fable::ISF2019

## Flexible futures for fable functionality

.bottom[
### Mitchell O'Hara-Wild (<svg style="height:0.8em;top:.04em;position:relative;fill:#1da1f2;" viewBox="0 0 512 512"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>[@mitchoharawild](https://twitter.com/mitchoharawild))
### Rob Hyndman (<svg style="height:0.8em;top:.04em;position:relative;fill:#1da1f2;" viewBox="0 0 512 512"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg>[@robjhyndman](https://twitter.com/robjhyndman/))
### 19 June 2019
### Slides @ [slides.mitchelloharawild.com/isf2019](https://slides.mitchelloharawild.com/isf2019)
]

---
class: center

.animated.fadeIn[
## Forecasting with the tidyverts

]

---
class: center

## Forecasting with the tidyverts

.animated.fadeIn[
.sticker[![tsibbledata](resources/tsibbledata.svg)]
.sticker[![feasts](resources/feasts.svg)]
.sticker[![tsibble](resources/tsibble.svg)]

## [tidyverts.org](http://www.tidyverts.org)
]

---

# Tidy temporal data structure

### Domestic tourism in Australia

```r
library(tsibble)
tourism
```

```
#> # A tsibble: 24,320 x 5 [1Q]
#> # Key:       Region, State, Purpose [304]
#>    Quarter Region   State           Purpose  Trips
#>      <qtr> <chr>    <chr>           <chr>    <dbl>
#>  1 1998 Q1 Adelaide South Australia Business  135.
#>  2 1998 Q2 Adelaide South Australia Business  110.
#>  3 1998 Q3 Adelaide South Australia Business  166.
#>  4 1998 Q4 Adelaide South Australia Business  127.
#>  5 1999 Q1 Adelaide South Australia Business  137.
#>  6 1999 Q2 Adelaide South Australia Business  200.
#>  7 1999 Q3 Adelaide South Australia Business  169.
#>  8 1999 Q4 Adelaide South Australia Business  134.
#>  9 2000 Q1 Adelaide South Australia Business  154.
#> 10 2000 Q2 Adelaide South Australia Business  169.
#> # … with 24,310 more rows
```

---

# A peak at the features

### Compute features relating to STL decompositions

```r
library(feasts)
tourism_features <- tourism %>% 
  features(Trips, feature_set(tags = "stl"))
```

```
#> # A tibble: 304 x 10
#>    Region  State Purpose trend_strength seasonal_streng… spikiness linearity curvature seasonal_peak_y… seasonal_trough…
#>    <chr>   <chr> <chr>            <dbl>            <dbl>     <dbl>     <dbl>     <dbl>            <dbl>            <dbl>
#>  1 Adelai… Sout… Busine…          0.451            0.380   1.62e+2    -5.51     71.4                  3                1
#>  2 Adelai… Sout… Holiday          0.541            0.601   9.95e+0    48.9      78.2                  1                3
#>  3 Adelai… Sout… Other            0.743            0.189   2.28e+0    95.0      43.4                  2                1
#>  4 Adelai… Sout… Visiti…          0.433            0.446   6.01e+1    34.9      71.1                  1                3
#>  5 Adelai… Sout… Busine…          0.453            0.140   1.18e-1     0.944    -3.30                 3                1
#>  6 Adelai… Sout… Holiday          0.512            0.244   1.92e-1    10.4      23.8                  2                1
#>  7 Adelai… Sout… Other            0.584            0.374   5.02e-4     4.29      3.21                 2                2
#>  8 Adelai… Sout… Visiti…          0.481            0.228   7.56e+0    34.3      -0.587                0                3
#>  9 Alice … Nort… Busine…          0.526            0.224   1.79e-1    23.8      19.6                  0                1
#> 10 Alice … Nort… Holiday          0.377            0.827   8.13e-1   -19.6      10.3                  3                1
#> # … with 294 more rows
```

---

# A peak at the features

```r
library(ggplot2)
tourism_features %>% 
  ggplot(aes(x = trend_strength, y = seasonal_strength_year, colour = Purpose)) + 
  geom_point() + stat_density_2d(aes(fill = Purpose, alpha = ..level..), bins = 5, geom = "polygon") + 
  facet_wrap(vars(Purpose), nrow = 1) + coord_equal() + xlim(c(0,1)) + ylim(c(0,1))
```

<img src="figure/tourism-features-plot-1.svg" style="display: block; margin: auto;" />
]

---

# Total holidays across Australia

### Starting from the top

```r
library(dplyr)
holiday_aus <- tourism %>% 
  filter(Purpose == "Holiday") %>% 
  summarise(Trips = sum(Trips))

holiday_aus %>% 
  autoplot(Trips)
```

```
#> # A tsibble: 80 x 2 [1Q]
#>    Quarter  Trips
#>      <qtr>  <dbl>
#>  1 1998 Q1 11806.
#>  2 1998 Q2  9276.
#>  3 1998 Q3  8642.
#>  4 1998 Q4  9300.
#>  5 1999 Q1 11172.
#>  6 1999 Q2  9608.
#>  7 1999 Q3  8914.
#>  8 1999 Q4  9026.
#>  9 2000 Q1 11071.
#> 10 2000 Q2  9196.
#> # … with 70 more rows
```
.full-width[
<img src="figure/tourism-total-plot-1.svg" style="display: block; margin: auto;" />
]
]

