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Table 1 Forecasting accuracy based on synthetic data in terms of MAPE and sMAPE

From: Tensor extrapolation: an adaptation to data sets with missing entries

Method

Fraction of missing values

-

5%

10%

20%

30%

40%

50%

 

MAPE

      

Baseline

       

ETSModel

229.216

229.472

231.271

237.175

238.353

243.600

244.766

Tensor extr.

       

\(R=3\)

185.401

185.852

185.971

186.892

185.449

187.114

186.936

\(R=4\)

179.852

180.387

180.647

181.473

179.836

187.041

184.915

\(R=5\)

181.227

180.432

182.375

183.499

179.717

181.763

180.465

\(R=6\)

181.171

180.361

181.318

182.286

179.604

184.152

180.426

\(R=7\)

180.548

182.183

181.131

181.483

179.523

182.712

180.630

Ensemble

       

\(R=4-6\)

180.738

180.424

182.027

182.587

180.870

183.901

181.857

\(R=3-7\)

181.573

181.813

182.851

182.585

182.167

182.966

183.291

 

sMAPE   

      

Baseline

       

ETSModel

45.356

45.894

46.526

48.002

49.953

52.029

53.910

Tensor extr.

       

\(R=3\)

46.985

47.050

47.058

47.073

47.138

47.146

47.660

\(R=4\)

46.849

46.900

46.914

46.945

47.144

47.153

47.644

\(R=5\)

46.789

46.902

46.823

46.850

47.014

47.041

47.633

\(R=6\)

46.794

46.912

46.897

46.935

47.032

46.919

46.636

\(R=7\)

46.812

46.814

46.907

49.945

46.996

47.029

47.609

Ensemble

       

\(R=4-6\)

46.796

46.901

46.854

46.900

46.968

46.955

47.548

\(R=3-7\)

46.761

46.825

46.828

46.917

46.930

46.965

47.500

  1. The estimation sample includes the first 80 time steps, and the hold-out sample covers the next 20 time steps. Different sized fractions of the data are eliminated; the respective elements are missing completely at random. The results obtained from tensor extrapolation are grouped with respect to the selected hyperparameter, the number of components R. Ensemble contains the scores of (equally weighted) combinations of forecasts associated with different specifications of R