fable::useR2019

.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))
<br>
### 11 July 2019
### Slides @ [slides.mitchelloharawild.com/user2019](https://slides.mitchelloharawild.com/user2019)
]

---
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)
]

---
class: center

## Forecasting with the tidyverts

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

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

.animated.fadeIn[
.sticker-hint[
(see me later for some stickers!)
]
]

---

* A modern temporal data structure
* Provides tools for time-related analysis
* Integrates seamlessly with the tidyverse

<br>

More information:

* <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 496 512"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> [tidyverts/tsibble](https://github.com/tidyverts/tsibble)
* <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> [tsibble site](https://tsibble.tidyverts.org/)
* <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 576 512"><path d="M528 0H48C21.5 0 0 21.5 0 48v320c0 26.5 21.5 48 48 48h192l-16 48h-72c-13.3 0-24 10.7-24 24s10.7 24 24 24h272c13.3 0 24-10.7 24-24s-10.7-24-24-24h-72l-16-48h192c26.5 0 48-21.5 48-48V48c0-26.5-21.5-48-48-48zm-16 352H64V64h448v288z"/></svg> [rstudio::conf 2019](https://slides.earo.me/rstudioconf19/#1) & [useR!2018](http://slides.earo.me/useR18/)

---

# Tidy temporal data structure

### From `ts` to `tsibble`

```r
co2
```

```
#>         Jan    Feb    Mar    Apr    May    Jun    Jul    Aug    Sep    Oct    Nov    Dec
#> 1959 315.42 316.31 316.50 317.56 318.13 318.00 316.39 314.65 313.68 313.18 314.66 315.43
#> 1960 316.27 316.81 317.42 318.87 319.87 319.43 318.01 315.74 314.00 313.68 314.84 316.03
#> 1961 316.73 317.54 318.38 319.31 320.42 319.61 318.42 316.63 314.83 315.16 315.94 316.85
#> 1962 317.78 318.40 319.53 320.42 320.85 320.45 319.45 317.25 316.11 315.27 316.53 317.53
#> 1963 318.58 318.92 319.70 321.22 322.08 321.31 319.58 317.61 316.05 315.83 316.91 318.20
#> 1964 319.41 320.07 320.74 321.40 322.06 321.73 320.27 318.54 316.54 316.71 317.53 318.55
#> 1965 319.27 320.28 320.73 321.97 322.00 321.71 321.05 318.71 317.66 317.14 318.70 319.25
#> 1966 320.46 321.43 322.23 323.54 323.91 323.59 322.24 320.20 318.48 317.94 319.63 320.87
#> 1967 322.17 322.34 322.88 324.25 324.83 323.93 322.38 320.76 319.10 319.24 320.56 321.80
#> 1968 322.40 322.99 323.73 324.86 325.40 325.20 323.98 321.95 320.18 320.09 321.16 322.74
#> 1969 323.83 324.26 325.47 326.50 327.21 326.54 325.72 323.50 322.22 321.62 322.69 323.95
#> 1970 324.89 325.82 326.77 327.97 327.91 327.50 326.18 324.53 322.93 322.90 323.85 324.96
#> 1971 326.01 326.51 327.01 327.62 328.76 328.40 327.20 325.27 323.20 323.40 324.63 325.85
#> 1972 326.60 327.47 327.58 329.56 329.90 328.92 327.88 326.16 324.68 325.04 326.34 327.39
