forecasting intraday call arrivals - lancaster university · – monotonically increasing variable...

Forecasting Intraday Call

Arrivals Modelling Special Days

Devon K. Barrow

Nikolaos Kourentzes

27th European Conference on Operational Research

12-15 July 2015

University of Strathclyde

1. Research Questions

2. Call Arrival Data and Challenges

3. Experimental Design

4. Results

5. Conclusions and future work

Outline

Forecasting Intraday Call Arrivals Outline 2

• How do different forecasting methods

perform when forecasting (high frequency)

call centre arrivals?

• What is the impact of coding or not coding

of (functional) outlying periods on

forecasting performance?

Research Questions

Research Questions 3 Forecasting Intraday Call Arrivals




4. Results


Outline

Forecasting Intraday Call Arrivals Call Centre Data 4

• High dimensional and sampled at a high

frequency (Kourentzes and Crone, 2010).

• Complex seasonal patterns

– Intraday

– Intraweek

– interyear dependencies (De Livera et al., 2011)

Call Arrival Data and Challenges Challenges

5 Call Centre Data Forecasting Intraday Call Arrivals

Call Arrival Data and Challenges Some call centre data

6

• Two series from a large UK service provider call centre

• A leading entertainment company in Europe

• Data is sampled at half-hourly intervals

• Consists of 103 weeks and 3 days from 29 June 2012 to

23 June 2014 inclusive including bank holidays and

weekends.

Call Centre Data Forecasting Intraday Call Arrivals

Call Arrival Data and Challenges Complex seasonal patterns

7

Intraday Intraweek

Mean

Median

Monday

Intrayear


• Development of new methods

– Double seasonal exponential smoothing (Taylor, 2008)

– Multiplicative double seasonal ARMA model (Taylor, 2003)

– Exponential weighting (Taylor, 2008, 2010)

– Regression (Tych et al., 2002; Taylor, 2010)

– Singular vector decomposition (Shen and Huang, 2005, 2008;

Shen, 2009)

– Gaussian linear mixed-effects models (Aldor-Noiman et al.,

2009; Ibrahim and L’Ecuyer, 2013)

• Intraweek seasonal moving average performs well at medium to long horizons (Tandberg et al. 1995; Taylor, 2008; Taylor,

2010; Ibrahim and L’Ecuyer, 2013)

Call Arrival Data and Challenges Handling high frequency complex seasonality


!

• Data is context sensitive

– Effects of holidays, special events and

promotional activities

• Prone to quite sizeable unexplained

variations (outliers)

– E.g. due to system failures and data

processing

Call Arrival Data and Challenges Challenges


Call Arrival Data and Challenges Anomalies (outliers)

10

Series 1

Series 1I


Call centre data Seasonal profile

12

4 8 12 16 200

100

200

300

400

Calls

Monday

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Hour

Thursday

4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Median

25-75%

10-90%

05-95%

4 8 12 16 200

10

20

30

40

Calls

Monday

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Hour

Thursday

4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Median

25-75%

10-90%

05-95%

Series 1

Series 1I Large variation from the middle Call Centre Data Forecasting Intraday Call Arrivals

Call centre data Outliers vs. median pattern

Call Centre Data 13

4 8 12 16 200

100

200

300

400

Monday

Calls

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Thursday

Hour

4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Profile

Outliers

4 8 12 16 200

10

20

30

40

Monday

Calls

4 8 12 16 20

Tuesday

4 8 12 16 20

Wednesday

4 8 12 16 20

Thursday

Hour

4 8 12 16 20

Friday

4 8 12 16 20

Saturday

4 8 12 16 20

Sunday

Profile

Outliers

Series 1

Series 1I Regular profile very different from outliers

Forecasting Intraday Call Arrivals

• Approaches to handling ‘special days’: – Information is either available and/or data is pre-

cleansed

– The forecaster has an external methodology for tackling ‘special days’ (Jongbloed and Koole, 2001; Avramidis et al., 2004; Taylor, 2008a; Pacheco et al., 2009; Taylor, 2010b)

– Removing such days altogether (Taylor et al. 2006)

– Singular vector decomposition for automatic outlier detection (Shen and Huang, 2005)

• Kourentzes (2011) demonstrates that there are substantial accuracy benefits to be had from modelling irregular load patterns.

Call Arrival Data and Challenges Handling ‘special days’


!




