Economists expect inflation to have remained below the bottom of the Reserve Bank's 1 per cent to 3 per cent target band for the fourth quarter in a row when June quarter numbers are released next week.
But the prediction is that it will be heading up from here.
In a Reuters survey of 11 forecasters, the median prediction was 0.3 per cent for the quarter and 0.8 per cent for the year. That is also the Reserve Bank's forecast.
ANZ economists concur, though they expect annual inflation to climb to 1.8 per cent by this time next year and 2.2 per cent a year later.
But ASB chief economist Nick Tuffley, who is picking just 0.1 per cent for the June quarter and 0.6 per cent for the year, said that over the past two years inflation had come in consistently below Reserve Bank and market expectations.
That highlighted the danger in the central bank moving pre-emptively to head off the rise in inflation pressures that was widely expected, he said.
The bank was in a tricky situation, he said, with current inflation very muted but the housing market a growing concern from the point of view of financial stability.
"Continued downside inflation surprises may reduce the Reserve Bank's confidence in a lift in future inflation pressures.
"This additional uncertainty could keep the official cash rate on hold slightly longer, despite growing pressure from the housing market and the fall in the New Zealand dollar," Tuffley said.
Westpac economist Michael Gordon said that while the exchange rate had fallen since May, it was still at a record high on average over the quarter and it was up 7 per centon a year earlier.
"A rising exchange rate puts downward pressure on the prices of imported and import-competing goods. We suspect that this depressing force reached its peak in the last year.
"We estimate that tradeable goods prices fell 1.3 per cent in the year to June, the steepest decline since 2004, which in turn was the steepest on record," Gordon said.
But persistently low inflation required an ever-rising exchange rate so that even if the exchange rate steadied from here, its depressing effect on prices would wane.
"And if it extends its decline, it could become a major source of inflation," Gordon said. "Much of this is in the hands of the US Federal Reserve and the pace at which it draws back from its unconventional monetary policy measures.
"We think it will move more cautiously than the market is factoring in. If we're right, the New Zealand dollar could claw back some of its recent losses. Either way though, we suspect its long-running uptrend has broken."
Meanwhile, a strengthening economy, a hot housing market and massive pressures on the building industry were a recipe for higher home-grown inflation in the future, Gordon said.
Though house prices are not in the consumers price index, the state of the housing market registers in it in several ways: construction costs, rents, lawyers' and real estate agents' fees, and property maintenance costs.
"Housing-related inflation has been modest at a nationwide level (though rampant in Canterbury), but the pace is gradually increasing," he said.
Tuffley said that higher construction costs would be an unavoidable consequence of the Canterbury rebuilding and the previous housing cycle would make the Reserve Bank wary of the "sticky" nature of housing-related inflation.
The Statistics New Zealand figures for inflation are to be released on Tuesday.