#> 1973 328.37 329.40 330.14 331.33 332.31 331.90 330.70 329.15 327.35 327.02 327.99 328.48
#> 1974 329.18 330.55 331.32 332.48 332.92 332.08 331.01 329.23 327.27 327.21 328.29 329.41
#> 1975 330.23 331.25 331.87 333.14 333.80 333.43 331.73 329.90 328.40 328.17 329.32 330.59
#> 1976 331.58 332.39 333.33 334.41 334.71 334.17 332.89 330.77 329.14 328.78 330.14 331.52
#> 1977 332.75 333.24 334.53 335.90 336.57 336.10 334.76 332.59 331.42 330.98 332.24 333.68
#> 1978 334.80 335.22 336.47 337.59 337.84 337.72 336.37 334.51 332.60 332.38 333.75 334.78
#> 1979 336.05 336.59 337.79 338.71 339.30 339.12 337.56 335.92 333.75 333.70 335.12 336.56
#> 1980 337.84 338.19 339.91 340.60 341.29 341.00 339.39 337.43 335.72 335.84 336.93 338.04
#> 1981 339.06 340.30 341.21 342.33 342.74 342.08 340.32 338.26 336.52 336.68 338.19 339.44
#> 1982 340.57 341.44 342.53 343.39 343.96 343.18 341.88 339.65 337.81 337.69 339.09 340.32
#> 1983 341.20 342.35 342.93 344.77 345.58 345.14 343.81 342.21 339.69 339.82 340.98 342.82
#> 1984 343.52 344.33 345.11 346.88 347.25 346.62 345.22 343.11 340.90 341.18 342.80 344.04
#> 1985 344.79 345.82 347.25 348.17 348.74 348.07 346.38 344.51 342.92 342.62 344.06 345.38
#> 1986 346.11 346.78 347.68 349.37 350.03 349.37 347.76 345.73 344.68 343.99 345.48 346.72
#> 1987 347.84 348.29 349.23 350.80 351.66 351.07 349.33 347.92 346.27 346.18 347.64 348.78
#> 1988 350.25 351.54 352.05 353.41 354.04 353.62 352.22 350.27 348.55 348.72 349.91 351.18
#> 1989 352.60 352.92 353.53 355.26 355.52 354.97 353.75 351.52 349.64 349.83 351.14 352.37
#> 1990 353.50 354.55 355.23 356.04 357.00 356.07 354.67 352.76 350.82 351.04 352.69 354.07
#> 1991 354.59 355.63 357.03 358.48 359.22 358.12 356.06 353.92 352.05 352.11 353.64 354.89
#> 1992 355.88 356.63 357.72 359.07 359.58 359.17 356.94 354.92 352.94 353.23 354.09 355.33
#> 1993 356.63 357.10 358.32 359.41 360.23 359.55 357.53 355.48 353.67 353.95 355.30 356.78
#> 1994 358.34 358.89 359.95 361.25 361.67 360.94 359.55 357.49 355.84 356.00 357.59 359.05
#> 1995 359.98 361.03 361.66 363.48 363.82 363.30 361.94 359.50 358.11 357.80 359.61 360.74
#> 1996 362.09 363.29 364.06 364.76 365.45 365.01 363.70 361.54 359.51 359.65 360.80 362.38
#> 1997 363.23 364.06 364.61 366.40 366.84 365.68 364.52 362.57 360.24 360.83 362.49 364.34
```

---

# Tidy temporal data structure

### From `ts` to `tsibble`

```r
as_tsibble(co2)
```

```
#> # A tsibble: 468 x 2 [1M]
#>       index value
#>       <mth> <dbl>
#>  1 1959 Jan  315.
#>  2 1959 Feb  316.
#>  3 1959 Mar  316.
#>  4 1959 Apr  318.
#>  5 1959 May  318.
#>  6 1959 Jun  318 
#>  7 1959 Jul  316.
#>  8 1959 Aug  315.
#>  9 1959 Sep  314.
#> 10 1959 Oct  313.
#> # … with 458 more rows
```

---

# 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
```

---

# Exploring tourism in Australia

### How does travel vary by purpose?