---

# Forecasting with fable

### Look at the data

<br>

```r
*holiday_aus
```
]
.right-plot[

---

# Forecasting with fable

### Specify and estimate a model

<br>

```r
holiday_aus %>% 
* model(ETS(Trips))
```
]
.right-plot[

```
#> # A mable: 1 x 1
#>   `ETS(Trips)`
#>   <model>     
#> 1 <ETS(M,N,M)>
```
]

---

# Forecasting with fable

### Make some forecasts

<br>

```r
holiday_aus %>% 
  model(ETS(Trips)) %>% 
* forecast(h = "3 years")
```
]
.right-plot[

```
#> # A fable: 12 x 4 [1Q]
#> # Key:     .model [1]
#>    .model     Quarter  Trips .distribution   
#>    <chr>        <qtr>  <dbl> <dist>          
#>  1 ETS(Trips) 2018 Q1 13088. N(13088, 368663)
#>  2 ETS(Trips) 2018 Q2 10909. N(10909, 288993)
#>  3 ETS(Trips) 2018 Q3 10442. N(10442, 294873)
#>  4 ETS(Trips) 2018 Q4 10624. N(10624, 336446)
#>  5 ETS(Trips) 2019 Q1 13088. N(13088, 558216)
#>  6 ETS(Trips) 2019 Q2 10909. N(10909, 420721)
#>  7 ETS(Trips) 2019 Q3 10442. N(10442, 415586)
#>  8 ETS(Trips) 2019 Q4 10624. N(10624, 461447)
#>  9 ETS(Trips) 2020 Q1 13088. N(13088, 747978)
#> 10 ETS(Trips) 2020 Q2 10909. N(10909, 552594)
#> 11 ETS(Trips) 2020 Q3 10442. N(10442, 536433)
#> 12 ETS(Trips) 2020 Q4 10624. N(10624, 586585)
```
]

---

# Forecasting with fable

### See the results!

<br>

```r
holiday_aus %>% 
  model(ETS(Trips)) %>% 
  forecast(h = "3 years") %>% 
* autoplot(holiday_aus)
```
]
.right-plot[
<img src="figure/tourism-total-ets-plot-output-1.svg" style="display: block; margin: auto;" />
]

---

<br>

## It's easy to make forecasts...

<br>

# But are they good forecasts?

---
class: top

# Forecast accuracy evaluation

### MASE: Mean absolute scaled error

`$$\text{MASE} = \dfrac{1}{h}\sum_{t = T+1}^{T+h}\left|\frac{\displaystyle e_{t}}{\text{scale}}\right|, \hspace{2em}\text{scale} = \displaystyle\frac{1}{T-m}\sum_{t=m+1}^T |y_{t}-y_{t-m}|$$`

???

The scale is the mean absolute error (MAE) of the seasonal naive model. Essentially, MASE is an accuracy measure relative to the seasonal naive model.

---
class: top

# Comparing multiple models

### Estimate multiple models

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
*   ets_n = ETS(Trips ~ trend("N")),
*   ets_a = ETS(Trips ~ trend("A")),
*   arima = ARIMA(Trips)
  )
```
]
.right-plot[

```
#> # A mable: 1 x 3
#>   ets_n        ets_a        arima                   
#>   <model>      <model>      <model>                 
#> 1 <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(0,0,0)(0,1,2)[4]>
```
]

---

# Comparing multiple models

### Forecasts from multiple models

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
* forecast(h = "3 years") %>%
* autoplot(holiday_aus, level = NULL)
```
]
.right-plot[
<img src="figure/tourism-total-many-plot-output-1.svg" style="display: block; margin: auto;" />
]

---

# Comparing multiple models

### Forecast accuracy

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  forecast(h = "3 years") %>%
* accuracy(holiday_aus) %>%
* arrange(MASE)
```
]
.right-plot[

```
#> # A tibble: 3 x 9
#>   .model .type    ME  RMSE   MAE   MPE  MAPE  MASE  ACF1
#>   <chr>  <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 ets_a  Test   581.  700.  581.  5.36  5.36  1.46 0.304
#> 2 ets_n  Test   939. 1061.  939.  8.69  8.69  2.36 0.415
#> 3 arima  Test  1261. 1380. 1261. 11.7  11.7   3.16 0.425
```
]

---
class: inverse, top

<br>

# Improving forecast accuracy

## Idea 1: Model ensembling

### Is the combination better than its parts?

---

# Model ensembling

### A simple average of forecasts

```r
holiday_aus %>%
  filter(Quarter < yearquarter("2015 Q1")) %>%  
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  mutate(
*   combn = (ets_n + ets_a + arima)/3
  )
```
]
.right-plot[

