The CES Ifo research institute reported another month of forecast-busting German business sentiment indicators, feeding optimism about the fourth-quarter outlook.

Ifo said its business climate index rose to 110.5 in October from 109.5, putting the index at its highest point since April 2014 and defying expectations for the barometer to stagnate or rise only marginally.

"Companies were more satisfied with their current business situation. They also expressed far greater optimism about the months ahead. The upturn in the German economy is gathering impetus," noted Ifo president Clemens Fuest in the report.

The Ifo index of business expectations rose to 106.1 from 104.5, compared with expectations for a flat reading. And businesses' assessment of the current situation also rose more than expected, to 115 from 114.7.

The figures come after strong Markit purchasing managers' indices for Germany on Monday as the service sector PMI recovered from a blip the previous month.

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Capital Economics said the Ifo figures point to an acceleration of annual German GDP growth from 1.8% in the second quarter to about 2.0%, and support indications from the PMI data that the economy is expanding at a pace of about 0.4% a quarter.

"The good news about the start of Q4, together with the sharp rebound in industrial production in August, suggests that the German economy continued to perform well in the second half of 2016. Indeed, growth may even have accelerated towards the end of the year," noted Capital Economics' chief European economist Jennifer McKeown. "While we still expect growth to slow next year as rising inflation dampens consumer spending growth, the German economy should still record a reasonable expansion of 1.2% or so."

However, she noted that inflationary pressures remain largely absent from Germany and elsewhere in the euro zone, perpetuating a headache for the European Central Bank.

European stocks were up on Tuesday, with the DAX recently up 0.51% at 10,816.41.

The euro was recently up 0.06% against the dollar at $1.088.