Time series models of peak daily electricity demand (June 2010-May 2011) are constructed using half hourly demand data from New South Wales, Australia. We are interested in predicting the peak electricity demand for the first seven days of June 2011 starting from 31 the May 2011. How much of the past data should be used for constructing an appropriate model which is able to provide a better forecast for the peak demand? Four appropriate ARIMA (autoregressive integrated moving average) models based past three, six, nine and twelve months of data are considered. Using RMSE (root mean square error) and MAPE (mean absolute percentage error) to measure forecast accuracy, it is shown that the ARIMA model build based on past three months data is the best model in term of forecasting two to seven days ahead and ARIMA model based on past six months data is the best model to forecast one day ahead.