It is known that trend estimates in serially correlated time series cannot be obtained using an ordinary least squares fit and that the precision of a trend estimate depends critically on the magnitude of the serial correlation in the data used. In this paper a model is developed to estimate simultaneously both the trend and the serial correlations in a time series. The model is tested using a time series that is set up as the sum of a trend and a simple Markov process. The errors (and confidence limits) of the trend slope and serial correlation coefficient estimates are inferred using the balanced bootstrap method. In support of the model, it is shown that for long time series (large sample) the efficiencies of the trend and lag-l autocorrelation coefficient estimates are in accord with known analytical formulae. The important feature of the model is its possibility to provide the confidence limits both for the trend and the autocorrelation coefficients even for short time series (small sample).The use of the model is illustrated by the trend analyses of 100-50 hPa layer mean temperatures over the north temperate region in the period 1958-1991. It is shown that the claimed negative trend is not significant.