use the p-value as a substitute for t-statistics?

I've been told I could use the delta method but I am not sure how that can help me find the t-statistics. Furthermore, I had some difficulty using the function even after installing the package "car". Is there any other way I can get the t-stat without this delta method function?

Any kind of help you can provide would be very much appreciated.

Thank you

Answer 1

t-statistics are used when you have relatively small number of observations (typically fewer than 60) and need to account for the small numbers of observations that are in the "denominator" of var(x)/sqrt(n-1) which is the "standard error of the mean". The authors of the arima function are giving you the z-statistic and that is going to be reasonably close to a t-statistic.

I think using the z-score from coeftest is reasonable assuming you have done your exploratory work with ar and acf to see if the order parameters that you used is reasonable. If you haven't done that exploratory analysis, then you should probably do more reading on the topic. This is an area where you cannot really just throw a function at some data and assume correctness on the basis of no ERROR message. (It's also a bad idea to use ar as an object name, since that is one of the basic analysis function names as well.)