Any incoming president inherits the economy of their predecessor for about a year thereafter. The 2000 dot-com bust was Clinton's (though the 2008 housing bust was wholly Bush). The one major exception I can think of was Obama in 2009, when it was largely his emergency policies that caused the DOW to bottom and rebound in April. Trump becoming president encouraged investors who saw him as basically being very laissez faire and committed to a major business tax cut, which investors saw (incorrectly) as Bullish.

I suspect that we'd be in a mild recession at this point even under Clinton - the market has been overvalued for a while, and a small contraction I think was baked into the cards. However, I think that Trump's effects are now factoring into the mix as well, and he's doing a very good job of turning a mild recession into a severe one.