```
#> # A mable: 1 x 4
#>   ets_n        ets_a        arima                    combn        
#>   <model>      <model>      <model>                  <model>      
#> 1 <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(0,0,0)(0,1,2)[4]> <COMBINATION>
```
]

---

# Model ensembling

### A simple average of forecasts

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  mutate(
    combn = (ets_n + ets_a + arima)/3
  ) %>% 
* select(combn) %>%
* forecast(h = "3 years")
```
]
.right-plot[

```
#> # A fable: 12 x 4 [1Q]
#> # Key:     .model [1]
#>    .model Quarter  Trips .distribution   
#>    <chr>    <qtr>  <dbl> <dist>          
#>  1 combn  2015 Q1 11254. N(11254, 253832)
#>  2 combn  2015 Q2  9523. N( 9523, 207426)
#>  3 combn  2015 Q3  8981. N( 8981, 201685)
#>  4 combn  2015 Q4  9188. N( 9188, 214675)
#>  5 combn  2016 Q1 11265. N(11265, 314195)
#>  6 combn  2016 Q2  9466. N( 9466, 256278)
#>  7 combn  2016 Q3  9006. N( 9006, 249327)
#>  8 combn  2016 Q4  9175. N( 9175, 265807)
#>  9 combn  2017 Q1 11330. N(11330, 376395)
#> 10 combn  2017 Q2  9520. N( 9520, 304698)
#> 11 combn  2017 Q3  9058. N( 9058, 296063)
#> 12 combn  2017 Q4  9227. N( 9227, 316203)
```
]

---

# Model ensembling

### Is it better? Check the forecasts.

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  forecast(h = "3 years") %>% 
* autoplot(holiday_aus, level = NULL)
```
]
.right-plot[
<img src="figure/tourism-total-combn-plot-output-1.svg" style="display: block; margin: auto;" />
]

---

# Model ensembling

### Is it better? Forecast accuracy

```r
holiday_aus %>% 
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  forecast(h = "3 years") %>% 
* accuracy(holiday_aus) %>%
* arrange(MASE)
```
]
.right-plot[

```
#> # A tibble: 4 x 9
#>   .model .type    ME  RMSE   MAE   MPE  MAPE  MASE  ACF1
#>   <chr>  <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 ets_a  Test   581.  700.  581.  5.36  5.36  1.46 0.304
#> 2 combn  Test   927. 1042.  927.  8.57  8.57  2.33 0.390
#> 3 ets_n  Test   939. 1061.  939.  8.69  8.69  2.36 0.415
#> 4 arima  Test  1261. 1380. 1261. 11.7  11.7   3.16 0.425
```
]

---

# Inconclusive for just one series

### Consider all series in the data...

