• Airlines are raising their unit revenue forecasts for the third quarter.
• Flights are getting more expensive again, according to the latest inflation report.
• Carriers have been moderating capacity growth after a glut of flights pushed down fares.

Airlines are reporting better unit revenues for the tail end of summer, a sign customers will continue to have to shell out more to fly in the coming months.

Alaska Airlines on Thursday raised its third-quarter profit forecast to a range of $2.15 to $2.25 per share from a previous outlook of no more than $1.60 per share. It also said it expects unit revenue to rise by as much as 2% after previously estimating flat to "positive" unit revenue growth over last year.

Delta Air Lines said domestic and trans-Atlantic unit revenue would be up in September from last year, though it said the CrowdStrike outage in July will mean unit sales will rise no more than 1% compared with a previous forecast of as much as 4% higher for the quarter. Delta has said it expected a $500 million hit from the outage and its aftermath, when it canceled some 7,000 flights.

Alaska said it had a tail wind from the outage, which affected Delta customers more than those on other airlines.

"While capacity remains in line with prior expectations, revenue has performed better than anticipated driven by additional revenue in July related to CrowdStrike disruptions across the industry and stronger performance in August and September," Alaska said in a securities filing.

Delta's president, Glen Hauenstein, told a Morgan Stanley conference on Thursday that Delta isn't seeing a lingering impact on bookings from the outage.

Airlines had been wrestling with record numbers of travelers but lower fares and weaker-than-expected pricing power. That appears to be changing.

Wednesday's U.S. inflation report showed an airfare price index rose 3.9% in August after five consecutive months of declines.

Frontier Airlines said Wednesday that it might break even this quarter, on an adjusted basis, after a previous forecast of margins ranging from -3% to -6%, after it moderated capacity. Last week, JetBlue Airways raised its unit revenue growth forecast for the current quarter because of higher demand and a benefit from the "re-accommodation of customers affected by other airlines' cancellations due to technology outages in July."

Airlines from full-service carriers like Delta and United to budget airlines like Frontier and Spirit have been chasing higher-spending travelers with perks like more space on board.

"We are constantly thinking about what we can do to continue to increase that competitive gap with premium products, from improving the food we serve on our planes to improving our loyalty program, to improving our Wi-Fi product, to improving particularly our Polaris product on international first class," United's CFO Mike Leskinen said at the Morgan Stanley conference on Thursday.

U.S. airlines have also slowed if not halted hiring altogether this year as aircraft arrive late from Boeing and Airbus, and demand moderates after a massive hiring spree.