Deborah, thank you for your thoughtful response... I especially see your point regarding the weather forecast, although Jesus even gives us an example of weather prediction in the word as being acceptable.   Because Jesus creates the weather, we can look to it as being faithful and true (notwithstanding mans attempts to control it).  But these bots are using mans words to tell the future.   
 
But I still have a SEVERE check in my spirit...  Satan is the father of lies and an imitator of light.   I believe that one of his main tactics is to spread half truths (garden of Eden, Jesus in the desert) and distract Christians from THE truth.  
 
When we are looking at these predictions and seeing if they come true or to gauge their nearness to scripture.... our focus is on them and not on the word.... When we are looking at them to ADD to the scriptures... i.e.  the scriptures say abc will happen and this web bot can tell me when or give me more information about it... IMHO that is very, very, very wrong.
 
To look at the headlines and say this IS happening and it fulfulls scripture is one thing, to look at these programs and say this is one more way to tell what is going to happen in the future is another.   To say they are secular programs is the best neutral thing one could say about them... Can you honestly say you know where the inspiration for this program came from??  They might very well be demonic.  The PURPOSE of them is to tell the future and they are not scriptural.  I do not believe they are just harmless words.  
 
All that being said.  You are my sister in Christ and obviously very close to the Lord.  If He is not telling you to stop, then you have the liberty to proceed.  I do not though.  I believe that regardless their origen the Lord can use them for His purposes, as he can all evil, but I also believe we have a responsibility to expose evil where we see it.  
 
Blessings and peace to you my sister,  Susanna