Numis Securities has upgraded its rating for Admiral, saying that it sees further upside for car insurance stocks as confidence in earnings, dividends and growth improves.Recent data from Confused.com showed that motor premiums were down by just 1.9% in the fourth quarter of 2013, the smallest quarterly decline since rates began to fall in 2012. Rates had fallen by 4.2% in the third quarter."Although it is too early to call a turn in the cycle, we read the slowdown as an encouraging sign of greater price discipline than we had anticipated. Our earnings forecasts currently aim to reflect rate decreases of 4% in 2014 and 2% in 2015," said Numis analyst Nick Johnson.Meanwhile, figures from the Ministry of Justice showed that road-traffic accident claims volumes declined by an annual rate of 10-15% during August to November last year, showing that the ban on legal referral fees in April is having a positive effect, Johnson said."The news on rates is tentatively good news, but not critical to our positive investment case. We turned positive on Admiral in October last year on the basis of earnings upside risk from favourable claims trends, low valuation and longer-term UK and International growth potential. "We think the first two of these positive dynamics also apply to Direct Line and esure shares. High dividend yields are also a key attraction."Admiral has been raised from 'add' to 'buy', with its target price lifted from 1,425p to 1,710p. Johnson said that the current valuation "materially undervalues the company's quality and medium-term prospects".In contrast, Direct Line has been cut from 'buy' to 'add' after a strong run, though its target price has been upped from 265p to 300p. esure has been held at 'add', while its target is up now from 250p to 320p.BC