```r
library(dplyr)
aus_travel <- tourism %>% 
  group_by(Purpose) %>% 
  summarise(Trips = sum(Trips))
```

```
#> # A tsibble: 320 x 3 [1Q]
#> # Key:       Purpose [4]
#>    Purpose  Quarter Trips
#>    <chr>      <qtr> <dbl>
#>  1 Business 1998 Q1 3599.
#>  2 Business 1998 Q2 3724.
#>  3 Business 1998 Q3 4356.
#>  4 Business 1998 Q4 3796.
#>  5 Business 1999 Q1 3335.
#>  6 Business 1999 Q2 4714.
#>  7 Business 1999 Q3 4190.
#>  8 Business 1999 Q4 3701.
#>  9 Business 2000 Q1 3562.
#> 10 Business 2000 Q2 4018.
#> # … with 310 more rows
```

---

# Exploring tourism in Australia

### How does travel vary by purpose?

```r
library(ggplot2)
aus_travel %>% 
  ggplot(aes(x = Quarter, y = Trips, colour = Purpose)) + 
  geom_line()
```

---

* Graphics for time series
* Decompositions into structural components
* Feature extraction (summaries and statistical tests)

<br>

More information:

* <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 496 512"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> [tidyverts/feasts](https://github.com/tidyverts/feasts)
* <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> [feasts site](https://feasts.tidyverts.org/)
* <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> Rob Hyndman's talk at 11:48 tomorrow! (Ariane 1+2)

---

# Exploring tourism in Australia

### Time series graphics: season plots

```r
library(feasts)
aus_travel %>% 
  gg_season(Trips)
```

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

.pull-right[
<br>
Highlights seasonal structure by wrapping the x-axis over seasonal periods (years).

- Peak holiday travel in Q1 (summer)
- Peak business travel in Q2 & Q3
- Peak visiting travel in Q4 & Q1
- Other travel is largely non-seasonal
]

---

# Exploring tourism in Australia

### Time series decomposition: STL

```r
aus_travel_stl <- aus_travel %>% 
  STL(Trips ~ season(window = "periodic"))
```

```
#> # A dable:           320 x 7 [1Q]
#> # Key:               Purpose [4]
#> # STL Decomposition: Trips = trend + season_year + remainder
#>    Purpose  Quarter Trips trend season_year remainder season_adjust
#>    <chr>      <qtr> <dbl> <dbl>       <dbl>     <dbl>         <dbl>
#>  1 Business 1998 Q1 3599. 3949.      -577.      227.          4175.
#>  2 Business 1998 Q2 3724. 3910.       109.     -296.          3614.
#>  3 Business 1998 Q3 4356. 3886.       393.       77.0         3963.
#>  4 Business 1998 Q4 3796. 3910.        74.0    -188.          3722.
#>  5 Business 1999 Q1 3335. 4034.      -577.     -123.          3911.
#>  6 Business 1999 Q2 4714. 4034.       109.      571.          4605.
#>  7 Business 1999 Q3 4190. 4006.       393.     -210.          3797.
#>  8 Business 1999 Q4 3701. 3928.        74.0    -301.          3627.
#>  9 Business 2000 Q1 3562. 3889.      -577.      250.          4139.
#> 10 Business 2000 Q2 4018. 3981.       109.      -73.1         3908.
#> # … with 310 more rows
```

---

# Exploring tourism in Australia

### Time series decomposition: STL

```r
aus_travel_stl %>% 
  autoplot()
```

---

# Exploring tourism in Australia

### Time series features: STL

```r
aus_travel %>% 
  features(Trips, feature_set(tags = "stl"))
```

```
#> # A tibble: 4 x 8
#>   Purpose  trend_strength seasonal_strength_year spikiness linearity curvature seasonal_peak_year seasonal_trough_year
#>   <chr>             <dbl>                  <dbl>     <dbl>     <dbl>     <dbl>              <dbl>                <dbl>
#> 1 Business          0.899                  0.785   496322.     2327.     3611.                  3                    1
#> 2 Holiday           0.813                  0.910  2540902.     2019.     4257.                  1                    3
#> 3 Other             0.927                  0.357     3537.     1410.      908.                  3                    1
#> 4 Visiting          0.926                  0.796   601067.     3897.     3070.                  1                    3
```

* All series are trended
* Holiday travel is most seasonal, "Other" travel is least seasonal
* Seasonal peaks and troughs switch are Q1 and Q3 (varied by purpose)

---

# Exploring tourism in Australia

### Seeing the bigger picture

