The short term electric load forecasting which is generally from one hour to one week is one of the intelligent electric grid (smart grid), for control of stable load supply hour-to-hour or day-to-day. The difficulty of short time forecasting is that the trend of time series usually change, and the non-adaptive auto-regressive integrated moving average (ARIMA) could not fit accurately. To solve that problem, conventional adaptive ARIMA with constant forgetting factor that gives a larger weight to more recent train data for dealing with non-stationary change of stochastic disturbance. The forgetting factor governs the recursive least squares (RLS) algorithm. However, constant forgetting factor usually result in over-fitting that increases forecasting error. A new adaptive ARIMA is proposed in this paper to improve the accuracy with lazy learning algorithm to reduce over-fitting error.