```r
tourism
```

---

# But wait, there's more! Aggregations over keys.

<div id="htmlwidget-cc8cf9fc9228a7dd4f98" style="width:100%;height:550px;" class="collapsibleTree html-widget"></div>
<script type="application/json" data-for="htmlwidget-cc8cf9fc9228a7dd4f98">{"x":{"data":{"name":"Total Tourism","children":[{"name":"Business","children":[{"name":"South Australia","children":[{"name":"Adelaide"},{"name":"Adelaide Hills"},{"name":"Barossa"},{"name":"Clare Valley"},{"name":"Eyre Peninsula"},{"name":"Fleurieu Peninsula"},{"name":"Flinders Ranges and Outback"},{"name":"Kangaroo Island"},{"name":"Limestone Coast"},{"name":"Murraylands"},{"name":"Riverland"},{"name":"Yorke Peninsula"}]},{"name":"Northern Territory","children":[{"name":"Alice Springs"},{"name":"Barkly"},{"name":"Darwin"},{"name":"Kakadu Arnhem"},{"name":"Katherine Daly"},{"name":"Lasseter"},{"name":"MacDonnell"}]},{"name":"Western Australia","children":[{"name":"Australia's Coral Coast"},{"name":"Australia's Golden Outback"},{"name":"Australia's North West"},{"name":"Australia's South West"},{"name":"Experience Perth"}]},{"name":"Victoria","children":[{"name":"Ballarat"},{"name":"Bendigo Loddon"},{"name":"Central Highlands"},{"name":"Central Murray"},{"name":"Geelong and the Bellarine"},{"name":"Gippsland"},{"name":"Goulburn"},{"name":"Great Ocean Road"},{"name":"High Country"},{"name":"Lakes"},{"name":"Macedon"},{"name":"Mallee"},{"name":"Melbourne"},{"name":"Melbourne East"},{"name":"Murray East"},{"name":"Peninsula"},{"name":"Phillip Island"},{"name":"Spa Country"},{"name":"Upper Yarra"},{"name":"Western Grampians"},{"name":"Wimmera"}]},{"name":"New South Wales","children":[{"name":"Blue Mountains"},{"name":"Capital Country"},{"name":"Central Coast"},{"name":"Central NSW"},{"name":"Hunter"},{"name":"New England North West"},{"name":"North Coast NSW"},{"name":"Outback NSW"},{"name":"Riverina"},{"name":"Snowy Mountains"},{"name":"South Coast"},{"name":"Sydney"},{"name":"The Murray"}]},{"name":"Queensland","children":[{"name":"Brisbane"},{"name":"Bundaberg"},{"name":"Central Queensland"},{"name":"Darling Downs"},{"name":"Fraser Coast"},{"name":"Gold Coast"},{"name":"Mackay"},{"name":"Northern"},{"name":"Outback"},{"name":"Sunshine Coast"},{"name":"Tropical North Queensland"},{"name":"Whitsundays"}]},{"name":"ACT","children":[{"name":"Canberra"}]},{"name":"Tasmania","children":[{"name":"East Coast"},{"name":"Hobart and the South"},{"name":"Launceston, Tamar and the North"},{"name":"North West"},{"name":"Wilderness West"}]}]},{"name":"Holiday","children":[{"name":"South Australia","children":[{"name":"Adelaide"},{"name":"Adelaide Hills"},{"name":"Barossa"},{"name":"Clare Valley"},{"name":"Eyre Peninsula"},{"name":"Fleurieu Peninsula"},{"name":"Flinders Ranges and Outback"},{"name":"Kangaroo Island"},{"name":"Limestone Coast"},{"name":"Murraylands"},{"name":"Riverland"},{"name":"Yorke Peninsula"}]},{"name":"Northern Territory","children":[{"name":"Alice Springs"},{"name":"Barkly"},{"name":"Darwin"},{"name":"Kakadu Arnhem"},{"name":"Katherine Daly"},{"name":"Lasseter"},{"name":"MacDonnell"}]},{"name":"Western Australia","children":[{"name":"Australia's Coral Coast"},{"name":"Australia's Golden Outback"},{"name":"Australia's North West"},{"name":"Australia's South West"},{"name":"Experience Perth"}]},{"name":"Victoria","children":[{"name":"Ballarat"},{"name":"Bendigo Loddon"},{"name":"Central Highlands"},{"name":"Central Murray"},{"name":"Geelong and the Bellarine"},{"name":"Gippsland"},{"name":"Goulburn"},{"name":"Great Ocean Road"},{"name":"High Country"},{"name":"Lakes"},{"name":"Macedon"},{"name":"Mallee"},{"name":"Melbourne"},{"name":"Melbourne East"},{"name":"Murray East"},{"name":"Peninsula"},{"name":"Phillip Island"},{"name":"Spa Country"},{"name":"Upper Yarra"},{"name":"Western Grampians"},{"name":"Wimmera"}]},{"name":"New South Wales","children":[{"name":"Blue Mountains"},{"name":"Capital Country"},{"name":"Central Coast"},{"name":"Central NSW"},{"name":"Hunter"},{"name":"New England North West"},{"name":"North Coast NSW"},{"name":"Outback NSW"},{"name":"Riverina"},{"name":"Snowy Mountains"},{"name":"South Coast"},{"name":"Sydney"},{"name":"The Murray"}]},{"name":"Queensland","children":[{"name":"Brisbane"},{"name":"Bundaberg"},{"name":"Central Queensland"},{"name":"Darling Downs"},{"name":"Fraser Coast"},{"name":"Gold Coast"},{"name":"Mackay"},{"name":"Northern"},{"name":"Outback"},{"name":"Sunshine Coast"},{"name":"Tropical North Queensland"},{"name":"Whitsundays"}]},{"name":"ACT","children":[{"name":"Canberra"}]},{"name":"Tasmania","children":[{"name":"East Coast"},{"name":"Hobart and the South"},{"name":"Launceston, Tamar and the North"},{"name":"North West"},{"name":"Wilderness