Adaptive short term forecasting How to approach short term forecasting of multiple interdependent
time series and reduce forecasting error twice [spoiler]
A. AkimenkoMoscow’16
Contents
First glance on the data
Forecasting algorithm
Data preparation and new features
Modeling
Final results & summary
First glance on the data
• Daily bucket volumes - 14 time series; • Correlated with the neighbour with some lag;
Example of one of the time series
• White squares are weekends/holidays or were excluded as outliers; • The time series have dual seasonality (weekly and monthly) and trend;
The task is to develop an algorithm which will predict Y for the next month for each time series with Mean
Absolute Percentage Error (MAPE) < 3%.
Forecasting algorithm
Auto-regression models and moving average (ARMA, ARIMA, GARCH)
SSA/Gusenitca
Neural networks (RNN)
Adaptive short term forecasting:• Exponential smoothing; • Seasonal and trend decomposition;• Adaptive auto-regression;
Adaptive model selection & composition
...
Auto-regression models and moving average (ARMA, ARIMA, GARCH)
SSA/Gusenitca
Neural networks (RNN)
Adaptive short term forecasting:• Exponential smoothing; • Seasonal and trend decomposition);• Adaptive auto-regression;
Adaptive model selection & composition
...
Data preparation and new features
Normalization
Outliers
Observation period
Lagged features
Calendar features
Weighing
Modeling
Regular Linear Model
Penalized Linear Model
Accuracy measureScaled Errors:
• Mean absolute error (MAE) or mean absolute deviation (MAD)
• Mean squared error (MSE) or mean squared prediction error (MSPE)
• Root mean squared error (RMSE)
• Average of Errors (E)
Percentage Errors:
• Mean absolute percentage error (MAPE) or mean absolute percentage deviation (MAPD)
Scaled Errors:
• Mean absolute scaled error (MASE)
Other Measures:
• Forecast skill (SS)
Accuracy measureScaled Errors:
• Mean absolute error (MAE) or mean absolute deviation (MAD)
• Mean squared error (MSE) or mean squared prediction error (MSPE)
• Root mean squared error (RMSE)
• Average of Errors (E)
Percentage Errors:
• Mean absolute percentage error (MAPE) or mean absolute percentage deviation (MAPD)
Scaled Errors:
• Mean absolute scaled error (MASE)
Other Measures:
• Forecast skill (SS)
Challenger models0.Dimension reduction (Principal Component Analysis - PCA).
1.Ensembles (Random Forest, Gradient Boosted Models - GBM and XGBoost);
2.Regressions (Linear, Stepwise, Ridge and Lasso);
3.Distance based (k-Nearest Neighbor - kNN);
Final results & summary
As a result of testing, weighted penalized regression was chosen as base algorithm with α=0 (ridge regression) and λ=0.005. Observation period was set as 2 years.
• The proposed algorithm allows to build time series forecasting of multiple interdependent time series;
• Reveals any kind of seasonality;
• Deals with missing values/outliers;
• Removes overfitting/multicollinearity via penalization;
• Scalable for new features (both lagged and calendar), period of forecasting and number of interdependent time series.
Thank you for your attention!
Full research is available here: https://alexakimenko.github.io/time_series/2016/09/18/adaptive-short-term-forecasting/
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