4. Results


Outline

Forecasting Intraday Call Arrivals Experimental Design 15

Experimental Design Functional outlier modelling

16

• We evaluate seven alternative methodologies for

modelling functional outliers

• These are based on extensions of conventional outlier

modelling and novel approaches

• We assume that the data generating process of normal

observations is captured adequately and the outliers are

already labelled

Control

Single Binary

Dummy

Multiple Binary

Dummy

Single Integer

Profile Dummy

Trigonometric

Dummy

Model

Separately

Experimental Design Forecasting Intraday Call Arrivals


17

• Control/benchmark – A set of autoregressive lagged inputs (past values) are identified

using stepwise regression

– Outliers are not modelled

• Single Binary Dummy Variable – Indicator variable s.t. one = outlier; zero otherwise

• Multiple Binary Dummy Variable – S is the seasonal length (S=48)

– 48 (S) dummy variables to code each observation

– 47 (S – 1) dummy variables to code each observation

– Stepwise selection, s = {1,…,S=48} s.t. s is significantly different from normal observations



18

• Single Integer Dummy Variable – Monotonically increasing variable from 1 to 48 if outlier; zero

otherwise

• Profile Dummy Variable – This variable is equal to the profile if there is an outlier; zero

otherwise

• Trigonometric Dummy Variables – Sine and cosine if there is an outlier; zero otherwise

• Model Separately – Create a new series containing only outliers

– Replace outliers in original series with normal observations


Experimental Design Experimental setup

Experimental design 19

• Neural network setup – Inputs based on backwards regression + dummies + seasonal

dummies.

– Mode ensemble of 50 networks trained by scaled conjugate gradient descent

– Hidden nodes identified experimentally for each set of inputs

• Forecast creation – Forecast horizon is set to 1 day ahead (1-48 half hourly steps

ahead)

– Test set of 100 days (4800 data points x 48 forecasted horizons)

• Forecast evaluation – Mean Absolute Error (MAE)

– Relative Mean Absolute Error (RMAE) i.e. MAE_{Method} / MAE_{Control} AE = |Yt - Ft| Forecasting Intraday Call Arrivals




4. Results


Outline

Forecasting Intraday Call Arrivals Results 20

Results Neural networks versus benchmarks

21

Time Series 1 Overall Outlier Normal

Naïve 1 3.930 2.711 4.269

Naïve Day 1.417 1.211 1.475

Naïve Week 1.333 1.057 1.410

MA Day 1.238 1.278 1.226

MA Week 1.233 0.845 1.341

ETS Day 1.887 1.438 2.013

ETS Week 1.529 1.165 1.630

ETS Double 1.086 0.857 1.149

MAPA Day 1.522 1.362 1.566

MAPA Week 1.484 1.274 1.542

NN Control 1.000 1.000 1.000 Results Forecasting Intraday Call Arrivals

Results Neural networks versus benchmarks

Time Series II Overall Outlier Normal

Naïve 1 2.236 1.770 2.500

Naïve Day 1.415 1.119 1.582

Naïve Week 1.433 1.157 1.590

MA Day 1.415 1.119 1.582

MA Week 1.129 0.973 1.217

ETS Day 1.600 1.368 1.731

ETS Week 1.479 1.288 1.587

ETS Double 1.151 0.990 1.242

MAPA Day 1.347 1.242 1.406

MAPA Week 1.280 1.201 1.325

NN Control 1.000 1.000 1.000 22 Results Forecasting Intraday Call Arrivals

Results Outlier modelling versus control

Time Series 1 Overall Outlier Normal

NN Control 1.000 1.000 1.000

NN Bin1 0.996 0.933 1.013

NN BinS 0.884 0.822 0.901

NN BinS-1 0.873 0.831 0.885

NN Bin Step 0.897 0.858 0.908

NN Bin Back 0.895 0.850 0.907

NN Int 0.935 0.913 0.941

NN SinCos 0.980 0.865 1.012

NN Profile 0.986 0.953 0.995

NN Replace 1.002 1.019 0.997 23 Results Forecasting Intraday Call Arrivals

Results Outlier modelling versus control

Time Series II Overall Outlier Normal

NN Control 1.000 1.000 1.000

NN Bin1 0.956 0.930 0.970

NN BinS 0.922 0.866 0.954

NN BinS-1 0.923 0.870 0.954

NN Bin Step 0.929 0.876 0.958

NN Bin Back 0.931 0.875 0.963

NN Int 0.957 0.940 0.966

NN SinCos 0.951 0.912 0.972

NN Profile 0.963 0.936 0.979

NN Replace 1.030 1.090 0.996 Results 24 Forecasting Intraday Call Arrivals




4. Results


Outline

Forecasting Intraday Call Arrivals Conclusion and future work 25

Conclusion and future work

Conclusion and future work 26

• Conclusion

– Neural networks are good for call centre data for two reasons:

• They can do complex structures

• They can do complex outliers with relatively simple modelling

• Future work

– Automatic functional outlier detection and modelling for call centre arrival data

Forecasting Intraday Call Arrivals

Devon K. Barrow Coventry Business School

Coventry University, Priory Street, Coventry, CV1

5FB

Direct line: + 44 024 7765 7413

Skype: devon.k.barrow

Email: [email protected]

forecasting intraday call arrivals - lancaster university · – monotonically increasing variable...

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