Forecasting nonstationary time series under asymmetric loss

Forecasting nonstationary time series under asymmetric loss V.Y. Chernykh, M.M. Stenina Moscow Institute of Physics and Technology; Higher School of Economics The problem of forecasting time series under asymmetric loss functions is considered in this paper. We present a new two-step forecasting algorithm ARIMA+Hist. At the first step autoregression integrated moving average algorithm ARIMA with seasonal components is used. Parameters of the model is selected according to Box-Jenkins methodology. At the second step the analysis of regression residuals is taken place and optimal addition to the forecast of the first step which minimize the expected value of losses is found. Expected loss is estimated by convolution of loss function with histogram of regression residuals. We demonstrate the work of their algorithm on time series with different types of nonstationarity (i.e. trend or seasonality) and for different symmetric and asymmetric loss functions. The results obtained during this experiment show that the quality of the forecast of two-step ARIMA+Hist exceed the quality of usual ARIMA in case of asymmetric loss functions.