Activity in Germany's services sector grew at its strongest pace in a year in May, boosted by increased business optimism and weaker inflation, a survey showed on Wednesday.

The HCOB final services Purchasing Managers' Index (PMI) rose to 54.2 in May from 53.2 in April, slightly above a preliminary flash estimate and holding above the 50.0 mark that separates growth from contraction for a third straight month.

New business grew for a second straight month, and firms' optimism for the coming year notched its highest since February 2022, well above the long-run average.

"The mood in the German service sector is improving month by month," said Cyrus de la Rubia, chief economist at Hamburg Commercial Bank. "There's growing hope that the German economy is not the sick man of Europe after all."

Job creation rose, while rates of input cost and output price inflation were their lowest for three years - though they remain above their historical average.

"The positive side of this development is that service sector companies still seem to have some pricing power, which bodes well for the economic stability of the sector," said de la Rubia.

The composite PMI index, which comprises services and manufacturing, climbed to 52.4 in May from 50.6 in April, its highest reading for a year and the second month in a row above the 50 threshold. (Reporting by Miranda Murray Editing by Christina Fincher)