How to calculate p-value for AR model? How to determine significance?

Hello everyone!!

I am using the arima model command to create an AR(2) model. When running the program matlab tells the me value of the t-Statistic for each of the two AR parameters.

How can I tell from the output whether the parameter is significant? Is there a way to calculate the p-value for each of my two AR parameters?

Thanks alot!!

Answer 1

[Roger Wohlwend]

You don't need the p-values. If the absolute value of the t-statistics is 2 or greater, the coefficient is significant.

[MC3105]

how do I know it has to be 2 or greater?

[Roger Wohlwend]

If the degrees of freedom is high enough the t distribution approaches the standard normal distribution. In such a distribution the values between -2 and 2 (twice the standard deviation from the mean) occur approximately in 95 % of the cases. That is why a t-statistics of 2 or greater corresponds to a confidence level of 5 %.

The exact value is not 2 but 1.96. You can calculate it with the following formula:

 tstat =  norminv(1-confidenceLevel/2,0,1)

The exact formula is

tstat = -tinv(confidenceLevel/2,DegreesOfFreedom)

So if you want a different confidence level than 5 % use the formula above to see what the t-statistics must be.

If you want to calculate the p-value from the t-statistics, use the following formula:

pVal = 2*(tcdf(-abs(tValue), dof));

where tValue is the coefficient divided by its standard deviation and dof is the degrees of freedom.