West"}]}]},{"name":"Other","children":[{"name":"South Australia","children":[{"name":"Adelaide"},{"name":"Adelaide Hills"},{"name":"Barossa"},{"name":"Clare Valley"},{"name":"Eyre Peninsula"},{"name":"Fleurieu Peninsula"},{"name":"Flinders Ranges and Outback"},{"name":"Kangaroo Island"},{"name":"Limestone Coast"},{"name":"Murraylands"},{"name":"Riverland"},{"name":"Yorke Peninsula"}]},{"name":"Northern Territory","children":[{"name":"Alice Springs"},{"name":"Barkly"},{"name":"Darwin"},{"name":"Kakadu Arnhem"},{"name":"Katherine Daly"},{"name":"Lasseter"},{"name":"MacDonnell"}]},{"name":"Western Australia","children":[{"name":"Australia's Coral Coast"},{"name":"Australia's Golden Outback"},{"name":"Australia's North West"},{"name":"Australia's South West"},{"name":"Experience Perth"}]},{"name":"Victoria","children":[{"name":"Ballarat"},{"name":"Bendigo Loddon"},{"name":"Central Highlands"},{"name":"Central Murray"},{"name":"Geelong and the Bellarine"},{"name":"Gippsland"},{"name":"Goulburn"},{"name":"Great Ocean Road"},{"name":"High Country"},{"name":"Lakes"},{"name":"Macedon"},{"name":"Mallee"},{"name":"Melbourne"},{"name":"Melbourne East"},{"name":"Murray East"},{"name":"Peninsula"},{"name":"Phillip Island"},{"name":"Spa Country"},{"name":"Upper Yarra"},{"name":"Western Grampians"},{"name":"Wimmera"}]},{"name":"New South Wales","children":[{"name":"Blue Mountains"},{"name":"Capital Country"},{"name":"Central Coast"},{"name":"Central NSW"},{"name":"Hunter"},{"name":"New England North West"},{"name":"North Coast NSW"},{"name":"Outback NSW"},{"name":"Riverina"},{"name":"Snowy Mountains"},{"name":"South Coast"},{"name":"Sydney"},{"name":"The Murray"}]},{"name":"Queensland","children":[{"name":"Brisbane"},{"name":"Bundaberg"},{"name":"Central Queensland"},{"name":"Darling Downs"},{"name":"Fraser Coast"},{"name":"Gold Coast"},{"name":"Mackay"},{"name":"Northern"},{"name":"Outback"},{"name":"Sunshine Coast"},{"name":"Tropical North Queensland"},{"name":"Whitsundays"}]},{"name":"ACT","children":[{"name":"Canberra"}]},{"name":"Tasmania","children":[{"name":"East Coast"},{"name":"Hobart and the South"},{"name":"Launceston, Tamar and the North"},{"name":"North West"},{"name":"Wilderness West"}]}]},{"name":"Visiting","children":[{"name":"South Australia","children":[{"name":"Adelaide"},{"name":"Adelaide Hills"},{"name":"Barossa"},{"name":"Clare Valley"},{"name":"Eyre Peninsula"},{"name":"Fleurieu Peninsula"},{"name":"Flinders Ranges and Outback"},{"name":"Kangaroo Island"},{"name":"Limestone Coast"},{"name":"Murraylands"},{"name":"Riverland"},{"name":"Yorke Peninsula"}]},{"name":"Northern Territory","children":[{"name":"Alice Springs"},{"name":"Barkly"},{"name":"Darwin"},{"name":"Kakadu Arnhem"},{"name":"Katherine Daly"},{"name":"Lasseter"},{"name":"MacDonnell"}]},{"name":"Western Australia","children":[{"name":"Australia's Coral Coast"},{"name":"Australia's Golden Outback"},{"name":"Australia's North West"},{"name":"Australia's South West"},{"name":"Experience Perth"}]},{"name":"Victoria","children":[{"name":"Ballarat"},{"name":"Bendigo Loddon"},{"name":"Central Highlands"},{"name":"Central Murray"},{"name":"Geelong and the Bellarine"},{"name":"Gippsland"},{"name":"Goulburn"},{"name":"Great Ocean Road"},{"name":"High Country"},{"name":"Lakes"},{"name":"Macedon"},{"name":"Mallee"},{"name":"Melbourne"},{"name":"Melbourne East"},{"name":"Murray East"},{"name":"Peninsula"},{"name":"Phillip Island"},{"name":"Spa Country"},{"name":"Upper Yarra"},{"name":"Western Grampians"},{"name":"Wimmera"}]},{"name":"New South Wales","children":[{"name":"Blue Mountains"},{"name":"Capital Country"},{"name":"Central Coast"},{"name":"Central NSW"},{"name":"Hunter"},{"name":"New England North West"},{"name":"North Coast NSW"},{"name":"Outback NSW"},{"name":"Riverina"},{"name":"Snowy Mountains"},{"name":"South Coast"},{"name":"Sydney"},{"name":"The Murray"}]},{"name":"Queensland","children":[{"name":"Brisbane"},{"name":"Bundaberg"},{"name":"Central Queensland"},{"name":"Darling Downs"},{"name":"Fraser Coast"},{"name":"Gold Coast"},{"name":"Mackay"},{"name":"Northern"},{"name":"Outback"},{"name":"Sunshine Coast"},{"name":"Tropical North Queensland"},{"name":"Whitsundays"}]},{"name":"ACT","children":[{"name":"Canberra"}]},{"name":"Tasmania","children":[{"name":"East Coast"},{"name":"Hobart and the South"},{"name":"Launceston, Tamar and the North"},{"name":"North West"},{"name":"Wilderness West"}]}]}]},"options":{"hierarchy":["Purpose","State","Region"],"input":null,"attribute":"leafCount","linkLength":null,"fontSize":14,"tooltip":false,"collapsed":true,"zoomable":false,"margin":{"top":20,"bottom":20,"left":116,"right":242},"fill":"lightsteelblue"}},"evals":[],"jsHooks":[]}</script>

---

# Consider _all_ series in the data...

