Wharton professor Jeremy Siegel expects the stock market to continue its trend higher into the end of the year, according to a Friday interview with CNBC.

He said the S&P 500 could ultimately surge 25% this year, which translates to an additional 9% upside from current levels, if two things happen.

First, Federal Reserve Chairman Jerome Powell needs to fully acknowledge that inflation is indeed falling, in part thanks to a significant rise in productivity growth.

"What's happened in the market is that yields have risen, real yields have risen, real growth has risen, and the reason that real growth has risen is because productivity has been so strong. He [Powell] didn't address any of that [at Jackson Hole]," Siegel said.

He added that Powell is "stuck" in the idea that because real growth is higher, that's going to put pressure on wages, adding to inflation and ultimately forcing the Fed to continue hiking interest rates.

"That's not the story!" Siegel said. "The story is we're getting real growth higher because we're getting productivity higher. In fact, the labor market is slowing down."

Estimates for the upcoming the August payroll report are for about 160,000 new jobs being added, which would be about half of the job gains seen last August.

"I don't think he [Powell] really addressed what the market has been seeing over the last few weeks," Siegel said.

Second, the Fed needs to hold off on any further interest rate hikes for Siegel's bullish stock market projection to materialize. While futures markets are currently not pricing in another increase this year, Powell's Jackson Hole speech increased the odds of at least one more 25-basis-point hike by year's end.

But even if the Fed delivers on those two criteria set by Siegel, the stock market could still see some choppiness over the next couple of months before ultimately turning higher.

"September for decades had been the worst month of the year... August became a tough month, especially second half of August... The higher real interest rates are certainly challenging the stocks at the same time. But I don't see any major crack," he said.

"After that we have September, October, choppy months, [with] November [and] December usually being much better year ending on an upturn. So I think for the rest of the year, we're stable to upward... and if [Powell] doesn't raise [interest rates] anymore and says inflation [is] falling, it could be 20% to 25% for the full year."