Frequency independent automatic input variable selection for neural networks for forecasting

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1 Universiä Hamburg Insiu für Wirschafsinformaik Prof. Dr. D.B. Preßmar Frequency independen auomaic inpu variable selecion for neural neworks for forecasing Nikolaos Kourenzes Sven F. Crone LUMS Deparmen of Managemen Science

2 Moivaion Large Scale Auomaic Forecasing Problems Large numbers of univariae ime series are ofen needed o be forecased auomaically in business and oher conexs [Hyndman & Khandakar, 08] 0,000 + producs Forecas daily Auomaic forecasing Necessary! Quesions: Appropriae forecasing mehod? Correc specificaion? [Goodrich, 00] Typically ime series periodiciy is provided by expers Fully auomaic?

3 Moivaion Why Neural Neworks? NN in Business Time Series Forecasing Promising performance 64% (ou of 26) aricles found ANNs ouperforming benchmarks [Kourenzes, 0](73% according o Adya& Collopy, 98) Large scale sudies (00+ ime series)nn a leas as good as benchmarks [Hilleal.,96, Liao& Fildes, 05] Evidence of auomaic forecasing wih NNs [Crone& Kourenzes, 0] Forecasing Compeiions (M3) NN lower accuracy han saisical models [Makridakis& Hibbon, 00] NN produce unreliable forecass criicised o offer lile promise even afer much research [Armsrong, 06] Why? Wha does NN research sugges?

4 Moivaion Focus on he inpu vecor Modelling complexiy gives rise o he problems Problem caused by inconsisen rial and error modelling approaches [Zhang e al., 98] Inpu variable selecion The mos imporan issue in forecasing wih NN [Zhang,0,Zhangeal.,0,Zhangeal., 98,DarbellayandSlama,00] No widely acceped mehodology on how o selec he inpu variables [Anders andkorn,99,zhangeal.,98] Fully auomaic inpu selecion implies knowledge of ime series frequency/periodiciies Ignored in auomaed forecasing applicaions Focus on frequency idenificaion & he inpu variables selecion

5 Ieraive Neural Filer A mehodology o idenify seasonal frequencies and inpus Sep. Idenify seasonal frequencies using he Ieraive Neural Filer (INF) Sep 2. Idenify lagged inpus Sep 3. Fi model & produce forecass

6 Ieraive Neural Filer Sep. Idenify seasonal frequencies Euclidean Disance o Idenify Seasonaliy Spli ime series in differen possible seasonaliies find mean euclidean disance Y = sin(2π/2) s = 5 - Disance: s = 2 - Disance: 0 s = 9 - Disance: s = 24 - Disance: 0 y 0 y 0 y 0 y Muliple seasonaliies (2, 24, 36,...) Idenificaion problem

7 Penalised Euclidean Disance Ieraive Neural Filer Sep. Idenify seasonal frequencies Spli ime series in differen possible seasonaliy (periodiciy) find euclidean disance 60 Season 4 60 Season Mean Euclidean Disance: Mean Euclidean Disance: 7.2 Disance D ps ( s) = log( D + ) τ log( s) s Penalised Euclidean Disance Idenify seasonaliy avoiding muliples Season

8 Ieraive Neural Filer Sep. Idenify seasonal frequencies The ieraive neural filer removes each idenified seasonaliies explore remaining informaion for addiional seasonaliies Idenified seasonaliy Deerminisic inpus Trends, level shifs, ec 2π ψ ( ) = sin S 2π ψ 2 ( ) = cos S ψ 3 ( ) = ψ 4 ( ) = N + I I 2 I 3 I 4... H H n O Y If more seasonaliies are idenified add more inpus in each ieraion... ψ ( ) ψ ( ) 2 = = 2π sin S 2π cos S

9 Ieraive Neural Filer Sep. Idenify seasonal frequencies Inpu Time series 550 Penalised Disance 2.5 Penalised Euclidean Disance 550 INF oupu Ieraion : 500 Disance Season Subrac he INF oupu from he inpu ime series and repea Inpu Time series Penalised Disance 30.8 Ieraion 2: Disance Season = Sop! Season

10 Ieraive Neural Filer Ieraive Neural Filer Sep. Idenify seasonal frequencies

11 Ieraive Neural Filer Sep 2. Idenify inpus Fi wo compeing regressions: Deerminisic Yˆ D N s j = a+ M + S j= i= b ji d ji + ε Sochasic Yˆ S N s = a+ j= b j Y Sj + ε Compare using AIC Moving average of order max(s j )

12 Ieraive Neural Filer Sep 2. Idenify inpus Use sepwise regression Force as iniial inpus he pre-idenified inpus (deerminisic/sochasic) Inpu vecor idenified

13 Synheic ime series: Deerminisic / Sochasic Empirical Evaluaion Time series Four differen levels of noise (None, Low, Medium, High) Experimenal Seup Time series Quarerly and monhly seasonaliy & Day of he week and year double seasonaliy Toal ime series: 520 Real ime series: US air passenger miles Average bus ridership for Porland Oregon Toal number of room nighs and akings in Vicoria Number of serious injuries and deahs in UK road accidens

14 Resuls Use INF o idenify inpus for neural neworks (Primed NN) Use NNs wih auomaically idenified inpus as benchmarks (Soch_NN) Inpus idenified using regression [Swanson & Whie, 98, Kourenzes, 0] Use exponenial smoohing as saisical benchmark (EXSM) Robus and accurae benchmark [Makridakis & Hibbon, 00] Use INF seasonaliy oupu o seup seasonal models Synheic Daa Real Daa Subse Primed_NN Soch_NN EXSM Subse Primed_NN Soch_NN EXSM Train 7.25% 7.45% 7.68% Train 8.52% 7.86% 7.82% Valid 7.6% 7.47% 7.52% Valid 5.06% 5.9% 6.83% Tes 7.37% 7.70% 7.47% Tes 7.86%.95% 0.72%

15 Conclusions Proposed mehodology idenifies seasonal frequencies and inpus for neural neworks auomaically Ouperforms saisical and neural nework benchmarks INF is useful o fully auomae oher forecasing mehods seasonal frequency idenificaion wihou he need for human expers Fuure work: Inroduce sochasic elemens in IMF o separae more accuraely he seasonal componens

16 Nikolaos Kourenzes Lancaser Universiy Managemen School Cenre for Forecasing Lancaser, LA 4YX, UK Tel. +44 (0)