DAT320 Basic Forecasting PDF

DAT320: Forecasting Basic concepts Kristian Hovde Liland [email protected] Autumn 2024 Norwegian University of Life Sciences Forecasting: problem setup Baseline models Experimental setup 1 Norwegian University of Life Sciences Forec...

DAT320: Forecasting Basic concepts Kristian Hovde Liland [email protected] Autumn 2024 Norwegian University of Life Sciences Forecasting: problem setup Baseline models Experimental setup 1 Norwegian University of Life Sciences Forecasting I prediction model I target variable: future values xt+1 , xt+2 ,... I predictors: present and past values (history) xt , xt−1 ,... 2 Norwegian University of Life Sciences Forecasting I prediction horizon = maximum number of time steps h to predict ahead I in general: the more steps ahead, the more uncertain Single-step ahead Multi-step ahead I target variable xt+1 I target variable xt+h , h > 1 3 Norwegian University of Life Sciences Uni- and multivariate time series I which information should be used for predictors? I history / present state of (xt )t∈T I history / present state of other variables (exogeneous variables, covariates) (zt )t∈T Univariate forecasting Univariate forecasting with covariates Multivariate forecasting I predictors xs , s ≤ t I predictor xs and zs , I predictors xs , s ≤ t I target variable s≤t I target variable xt+1 ,... , xt+h I target variable xt+1 ,... , xt+h xt+1 ,... , xt+h 4 Norwegian University of Life Sciences Baseline models I 4 baseline models should be evaluated as minimum benchmarks for any more complex forecasting models I average method I drift method I naïve method I seasonal naïve method I Any forecasting model has to beat these 4! I [Hyndman and Athanasopoulos, 2021, ch. 5.2] 5 Norwegian University of Life Sciences Average method I given x1 ,... , xt , estimate future time point t + h, h > 0, by average over history, t 1X x̂t+h = xs t s=1 I → same as global missing value replacement xt x̂t+2 x̂t+1 6 Norwegian University of Life Sciences Drift method I given x1 ,... , xt , estimate future time point t + h, h > 0, by the last observed value plus average drift (trend), xt − x1   x̂t+h = xt + h t−1 xt x̂ x̂t+2 t+1 7 Norwegian University of Life Sciences Average and drift method (a) Average method (b) Drift method Figure 1: Baseline forecasts – passenger data 8 Norwegian University of Life Sciences Naïve method I given x1 ,... , xt , estimate future time point t + h, h > 0, by the last observed value, x̂t+h = xt I → last observation carried forward (LOCF) xt x̂t+2 x̂t+1 9 Norwegian University of Life Sciences Seasonal naïve method I given x1 ,... , xt and a period of p, estimate future time point t + h, p ≥ h > 0, by the same value from the last period, x̂t+h = xt+h−p(k+1) , where p is the seasonal period and k = b h−1 p c x̂t+1 xt x̂t+2 10 Norwegian University of Life Sciences Naïve and seasonal naïve method (a) Naïve method (b) Seasonal naïve method Figure 2: Baseline forecasts 11 Norwegian University of Life Sciences Baseline models library ( forecast ) library ( datasets ) data ( " AirPassengers " ) # average method ( mean f o r e c a s t ) mod _ avg