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Two Algorithms for Time Series Forecasting
Danny Yuan
Two Algorithms for Time Series Forecasting Danny Yuan Forecasting - - PowerPoint PPT Presentation
Two Algorithms for Time Series Forecasting Danny Yuan Forecasting - - PowerPoint PPT Presentation
Two Algorithms for Time Series Forecasting Danny Yuan Forecasting with Fast Fourier Transformation Key Idea: Decomposition A reasonably continuous and periodic function can be expressed as the sum of a series of sine terms FFT Is Simple 1.
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Key Idea: Decomposition
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A reasonably continuous and periodic function can be expressed as the sum of a series of sine terms
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1. Run FFT on input data 2. Filter out low-amplitude, high-frequency components 3. Forecast on each individual component 4. Run inverse of FFT of filtered data 5. Profit!
FFT Is Simple
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FFT Is Simple
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Solution: Iteratively Compensate Input with Error
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When Should We Use FFT?
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When There Is Periodicity
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When You Need a Quick Job
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Decomposition Is Powerful
Reference
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Decomposition Is Powerful
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Decomposition Is Powerful
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Decomposition Is Powerful
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Where Is The Bottleneck?
- Not easy to combine new signals
- E.g. events, weather
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Forecasting With Deep Learning
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- Time series can be discretized into sequence
- We can apply techniques of seq2seq
Key Idea: Time Series Are Sequences
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t
H_1
Input1
H_2
Input2
H_3
Input 3
H_n
Input n-1
H_0
Start Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast n
T0 T1 T2 T3 Tn
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t
H_1
Input1
H_2
Input2
H_3
Input 3
H_n
Input n-1
H_0
Start Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast n
[Forecast 1, Time of Week 1]
…... [F_(n-1), TOW_(n-1)]
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t
H_1
Input1
H_2
Input2
H_3
Input 3
H_n
Input n-1
H_0
Start Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast n
…... [F_(n-1), TOW_(n-1), Weather_(n-1), X_(n-1)]
[Forecast 1, Time of Week 1, Weather 1]
[Temperature, Humidity, Precipitation, Wind, Weather Type]
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What About Recent Context?
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t t - 1 t - m + 2 t - m + 1 t - m
[F_1, TOW_1, Weather_1, X_1] …... [F_(n-1), TOW_(n-1), Weather_(n-1), X_(n-1)] h_1
Input 1
h_2
Input 2
h_3
Input 3
h_m
Input m
H_1
Input 1
H_2
Input 2
H_3
Input 3
H_n
Input n-1
H_0
Start Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast n
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t t - 1 t - m + 2 t - m + 1 t - m
[F_1, TOW_1, Weather_1, X_1] …... [F_(n-1), TOW_(n-1), Weather_(n-1), X_(n-1)] h_1
Input 1
h_2
Input 2
h_3
Input 3
h_m
Input m
H_1
Input 1
H_2
Input 2
H_3
Input 3
H_n
Input n-1
H_0
Start Forecast 1 Forecast 2 Forecast 3 Forecast 4 Forecast n
Encoder Decoder
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Summary
- Decomposition is a powerful tool in time series forecasting
- Time series forecasting can be modeled as a seq2seq problem