Electricity Demand Probabilistic Forecasting With Quantile Regression Averaging

Transcription

1 Electricity Demand Probabilistic Forecasting With Quantile Regression Averaging Bidong Liu, Jakub Nowotarski, Tao Hong, Rafa l Weron Department of Operations Research, Wroc law University of Technology, Poland Big Data Energy Analytics Laboratory, University of North Carolina at Charlotte Riverside, Based on: Bidong Liu, Jakub Nowotarski, Tao Hong and Rafal Weron, Probabilistic Load Forecasting via Quantile Regression Averaging on Sister Forecasts, IEEE Transactions on Smart Grid, forthcoming This work was supported by funds from NCN (Poland) through grant no. 2013/11/N/HS4/03649 B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

2 Motivation: probabilistic forecasts Stochastic nature of forecasting Assessment of future uncertainty Ability to plan different strategies for the range of possible outcomes indicated by the probabilistic forecast Variability of the electricity demand becoming a challenge to the utility industry useful in practice (risk management and decision-making) B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

3 Motivation: combining forecasts Similar to portfolio diversification and management Availability of various models/experts predictions No single best forecasting method Generally believed to improve forecast accuracy B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

4 Motivation: load forecasting Interval/density forecast, combining not so popular in load forecasting Combine point predictions for probabilistic forecasting opportunity to leverage existing research Use methodology proved to work well (J. Nowotarski and R. Weron (2014), T. Hong, B.Liu, and P. Wang (2015)) Relative simplicity of the two key components B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

5 Individual forecasts Background: Point forecast averaging f 1 f 2 f N Weights estimation f C Combined forecast B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

6 Background: Interval forecast averaging For point forecasts: f c = M i=1 w if i (e.g. a linear regression model) For interval forecasts the above formula may not hold A linear combination of α-th quantiles is not an α-th quantile of a linear combination of random variables q α c M w i qi α i=1 A possibility for development of new approaches B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

7 Background: quantile regression 300 Linear regression Y X B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

8 Background: quantile regression Linear regression Quantile regression, α=0.95, α= Y Interval forecast X B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

9 Individual point forecasts Proposed model: Quantile Regression Averaging f 1 f 2 f N Quantile regression f C Combined interval forecast (2 quantiles) B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

10 Methodology: sister models and sister forecasts Motivation: variable selection is core in regression model for load forecasting Sister models constructed by different subsets of variables with overlapping components Here: 2 or 3 years for calibration and 4 ways of partitioning training and validation periods Sister forecasts are generated from sister models The family of sister recency effect models: ŷ t = β 0 + β 1 M t + β 2 W t + β 3 H t + β 4 W t H t + f (T t ) + + d f ( T t,d ) + lag f (T t lag ), B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

11 Methodology: the data (GEFCom2014) 2 or 3 years for calibration of sister (individual) models 1 year for validation of sister (individual) models (variable selection) 1 year for validation of probabilistic forecasts (best models selection) 1 year for testing probabilistic forecasts B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

12 Methodology: benchmarks Two naive benchmarks Scenario generation from historical weather data, no recency effect (Vanilla) Quantiles interpolated from 8 individual forecasts (Direct) Benchmarks from individual models 8 individual models (Ind) with residuals distribution Best Individual (BI) individual model according to MAE B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

13 Methodology: evaluation of forecasts Pinball loss function for 99 percentiles { (1 q)(ŷ q t y t ), y t < ŷ q t P t = q(y t ŷ q t ), y t ŷ q t Winkler score for 50% and 90% two-sided day-ahead prediction intervals: δ t for p t [L t t 1, U t t 1 ], W t = δ t + 2 α (L t t 1 p t ) for p t < L t t 1, δ t + 2 (p α t U t t 1 ) for p t > U t t 1, where δ t = U t t 1 L t t 1 is the interval s width B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

14 Results: validation period 7 QRA models, 8+1 individual models 4 lengths of calibration period One year of validation to pick up best (model, length) pairs QRA models are dominantly better than the benchmark models B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

15 Results: test period Model class Pinball Winkler (50%) Winkler (90%) QRA(8,183) Ind(1,91) BI(-,365) Direct Vanilla B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

16 Discussion Resolution log-transform caused intervals to be wider in peak hours Practicality Sister forecasts easy to generate No need of independent expert forecasts Simple way to leverage from point to probabilistic forecasts Extensions Sister forecasts eg. for machine learning methods QRA for expert forecasts B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

17 Summary QRA a new technique the load forecasting literature Practical value (1) input to QRA from point forecasts Practical value (2) the sister forecasts are easy to generate Publicly available data (GEFCom2014) Accurate confirmed by the pinball loss function and Winkler scores B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

18 Questions? B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

19 Methodology: sister models and sister forecasts where: ŷ t = β 0 + calendar effects temp. dependence {}}{{}}{ β 1 M t + β 2 W t + β 3 H t + β 4 W t H t + f (T t ) + + f ( T t,d ) + f (T t lag ), d lag }{{} recency effect f (T t ) = β 5 T t + β 6 Tt 2 + β 7 Tt 3 + β 8 T t M t + β 9 Tt 2 M t + + β 10 Tt 3 M t + β 11 T t H t + β 12 Tt 2 H t + β 13 Tt 3 H t T t,d = d lag=24d 23 T t lag B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

20 Individual point forecasts Extension: Factor Quantile Regression Averaging f 1 f 2 f N PCA F 1 F K K factors extracted from a panel of point forecasts, K<N Quantile regression f C Combined interval forecast (2 quantiles) B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

21 Price forecasting results: case study 1 J. Nowotarski and R. Weron (2014, Computational Statistics) 20 Conditional coverage LR 20 Unconditional coverage LR AR SNAR QRA Hour 50% PI 90% PI B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21

22 Price forecasting results: case study 2 K. Maciejowska, J. Nowotarski and R. Weron (2015, IJF) Relative Winkler score, 50% PI 25% 20% 15% 10% 5% 0% 5% 1 W h QRA /W h ARX 1 W h FQRA /W h ARX Relative Winkler score, 90% PI 25% 20% 15% 10% 5% 0% 5% Load period (h) B. Liu, J. Nowotarski, T. Hong & R. Weron Electricity Demand Probabilistic Forecasting Riverside, / 21