1 High-dimensional time series Rob J Hyndman robjhyndman.com

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 2

Pedestrian counts 3

Pedestrian counts 3 −37.83 −37.82 −37.81 −37.80 −37.79 144.93 144.94 144.95 144.96 144.97 144.98 Longitude Latitude

Pedestrian counts 3 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec M T W T F S S M T W T F S S M T W T F S S M T W T F S S

Sub-daily time series analysis How to visualize many series of sub-daily data over several years? How to identify unusual patterns/incidents? How to forecast sub-daily data taking account of public holidays and special events? 4

Sub-daily time series analysis How to visualize many series of sub-daily data over several years? How to identify unusual patterns/incidents? How to forecast sub-daily data taking account of public holidays and special events? Di Cook Earo Wang Mitchell O’Hara-Wild 4

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 5

Walmart weekly sales data 6

Time series feature analysis Can we use time series features for fast identification of forecasting models? How to generate new time series with specified feature vectors? What can we say about the feature space of time series? 7

Time series feature analysis Can we use time series features for fast identification of forecasting models? How to generate new time series with specified feature vectors? What can we say about the feature space of time series? Kate Smith-Miles George Athanasopoulos Thiyanga Talagala 7

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 8

Security monitoring 9

Security monitoring 10

Time series anomaly detection How to identify anomalous behaviour within streaming data? How to define an anomaly in a large multivariate data set? 11

Time series anomaly detection How to identify anomalous behaviour within streaming data? How to define an anomaly in a large multivariate data set? Kate Smith-Miles Mario Andrés Muñoz Acosta Sevvandi Kandanaarachchi Dilini Talagala 11

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 12

Forecast reconciliation 13 Total A AA AAA AAB AAC AB ABA ABB ABC AC ACA ACB ACC B BA BAA BAB BAC BB BBA BBB BBC BC BCA BCB BCC C CA CAA CAB CAC CB CBA CBB CBC CC CCA CCB CCC

Forecast reconciliation Forecasts at all nodes must be coherent Bottom level typically has thousands or millions of time series How to define coherence probabilistically? How to visualize so many time series? 14

Forecast reconciliation Forecasts at all nodes must be coherent Bottom level typically has thousands or millions of time series How to define coherence probabilistically? How to visualize so many time series? 14 George Athanasopoulos Anastasios Panagiotelis Shanika Wickramasuriya Puwasala Gamakumara Earo Wang

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 15

Electricity demand 16

Electricity demand 16

Electricity demand 17 Monday Tuesday Wednesday Thursday Friday Saturday Sunday 1539 1549 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 6 12 18 24 0 2 4 6 0 2 4 6 Time of day Demand (kWh) Percentile 10 25 50 75 90

Electricity demand How to forecast future demand by household? How to reconcile household demand forecasts with state and national demand forecasts? How to identify unusual demand patterns? How to measure forecast accuracy when forecasts are probability distributions within a hierarchy? 18

Electricity demand How to forecast future demand by household? How to reconcile household demand forecasts with state and national demand forecasts? How to identify unusual demand patterns? How to measure forecast accuracy when forecasts are probability distributions within a hierarchy? Souhaib Ben Taieb Cameron Roach 18

Outline 1 Sub-daily time series analysis 2 Time series feature analysis 3 Time series anomaly detection 4 Forecast reconciliation 5 Probabilistic electricity demand analysis 6 NUMBAT 19

NUMBAT: Non-Uniform Monash Business Analytics Team 20 Test Post-docs Nick Tierney Sevvandi Kandanaarachchi Shanika Wickramasuriya