How to make blazing fast time series prediction ? A popular framework in ARIMA. But when the time series is periodic this algorithm is very slow. I explain here how to challenge this problem.

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Lightning fast time series
modeling and prediction:
(S)ARIMA on steroids
Meir TOLEDANO, Data science specialist

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in few words...

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We use ai to constantly
monitor and correlate
business performance,
providing real time alerts and
forecasts, reducing time to
detection and resolution,
dramatically impacting
bottom lines.

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THE COMPREHENSIVE SOLUTION
Automatically analyzes all data continuously, interacts with us only when relevant
CORRELATE ACT
● All the data
● Cross silo
● Continuous learning of 100%
● Adjusts to changes
● Root cause guidance
● Multiple correlation algorithms
● Realtime
● Significance learning
ANALYZECOLLECT
USER
PRODUCT
SYS. HEALTH
INFRA

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FROM BILLIONS TO ONES

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SOME OF OUR CUSTOMERS

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AUTONOMOUS DETECTION

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DETECTION PIPELINE

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ADAPTIVE LEARNING

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Learn the normal behavior

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CHALLENGES FOR LEARNING “NORMAL BEHAVIOR”
ADAPTATIONSEASONAL PATTERNSIGNAL DISTRIBUTIONSIGNAL TYPE
● Stationary / non
stationary
● Regularly Irregular
sampling
● Discrete/Real value
● Single/Mixture models
● Symmetric/non-symmetric
● Continuous/discrete
● Seasonal/non seasonal
● Single/multiple seasonal
patterns
● Additive/Convolutional
multi-seasonal patterns
● Optimal adaptation
during normal times
● Optimal adaptation
during anomalies
● Optimal adaptation
following anomalies

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STATIONARITY
Stationarity:
When the distribution of sub
series is time independent
• Weak stationarity:
only mean and variance
• Strong stationarity:
the complete distribution

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VOLATILITY
Homoscedasticity:
The volatility is constant over
time
Heteroscedasticity:
The volatility is a function of
time

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NOT ALL METRICS ARE CREATED EQUAL
SMOOTH IRREGULAR SAMPLING
MULTIMODAL
SPARSEDISCRETE
“STEP”

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REAL TIME ANOMALY DETECTION STRATEGY
Anomaly =
Too far from the
expected behavior
Prediction range

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Business problem Mathematical / algorithms problem
REAL – TIME ANOMALY
DETECTION PROBLEM
Learning: Time series
modeling
Inference: Real time
prediction calculation
REAL TIME ANOMALY DETECTION STRATEGY
CONDITIONAL PREDICTION PROBLEM

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TIME SERIES MODELING
● The modeling process in
finding a function, f, that
explain the present based on
the past: self history and
prediction error
● The model f can be linear,
neural networks, LSTM ...

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Down the ARIMA hole...

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WHY
ARIMA?
(S)ARIMA is the best linear time series model,
consequence of the Wold theorem. It has a very
strong theoretical basis
One model for season, trend, level and noise,
no need to model each part separately.
One to rule them all
Winner model in lots of prediction competitions

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WHAT IS
ARIMA?
Autoregressive part (AR)
Moving average part (MA)

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WHAT IS
SEASONAL
ARIMA?
Non-seasonal part
Seasonal part

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LEARNING ARIMA : THE BIRD EYE VIEW STRATEGY
Maximum likelihood estimation (MLE)
Likelihood :
The loss function
Maximum
finding
Newton algorithmKalman filtering Need to compute
the gradient of the
Kalman filter !

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NEED FOR SPEED

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Standard implementation for
seasonal time series are very slow:
up to 15 min in some cases
BUT...
Need to break the state of the art!

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• The system find the daily pattern (and not the 3h sub-pattern)
• The conditional prediction begins then to be very accurate.
• We are now able to catch even the smallest anomaly.
SEASON IS A KEY COMPONENT

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ANODOT’s scale
5.8 BILLION
DATA POINTS PER DAY
120 MILLION
UNIQUE METRICS
240 MILLION
MODELS
500 MILLION
CORRELATIONS
14 MILLION
SEASONAL METRICS
30 TYPES
OF LEARNING ALGORITHMS

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Probably the fastest
implementation
available in the market
YOU SAID SCALE ?
ANODOT’S PERFORMANCE BREAKTHROUGHS
• Likelihood = O(Ns6)
• BFGS
• Fast Lyapunov equation solver ► Likelihood = O(Ns3)
• Sparse Kalman Filter ► Likelihood = O(Ns2)
• T ~ 10 min
• Fast Hessian approximation, use Newton algorithm
• T ~ 10 sec
• Kalman convergence in likelihood and Gradient ► Likelihood =
O(Ns1.1)
• T ~ 750 ms
• Down sampled SARIMA estimation, Uncoupled estimation
• T ~ 80 ms, Independent of the length of the season !!! O(Ns0)
> 480000x
(4.8 E5)

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SARIMA ESTIMATION : WHERE IS THE TRICK ?
▪ We developed a divide and conquer strategy
Estimation of the slow (seasonal) dynamic
Downsampling
the series
Estimate the
downsampled model
Resample the model1.a. 1.b. 1.c.
1.
Estimation of the fast (non seasonal) dynamic2.
Model
merging
(Convolution)
3. Estimate the
residual
model
4.
Pending US patent

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SURGICAL PRECISION

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EXAMPLE
Before
After

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Anomaly count : 89 vs. 62
ANOTHER EXAMPLE
Before
After

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SUMMARY
● Anomaly detection require time series forecasting
● ARIMA is best in class technique for time series analysis
● Seasonal ARIMA is extremely challenging at scale
● Anodot break the state of the art for learning seasonal model
● As a result, the anomaly detection system sensitivity has been
drastically improved

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THANK YOU
https://www.linkedin.com/in/meirtoledano/