Shell : copying from one file to another file

Shell Programming and Scripting
1 
vat.log
--------
null
null statistics
null
 

null
null
Storage Response Time
disk space1
disk space2

I have a log as mentioned above in which I need to copy only the below content to another file using shell scripting. In between null statistics and final null it also includes blank line as well..

null statistics
null
 

null
null

Could anyone please help me in this regard?

Thanks in advance...

2 
$ awk 'p&&$1&&$1!="null"{p=0}; /null statistics/ {p=1}p' file
null statistics
null
 

null
null