data from business, demography, finance and economics. ¯ Series length between 14 and 126. ¯ Either non-seasonal, monthly or quarterly. ¯ All me series posi ve. ? Are we favouring methods that work well with data from these domains/lengths/frequencies? ? How representa ve are the M3 data even within these domains? ? How do we know that any me series collec on covers the range of possible me series pa erns? Exploring me series collec ons M3 compe on data 4
data from business, demography, finance and economics. ¯ Series length between 14 and 126. ¯ Either non-seasonal, monthly or quarterly. ¯ All me series posi ve. ? Are we favouring methods that work well with data from these domains/lengths/frequencies? ? How representa ve are the M3 data even within these domains? ? How do we know that any me series collec on covers the range of possible me series pa erns? Exploring me series collec ons M3 compe on data 4
data from business, demography, finance and economics. ¯ Series length between 14 and 126. ¯ Either non-seasonal, monthly or quarterly. ¯ All me series posi ve. ? Are we favouring methods that work well with data from these domains/lengths/frequencies? ? How representa ve are the M3 data even within these domains? ? How do we know that any me series collec on covers the range of possible me series pa erns? Exploring me series collec ons M3 compe on data 4
data from business, demography, finance and economics. ¯ Series length between 14 and 126. ¯ Either non-seasonal, monthly or quarterly. ¯ All me series posi ve. ? Are we favouring methods that work well with data from these domains/lengths/frequencies? ? How representa ve are the M3 data even within these domains? ? How do we know that any me series collec on covers the range of possible me series pa erns? Exploring me series collec ons M3 compe on data 4
+ Rt St is periodic with mean 0 3000 4000 5000 −500 0 500 1000 1500 3000 3250 3500 −500 0 500 1000 data seasonal trend remainder 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 Exploring me series collec ons Time series feature space 6
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
Tt + Rt Seasonal period Strength of seasonality: 1 − Var(Rt ) Var(Yt −Tt ) Strength of trend: 1 − Var(Rt ) Var(Yt −St ) Spectral entropy: H = − π −π fy (ω) log fy (ω)dω where fy (ω) is the spectral density of Yt. Low values of H suggest a me series that is easier to forecast (more signal). Autocorrela ons: r1 , r2 , r3 , . . . Op mal Box-Cox transforma on parameter: λ Exploring me series collec ons Time series feature space 7
space to: ¯ Generate new me series with similar features to exis ng series ¯ Generate new me series where there are “holes” in the feature space. Let {PC1, PC2, . . . , PCn} be a “popula on” of me series of specified length and period. Gene c algorithm uses a process of selec on, crossover and muta on to evolve the popula on towards a target point Ti . Op mize: Fitness (PCj ) = − (|PCj − Ti|2). Ini al popula on random with some series in neighbourhood of Ti . Exploring me series collec ons Genera ng new me series 20
space to: ¯ Generate new me series with similar features to exis ng series ¯ Generate new me series where there are “holes” in the feature space. Let {PC1, PC2, . . . , PCn} be a “popula on” of me series of specified length and period. Gene c algorithm uses a process of selec on, crossover and muta on to evolve the popula on towards a target point Ti . Op mize: Fitness (PCj ) = − (|PCj − Ti|2). Ini al popula on random with some series in neighbourhood of Ti . Exploring me series collec ons Genera ng new me series 20
space to: ¯ Generate new me series with similar features to exis ng series ¯ Generate new me series where there are “holes” in the feature space. Let {PC1, PC2, . . . , PCn} be a “popula on” of me series of specified length and period. Gene c algorithm uses a process of selec on, crossover and muta on to evolve the popula on towards a target point Ti . Op mize: Fitness (PCj ) = − (|PCj − Ti|2). Ini al popula on random with some series in neighbourhood of Ti . Exploring me series collec ons Genera ng new me series 20
space to: ¯ Generate new me series with similar features to exis ng series ¯ Generate new me series where there are “holes” in the feature space. Let {PC1, PC2, . . . , PCn} be a “popula on” of me series of specified length and period. Gene c algorithm uses a process of selec on, crossover and muta on to evolve the popula on towards a target point Ti . Op mize: Fitness (PCj ) = − (|PCj − Ti|2). Ini al popula on random with some series in neighbourhood of Ti . Exploring me series collec ons Genera ng new me series 20
space to: ¯ Generate new me series with similar features to exis ng series ¯ Generate new me series where there are “holes” in the feature space. Let {PC1, PC2, . . . , PCn} be a “popula on” of me series of specified length and period. Gene c algorithm uses a process of selec on, crossover and muta on to evolve the popula on towards a target point Ti . Op mize: Fitness (PCj ) = − (|PCj − Ti|2). Ini al popula on random with some series in neighbourhood of Ti . Exploring me series collec ons Genera ng new me series 20
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29
Generate new me series with controllable characteris cs. E.g., more M3-like data, or data unlike any seen before. M3 conclusions will not necessarily hold for other me series collec ons. Different forecas ng methods perform be er in some regions of the feature space than other methods. We could develop meta-forecas ng algorithms which choose a specific forecas ng method based on the loca on of a me series in the feature space. Exploring me series collec ons Conclusions 29 Further informa on ¯ Papers: robjhyndman.com ¯ Email: [email protected]
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