Holiday shopping in New York.

U.S. retail holiday sales showed a year-over-year gain for the week ended Dec. 24, according to The Retail Economist-Goldman Sachs Weekly Chain Store Sales Index – which also noted that the market is entering a bargain-hunting phase that runs through the first week of January.

Meanwhile, in separate reports, data showed strong online traffic as well as in-store traffic as consumers flocked to redeem gift cards and gobble up marked-down goods. For women’s apparel, holiday sales are shaping up to be weaker than last year.

In the sales index report, Michael P. Niemira, chief economist of The Retail Economist LLC, said that weekly sales rose 1.8 percent year over year. Compared to the prior week, sales declined 0.9 percent. “Phase one of the holiday season ended with cumulative sales growing about 1.5 percent from the prior year – a tad ahead of the 0.9 [percent] pace for the industry during the third quarter,” he noted. “Phase two of the season – which has already begun – is dominated by more bargain hunting and gift-card redemptions.”

Niemira added that the “bulk of phase-two holiday shopping will go through the early part of January.”

In a separate report from Telsey Advisory Group, analysts at the firm said in a research note this morning that last week, “malls were busy and traffic seemed average to above average as most consumers shopped for last-minute items for Christmas and Hanukkah. In addition, the traffic momentum continued post-Christmas as consumers redeemed gift cards, returned products and shopped clearance merchandise.”

The analysts added that online sales remained a “wild card.” Citing the latest Verizon Retail Index, e-commerce traffic was up 19 percent on Thursday, Dec. 22 and up 48 percent on Dec. 25. “Note that this speaks to traffic, not conversion, although one would think conversion was decent,” the analysts said. “In general, promotions remain elevated and inventory appears inline.”

Dana Telsey, chief research officer at the firm, said that 2016 holiday sales, overall, seem to be ahead of her 3.3 percent estimate as well as the National Retail Federation’s increase of 3.6 percent.

“This also is reflected in MasterCard’s SpendingPulse report that estimates (from Nov 1. through Dec. 24) holiday sales growth of 4 percent year-over-year, with e-commerce up 18.9 percent, home furnishings up 5.2 percent, furniture up 0.4 percent, and apparel up 0.2 percent (women’s down 2.9 percent; men’s up 7.4 percent), partly offset by electronics and appliances down 2.4 percent, and jewelry down 2.2 percent,” Telsey said.

The Telsey Advisory Group analysts also noted that department stores’ traffic “appeared above average and similar to that of Black Friday.”

“Conversion was high as shoppers walked through the mall with multiple shopping bags in hand,” the analysts said. “Promotions were front and center, but discount levels were reduced from the prior week – a chance for retailers to capitalize on heightened traffic and last-minute gifting.”

Telsey added that inventories “seem to be in good shape and noticeably lower than last year. For the third week in a row, Macy’s appeared to be the winner in terms of traffic and conversion, but J.C. Penney and Kohl’s received their fair share.”