The predictability of long time series of stock index levels and stock prices is investigated using both statistical and trading rule methodologies. The trading rule analysis uses a double moving-average rule and the methods of Brock, Lakonishok and LeBaron. Results are obtained for the FTA, FTSE-100, DJIA and S&P-500 indices, prices for twelve UK stocks and indices derived from these stock prices. Statistical analysis shows that the index and price series are not random walks. The trading rule analysis generally confirms this conclusion. However, small transaction costs would eliminate the profitability of the moving-average rule. Standard ARMA-ARCH models are estimated for time series of returns and bootstrap methods are used to decide if the models can explain the observed trading statistics. The models provide a reasonable description but there is evidence from the trading rule methodology that standard models sometimes fail to describe the dynamics of the indices and prices. Several comparisons are made: between an index and the stock prices that define the index, between spot levels and futures prices for indices, and between UK and US indices.