```r
tourism_aggregated <- tourism %>% 
* aggregate_key((State / Region) * Purpose, Trips = sum(Trips))
```

```
#> # A tsibble: 34,000 x 5 [1Q]
#> # Key:       State, Region, Purpose [425]
#>    State   Region  Purpose Quarter  Trips
#>    <chr>   <chr>   <chr>     <qtr>  <dbl>
#>  1 <total> <total> <total> 1998 Q1 23182.
#>  2 <total> <total> <total> 1998 Q2 20323.
#>  3 <total> <total> <total> 1998 Q3 19827.
#>  4 <total> <total> <total> 1998 Q4 20830.
#>  5 <total> <total> <total> 1999 Q1 22087.
#>  6 <total> <total> <total> 1999 Q2 21458.
#>  7 <total> <total> <total> 1999 Q3 19914.
#>  8 <total> <total> <total> 1999 Q4 20028.
#>  9 <total> <total> <total> 2000 Q1 22339.
#> 10 <total> <total> <total> 2000 Q2 19941.
#> # … with 33,990 more rows
```

---

# Modelling may take a while...

### Fortunately, this is embarrassingly parallel!

```r
*library(future)
*plan(multiprocess)
tourism_fit <- tourism_aggregated %>%
  filter(Quarter < yearquarter("2015 Q1")) %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  ) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3)
```

```
#> # A mable: 425 x 7
#> # Key:     State, Region, Purpose [425]
#>    State   Region  Purpose  ets_n        ets_a        arima                            combn        
#>    <chr>   <chr>   <chr>    <model>      <model>      <model>                          <model>      
#>  1 <total> <total> <total>  <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(1,0,1)(1,1,0)[4]>         <COMBINATION>
#>  2 <total> <total> Business <ETS(M,N,M)> <ETS(M,A,A)> <ARIMA(0,0,1)(2,1,0)[4]>         <COMBINATION>
#>  3 <total> <total> Holiday  <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(0,0,0)(0,1,2)[4]>         <COMBINATION>
#>  4 <total> <total> Other    <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,1,1)(1,0,0)[4]>         <COMBINATION>
#>  5 <total> <total> Visiting <ETS(M,N,M)> <ETS(A,A,A)> <ARIMA(1,0,1)(2,1,0)[4]>         <COMBINATION>
#>  6 ACT     <total> <total>  <ETS(A,N,N)> <ETS(M,A,N)> <ARIMA(0,0,0) w/ mean>           <COMBINATION>
#>  7 ACT     <total> Business <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,0,0)(1,0,0)[4] w/ mean> <COMBINATION>
#>  8 ACT     <total> Holiday  <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,0,0)(1,0,0)[4] w/ mean> <COMBINATION>
#>  9 ACT     <total> Other    <ETS(A,N,N)> <ETS(M,A,N)> <ARIMA(0,0,0) w/ mean>           <COMBINATION>
#> 10 ACT     <total> Visiting <ETS(A,N,N)> <ETS(A,A,N)> <ARIMA(1,0,0) w/ mean>           <COMBINATION>
#> # … with 415 more rows
```

---

## Producing forecasts are no different

```r
tourism_fc <- tourism_fit %>% forecast(h = "3 years")
```
.full-width[
<img src="figure/fc-agg-fc-plot-out-1.svg" style="display: block; margin: auto;" />
]

---

# Are the combinations better?

### Forecast accuracy

```r
tourism_fc %>% 
* accuracy(tourism_aggregated) %>%
* arrange(MASE)
```

```
#> # A tibble: 1,700 x 12
#>    .model State              Region          Purpose  .type      ME   RMSE    MAE      MPE   MAPE  MASE    ACF1
#>    <chr>  <chr>              <chr>           <chr>    <chr>   <dbl>  <dbl>  <dbl>    <dbl>  <dbl> <dbl>   <dbl>
#>  1 ets_a  South Australia    Kangaroo Island Other    Test   0.0294  0.253  0.114 -Inf     Inf    0.172 -0.0738
#>  2 ets_n  South Australia    Eyre Peninsula  Holiday  Test   0.513   4.59   3.70     0.169  10.5  0.328  0.117 
#>  3 ets_a  Victoria           Peninsula       Business Test   1.55    4.65   3.68     3.63   17.9  0.366 -0.131 
#>  4 ets_a  New South Wales    Sydney          <total>  Test  -4.38   71.1   64.6     -0.344   2.83 0.410 -0.189 
#>  5 ets_n  Victoria           High Country    Other    Test   0.909   4.34   3.03    -8.61   34.4  0.421 -0.353 
#>  6 arima  Victoria           High Country    Other    Test   0.912   4.37   3.06    -8.70   34.7  0.425 -0.352 
#>  7 combn  South Australia    Eyre Peninsula  Holiday  Test   2.13    5.64   4.81     3.41   12.8  0.427  0.0170
#>  8 ets_a  Victoria           Upper Yarra     Other    Test   0.854   2.50   1.41  -Inf     Inf    0.430 -0.238 
#>  9 ets_a  Northern Territory MacDonnell      Other    Test   0.316   0.816  0.318  NaN     Inf    0.436 -0.160 
#> 10 ets_n  Queensland         Mackay          Holiday  Test  -0.469  12.7    9.43   -12.6    25.8  0.444 -0.536 
#> # … with 1,690 more rows
```

---

# Are the combinations better?

### Forecast accuracy

```r
tourism_fc %>% 
  accuracy(tourism_aggregated) %>% 
* group_by(.model) %>%
* summarise_at(vars(ME:ACF1), median) %>%
  arrange(MASE)
```

```
#> # A tibble: 4 x 8
#>   .model    ME  RMSE   MAE   MPE  MAPE  MASE    ACF1
#>   <chr>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl>
#> 1 ets_n   8.73  18.9  15.1  7.23  25.0 0.982 -0.0852
#> 2 combn   8.77  19.4  15.5  7.39  24.1 0.995 -0.0848
#> 3 ets_a   7.65  20.2  15.8 NA     26.0 1.03  -0.0733
#> 4 arima   9.01  20.3  16.5  8.07  26.2 1.07  -0.0849
```

---
class: inverse, top

<br>

# Improving forecast accuracy

## Idea 2: Forecast reconciliation

### Does imposing aggregation structure improve the forecasts?

---

# Forecast reconciliation

<div id="htmlwidget-dc638aec296b6b43a83b" style="width:100%;height:550px;" class="collapsibleTree html-widget"></div>
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Queensland"},{"name":"Whitsundays"}]},{"name":"ACT","children":[{"name":"Canberra"}]},{"name":"Tasmania","children":[{"name":"East Coast"},{"name":"Hobart and the South"},{"name":"Launceston, Tamar and the North"},{"name":"North West"},{"name":"Wilderness West"}]}]}]},"options":{"hierarchy":["Purpose","State","Region"],"input":null,"attribute":"leafCount","linkLength":null,"fontSize":14,"tooltip":false,"collapsed":true,"zoomable":false,"margin":{"top":20,"bottom":20,"left":116,"right":242},"fill":"lightsteelblue"}},"evals":[],"jsHooks":[]}</script>

---

# Forecast reconciliation

### MinT with covariance shrink

