Adaptive short term forecasting

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  • Adaptive short term forecasting How to approach short term forecasting of multiple interdependent

    time series and reduce forecasting error twice [spoiler]

    A. AkimenkoMoscow16

  • 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 =0 (ridge regression) and =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/