"I expect the players to have been toughened up after playing back-to-back Test series against Australia," said Arthur, who will himself be under pressure if South Africa fail against New Zealand.
Australia won five out of six Tests, with one drawn, in the first two Test series under Arthur's charge.
Arthur pointed out that South Africa had managed to sort out some problems in the national One-day side, culminating in a series win against Australia, but admitted that there was work to be done to lift the team from their current sixth place on the International Cricket Council rankings.
"Our next three home series are against New Zealand, India and Pakistan, who are all rated above us," he said. "We have the opportunity to start moving up."
South Africa have named a squad of 16 players for the three Tests against New Zealand but both Arthur and selection convenor Haroon Lorgat have indicated that most of the players who struggled against Australia will be given another chance.
But Arthur said that changes had been made to improve the One-day team and the same might have to happen with the Test side if players continued to under-perform.
Fast bowler Andre Nel, who has struggled with a foot injury and did not bowl well in the home series against Australia, could be replaced by Dale Steyn or Garnett Kruger, while batsman Hashim Amla is expected to get a chance during the series.
Captain Graeme Smith remains doubtful because of a finger injury which kept him out of the final Test against Australia.
The Tests are being played after the end of the normal South African season.
Play at Centurion and in the third Test in Johannesburg will start at 9.30am - an hour earlier than usual - to try to avoid stoppages for bad light which affected the third Test against Australia in Johannesburg.
The cooler conditions and early starts are likely to mean the pitches will assist seam bowlers - and will be similar to conditions in New Zealand.
Fast bowler Shane Bond will be a key player for New Zealand.
He bowled only ten overs in a warm-up match against the Rest of South Africa because of a sore knee but is confident he will be fully fit for the Test.
Fellow fast bowler Chris Martin had an outstanding series when South Africa toured New Zealand two years ago, while Jacob Oram and left-armer James Franklin could also exploit seam-friendly conditions.
New Zealand captain Stephen Fleming, who made a century against the Rest of South Africa, will become the first New Zealander to play in 100 Tests, while all-rounder Shaun Pollock will become the second man after Gary Kirsten to play 100 Tests for South Africa.
Jacques Kallis, South Africa's star batsman, will also be notching a century of Tests, although one was for the World XI against Australia last October.
South Africa: Graeme Smith (captain), Jacques Kallis (vice-captain), AB de Villiers, Herschelle Gibbs, Ashwell Prince, Jacques Rudolph, Mark Boucher, Shaun Pollock, Nicky Boje, Andre Nel, Makhaya Ntini, Boeta Dippenaar, Andrew Hall, Garnett Kruger, Hashim Amla, Dale Steyn.
New Zealand squad: Stephen Fleming (captain), Daniel Vettori (vice-captain), Nathan Astle, Shane Bond, Peter Fulton, James Franklin, Jamie How, Brendon McCullum, Hamish Marshall, Chris Martin, Kyle Mills, Jacob Oram, Michael Papps, Jeetan Patel, Scott Styris.
Umpires: Mark Benson (Eng), Daryl Harper (Aus). Match referee: Ranjan Madugalle (SL).