```r
tourism
```

---

# Exploring tourism in Australia

### Seeing the bigger picture

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

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

---

* Tidy evolution of the forecast package
* Models for time series forecasting
* Tools for analysing and manipulating models

<br>

More information:

* <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 496 512"><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg> [tidyverts/fable](https://github.com/tidyverts/fable)
* <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> [fable site](https://fable.tidyverts.org/)
* <svg style="height:0.8em;top:.04em;position:relative;fill:white;" viewBox="0 0 448 512"><path d="M448 360V24c0-13.3-10.7-24-24-24H96C43 0 0 43 0 96v320c0 53 43 96 96 96h328c13.3 0 24-10.7 24-24v-16c0-7.5-3.5-14.3-8.9-18.7-4.2-15.4-4.2-59.3 0-74.7 5.4-4.3 8.9-11.1 8.9-18.6zM128 134c0-3.3 2.7-6 6-6h212c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm0 64c0-3.3 2.7-6 6-6h212c3.3 0 6 2.7 6 6v20c0 3.3-2.7 6-6 6H134c-3.3 0-6-2.7-6-6v-20zm253.4 250H96c-17.7 0-32-14.3-32-32 0-17.6 14.4-32 32-32h285.4c-1.9 17.1-1.9 46.9 0 64z"/></svg> [Forecasting: Principles and Practice (3rd Ed.)](https://otexts.com/fpp3/)

---

# Forecasting with fable

### Look at the data

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

---

# Forecasting with fable

### Specify and estimate a model

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

```
#> # A mable: 4 x 2
#> # Key:     Purpose [4]
#>   Purpose  `ETS(Trips)`
#>   <chr>    <model>     
#> 1 Business <ETS(M,N,A)>
#> 2 Holiday  <ETS(M,N,M)>
#> 3 Other    <ETS(M,N,A)>
#> 4 Visiting <ETS(M,N,M)>
```
]

---

# Forecasting with fable

### Make some forecasts

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

```
#> # A fable: 48 x 5 [1Q]
#> # Key:     Purpose, .model [4]
#>    Purpose  .model     Quarter Trips .distribution  
#>    <chr>    <chr>        <qtr> <dbl> <dist>         
#>  1 Business ETS(Trips) 2018 Q1 4937. N(4937, 137658)
#>  2 Business ETS(Trips) 2018 Q2 5604. N(5604, 209086)
#>  3 Business ETS(Trips) 2018 Q3 5888. N(5888, 268396)
#>  4 Business ETS(Trips) 2018 Q4 5575. N(5575, 293305)
#>  5 Business ETS(Trips) 2019 Q1 4937. N(4937, 295999)
#>  6 Business ETS(Trips) 2019 Q2 5604. N(5604, 367634)
#>  7 Business ETS(Trips) 2019 Q3 5888. N(5888, 427147)
#>  8 Business ETS(Trips) 2019 Q4 5575. N(5575, 452257)
#>  9 Business ETS(Trips) 2020 Q1 4937. N(4937, 455161)
#> 10 Business ETS(Trips) 2020 Q2 5604. N(5604, 527003)
#> # … with 38 more rows
```
]

---

# Forecasting with fable

### Visualise the results!

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

---
class: top

# Forecasting with fable

### Estimate multiple models

```r
aus_travel %>% 
  model(
*   ets_n = ETS(Trips ~ trend("N")),
*   ets_a = ETS(Trips ~ trend("A")),
*   arima = ARIMA(Trips)
  )
```
]
.right-plot[