```r
tourism_fc_reconciled <- tourism_fit %>% 
* reconcile(coherent = min_trace(combn, method = "shrink")) %>%
  forecast(h = "3 years")
```

```
#> # A fable: 25,500 x 7 [1Q]
#> # Key:     State, Region, Purpose, .model [2,125]
#>    State   Region  Purpose .model Quarter  Trips .distribution    
#>    <chr>   <chr>   <chr>   <chr>    <qtr>  <dbl> <dist>           
#>  1 <total> <total> <total> ets_n  2015 Q1 25108. N(25108, 1078489)
#>  2 <total> <total> <total> ets_n  2015 Q2 23339. N(23339, 1171475)
#>  3 <total> <total> <total> ets_n  2015 Q3 22771. N(22771, 1343242)
#>  4 <total> <total> <total> ets_n  2015 Q4 23417. N(23417, 1661871)
#>  5 <total> <total> <total> ets_n  2016 Q1 25108. N(25108, 2188347)
#>  6 <total> <total> <total> ets_n  2016 Q2 23339. N(23339, 2130906)
#>  7 <total> <total> <total> ets_n  2016 Q3 22771. N(22771, 2256904)
#>  8 <total> <total> <total> ets_n  2016 Q4 23417. N(23417, 2628507)
#>  9 <total> <total> <total> ets_n  2017 Q1 25108. N(25108, 3300157)
#> 10 <total> <total> <total> ets_n  2017 Q2 23339. N(23339, 3092023)
#> # … with 25,490 more rows
```

---

# Forecast reconciliation

### Is it better? Forecast accuracy

```r
tourism_fc_reconciled %>% 
  accuracy(tourism_aggregated) %>% 
  group_by(.model) %>%
  summarise_at(vars(ME:ACF1), median) %>% 
  arrange(MASE)
```

```
#> # A tibble: 5 x 8
#>   .model      ME  RMSE   MAE   MPE  MAPE  MASE    ACF1
#>   <chr>    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl>
#> 1 coherent  6.34  18.2  14.6 NA     22.6 0.934 -0.0834
#> 2 ets_n     8.73  18.9  15.1  7.23  25.0 0.982 -0.0852
#> 3 combn     8.77  19.4  15.5  7.39  24.1 0.995 -0.0848
#> 4 ets_a     7.65  20.2  15.8 NA     26.0 1.03  -0.0733
#> 5 arima     9.01  20.3  16.5  8.07  26.2 1.07  -0.0849
```

---
class: inverse

.title[Summary <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 512 512"><path d="M505 442.7L405.3 343c-4.5-4.5-10.6-7-17-7H372c27.6-35.3 44-79.7 44-128C416 93.1 322.9 0 208 0S0 93.1 0 208s93.1 208 208 208c48.3 0 92.7-16.4 128-44v16.3c0 6.4 2.5 12.5 7 17l99.7 99.7c9.4 9.4 24.6 9.4 33.9 0l28.3-28.3c9.4-9.4 9.4-24.6.1-34zM208 336c-70.7 0-128-57.2-128-128 0-70.7 57.2-128 128-128 70.7 0 128 57.2 128 128 0 70.7-57.2 128-128 128z"/></svg>]

```r
library(fable)
library(tidyverse)
tsibble::tourism %>% 
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>% 
  model(ets_n = ETS(Trips ~ trend("N")),
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  reconcile(coherent = min_trace(combn)) %>% 
  forecast(h = "3 years")
```

---
class: inverse

```r
*library(fable)
*library(tidyverse)
tsibble::tourism %>% 
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>% 
  model(ets_n = ETS(Trips ~ trend("N")),
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  reconcile(coherent = min_trace(combn)) %>% 
  forecast(h = "3 years")
```

### Integrates seamlessly with the tidyverse.

---
class: inverse

```r
library(fable)
library(tidyverse)
*tsibble::tourism %>%
* aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")),
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  reconcile(coherent = min_trace(combn)) %>% 
  forecast(h = "3 years")
```

### Tidy temporal data suitable for the future of time series.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>%
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
* model(ets_n = ETS(Trips ~ trend("N")),
*       ens_a = ETS(Trips ~ trend("A")),
*       arima = ARIMA(Trips)) %>%
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  reconcile(coherent = min_trace(combn)) %>% 
  forecast(h = "3 years")
```

### Flexible, and succinct model specification.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>%
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")), 
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
* mutate(combn = (ets_n + ets_a + arima)/3) %>%
  reconcile(coherent = min_trace(combn)) %>% 
  forecast(h = "3 years")
```

### Intuitive interface for model combinations.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>%
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")), 
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
* reconcile(coherent = min_trace(combn)) %>%
  forecast(h = "3 years")
```

### Flexible forecast reconciliation without changing workflow.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>%
  aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")), 
        ens_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips)) %>% 
  mutate(combn = (ets_n + ets_a + arima)/3) %>% 
  reconcile(coherent = min_trace(combn)) %>%
* forecast(h = "3 years")
```

### Distributional forecasts in a data format.

---
class: inverse