```
#> # A mable: 4 x 4
#> # Key:     Purpose [4]
#>   Purpose  ets_n        ets_a        arima                   
#>   <chr>    <model>      <model>      <model>                 
#> 1 Business <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,1,1)(0,1,1)[4]>
#> 2 Holiday  <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(0,1,1)(0,1,1)[4]>
#> 3 Other    <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,1,1)(1,0,0)[4]>
#> 4 Visiting <ETS(M,N,M)> <ETS(A,A,A)> <ARIMA(1,0,1)(2,1,0)[4]>
```
]

---

# Forecasting with fable

### Forecasts from multiple models

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

---
class: inverse, top

<br>

<br>
.center[
.larger[
## Combination forecasting
]

(models are better when they work together)*
]

# Ensemble forecasting

### A simple average of forecasts

```r
aus_travel %>% 
  model(
    ets_n = ETS(Trips ~ trend("N")),
    ets_a = ETS(Trips ~ trend("A")),
    arima = ARIMA(Trips)
  )
```
]
.right-plot[

---

# Ensemble forecasting

### A simple average of forecasts

```r
aus_travel %>%
  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: 4 x 5
#> # Key:     Purpose [4]
#>   Purpose  ets_n        ets_a        arima                    combn        
#>   <chr>    <model>      <model>      <model>                  <model>      
#> 1 Business <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,1,1)(0,1,1)[4]> <COMBINATION>
#> 2 Holiday  <ETS(M,N,M)> <ETS(M,A,M)> <ARIMA(0,1,1)(0,1,1)[4]> <COMBINATION>
#> 3 Other    <ETS(M,N,A)> <ETS(M,A,A)> <ARIMA(0,1,1)(1,0,0)[4]> <COMBINATION>
#> 4 Visiting <ETS(M,N,M)> <ETS(A,A,A)> <ARIMA(1,0,1)(2,1,0)[4]> <COMBINATION>
```
]

---

# Ensemble forecasting

### A simple average of forecasts

```r
aus_travel %>% 
  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: 48 x 5 [1Q]
#> # Key:     Purpose, .model [4]
#>    Purpose  .model Quarter Trips .distribution  
#>    <chr>    <chr>    <qtr> <dbl> <dist>         
#>  1 Business combn  2018 Q1 5004. N(5004, 122410)
#>  2 Business combn  2018 Q2 5731. N(5731, 174693)
#>  3 Business combn  2018 Q3 6036. N(6036, 218982)
#>  4 Business combn  2018 Q4 5759. N(5759, 244190)
#>  5 Business combn  2019 Q1 5144. N(5144, 260489)
#>  6 Business combn  2019 Q2 5871. N(5871, 321799)
#>  7 Business combn  2019 Q3 6176. N(6176, 375379)
#>  8 Business combn  2019 Q4 5898. N(5898, 409760)
#>  9 Business combn  2020 Q1 5284. N(5284, 435676)
#> 10 Business combn  2020 Q2 6010. N(6010, 507587)
#> # … with 38 more rows
```
]

---

# Ensemble forecasting

### A simple average of forecasts

```r
aus_travel %>% 
  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") %>% 
* autoplot(aus_travel)
```
]
.right-plot[
<img src="figure/tourism-total-combn-fc-plot-output-1.svg" style="display: block; margin: auto;" />
]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel_stl <- aus_travel %>% 
* STL(Trips ~ season(window = "periodic"))
```
]

]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel_stl <- aus_travel %>% 
  STL(Trips ~ season(window = "periodic"))
aus_travel_stl %>% 
* autoplot()
```
]

.right-plot[
<img src="figure/tourism-purpose-stl-plot-recall-output-1.svg" style="display: block; margin: auto;" />
]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel_stl <- aus_travel %>% 
  STL(Trips ~ season(window = "periodic"))
aus_travel_stl %>% 
  model(
*   deseas = ETS(trend + remainder)
  ) %>%
  forecast(h = "3 years") %>% 
  autoplot(aus_travel_stl)
```
]