```r
*library(fable)
*library(tidyverse)
*tsibble::tourism %>%
* aggregate_key((State / Region) * Purpose, Trips = sum(Trips)) %>%
* model(ets_n = ETS(Trips ~ trend("N")),
*       ens_a = ETS(Trips ~ trend("A")),
*       arima = ARIMA(Trips)) %>%
* mutate(combn = (ets_n + ets_a + arima)/3) %>%
* reconcile(coherent = min_trace(combn)) %>%
* forecast(h = "3 years")
```

### Reconciled ensemble forecasts for 425 series.

---
class: inverse, center

# Acknowledgements

.pull-left[
.face-border[![Rob Hyndman](https://pbs.twimg.com/profile_images/1103150025981321216/dV3Wz_ql_400x400.png)]

Rob Hyndman
]
.pull-right[
.face-border[![Earo Wang](https://pbs.twimg.com/profile_images/1122341439063519233/YanRXXLu_400x400.jpg)]

Earo Wang
]

### Join our group.

Monash University is now hiring in business analytics.

See [bit.ly/monash-ba](bit.ly/monash-ba) for details.

---

.title[Thanks! <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 576 512"><path d="M416 192c0-88.4-93.1-160-208-160S0 103.6 0 192c0 34.3 14.1 65.9 38 92-13.4 30.2-35.5 54.2-35.8 54.5-2.2 2.3-2.8 5.7-1.5 8.7S4.8 352 8 352c36.6 0 66.9-12.3 88.7-25 32.2 15.7 70.3 25 111.3 25 114.9 0 208-71.6 208-160zm122 220c23.9-26 38-57.7 38-92 0-66.9-53.5-124.2-129.3-148.1.9 6.6 1.3 13.3 1.3 20.1 0 105.9-107.7 192-240 192-10.8 0-21.3-.8-31.7-1.9C207.8 439.6 281.8 480 368 480c41 0 79.1-9.2 111.3-25 21.8 12.7 52.1 25 88.7 25 3.2 0 6.1-1.9 7.3-4.8 1.3-2.9.7-6.3-1.5-8.7-.3-.3-22.4-24.2-35.8-54.5z"/></svg>]

<br>

.larger[
<svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 496 512"><path d="M336.5 160C322 70.7 287.8 8 248 8s-74 62.7-88.5 152h177zM152 256c0 22.2 1.2 43.5 3.3 64h185.3c2.1-20.5 3.3-41.8 3.3-64s-1.2-43.5-3.3-64H155.3c-2.1 20.5-3.3 41.8-3.3 64zm324.7-96c-28.6-67.9-86.5-120.4-158-141.6 24.4 33.8 41.2 84.7 50 141.6h108zM177.2 18.4C105.8 39.6 47.8 92.1 19.3 160h108c8.7-56.9 25.5-107.8 49.9-141.6zM487.4 192H372.7c2.1 21 3.3 42.5 3.3 64s-1.2 43-3.3 64h114.6c5.5-20.5 8.6-41.8 8.6-64s-3.1-43.5-8.5-64zM120 256c0-21.5 1.2-43 3.3-64H8.6C3.2 212.5 0 233.8 0 256s3.2 43.5 8.6 64h114.6c-2-21-3.2-42.5-3.2-64zm39.5 96c14.5 89.3 48.7 152 88.5 152s74-62.7 88.5-152h-177zm159.3 141.6c71.4-21.2 129.4-73.7 158-141.6h-108c-8.8 56.9-25.6 107.8-50 141.6zM19.3 352c28.6 67.9 86.5 120.4 158 141.6-24.4-33.8-41.2-84.7-50-141.6h-108z"/></svg> Learn more: [fable.tidyverts.org](https://fable.tidyverts.org/)

<br>

.bottom[This work is licensed as <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 496 512"><path d="M254.8 214.8l-33.2 17.3c-9.4-19.6-25.2-19.9-27.5-19.9-22.1 0-33.2 14.6-33.2 43.8 0 23.6 9.2 43.8 33.2 43.8 14.5 0 24.7-7.1 30.6-21.3l30.6 15.5c-6.2 11.5-25.7 39-65.1 39-22.6 0-74-10.3-74-77.1 0-58.7 43-77.1 72.6-77.1 30.8.2 52.7 12.1 66 36zm143.1 0l-32.8 17.3c-9.5-19.8-25.7-19.9-27.9-19.9-22.1 0-33.2 14.6-33.2 43.8 0 23.6 9.2 43.8 33.2 43.8 14.5 0 24.6-7.1 30.5-21.3l31 15.5c-2.1 3.7-21.4 39-65.1 39-22.7 0-74-9.9-74-77.1 0-58.7 43-77.1 72.6-77.1 30.8.2 52.7 12.1 65.7 36zM247.6 8C389.4 8 496 118.1 496 256c0 147.1-118.5 248-248.4 248C113.6 504 0 394.5 0 256 0 123.1 104.7 8 247.6 8zm.8 44.7C130.2 52.7 44.7 150.6 44.7 256c0 109.8 91.2 202.8 203.7 202.8 103.2 0 202.8-81.1 202.8-202.8.1-113.8-90.2-203.3-202.8-203.3z"/></svg> BY-NC 4.0.]
]