.right-plot[
<img src="figure/tourism-purpose-stl-mdl-deseas-output-1.svg" style="display: block; margin: auto;" />
]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel_stl <- aus_travel %>% 
  STL(Trips ~ season(window = "periodic"))
aus_travel_stl %>% 
  model(
*   seas = SNAIVE(season_year)
  ) %>% 
  forecast(h = "3 years") %>% 
  autoplot(aus_travel_stl)
```
]

.right-plot[
<img src="figure/tourism-purpose-stl-mdl-seas-output-1.svg" style="display: block; margin: auto;" />
]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel_stl <- aus_travel %>% 
  STL(Trips ~ season(window = "periodic"))
aus_travel_stl %>% 
  model(
*   hybrid = ETS(trend + remainder) +
*     SNAIVE(season_year)
  ) %>% 
  forecast(h = "3 years") %>% 
  autoplot(aus_travel_stl)
```
]

.right-plot[
<img src="figure/tourism-purpose-stl-mdl-output-1.svg" style="display: block; margin: auto;" />
]

---

# Hybrid forecasting

### Combining forecasts of decomposed components

```r
aus_travel %>%
  model(
*   hybrid = decomposition_model(
*     STL, Trips ~ season(window = "periodic"),
*     ETS(trend + remainder),
*     SNAIVE(season_year)
*   )
  ) %>% 
  forecast(h = "3 years") %>% 
  autoplot(aus_travel_stl)
```
]

.right-plot[
<img src="figure/tourism-purpose-stl-mdl-alt-output-1.svg" style="display: block; margin: auto;" />
]

---
class: inverse, top

<br>

<br>
.center[
.larger[
## Extensibility
]

(get other people to implement models for you)
]

---
class: top

# Adding new models to fable

```r
*library(fasster)
*library(fable.prophet)
aus_travel %>% 
 model(
* fasster = fasster(Trips ~ season("year") + poly(2)),
* prophet = prophet(Trips ~ season("year"))
 ) %>% 
 forecast(h = "3 years") %>% 
 autoplot(aus_travel, level = NULL)
```
]
.pull-right[
<img src="figure/extensible-mdls-output-1.svg" style="display: block; margin: auto;" />
]

* Direct comparison of new models
* Unified modelling interface
* Ensemble and hybrid support
* and more...

---
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 %>% 
  group_by(Purpose) %>% 
  summarise(Trips = sum(Trips)) %>% 
  model(ets_n = ETS(Trips ~ trend("N")), 
        ets_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)),
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>% 
  forecast(h = "3 years")
```

---
class: inverse

```r
library(fable)
library(tidyverse)
*tsibble::tourism %>%
  group_by(Purpose) %>%
  summarise(Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")), 
        ets_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)),
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>% 
  forecast(h = "3 years")
```

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

---
class: inverse

```r
library(fable)
*library(tidyverse)
tsibble::tourism %>% 
* group_by(Purpose) %>%
* summarise(Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")), 
        ets_a = ETS(Trips ~ trend("A")), 
        arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)),
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>% 
  forecast(h = "3 years")
```

### Integrates seamlessly with the tidyverse.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>% 
  group_by(Purpose) %>%
  summarise(Trips = sum(Trips)) %>%
* model(ets_n = ETS(Trips ~ trend("N")),
*       ets_a = ETS(Trips ~ trend("A")),
*       arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)),
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>% 
  forecast(h = "3 years")
```

### Flexible, and succinct formula model specification.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>% 
  group_by(Purpose) %>%
  summarise(Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")),
        ets_a = ETS(Trips ~ trend("A")),
        arima = ARIMA(Trips),
*       fasster = fasster::fasster(Trips ~ season("year") + poly(2)),
*       prophet = fable.prophet::prophet(Trips ~ season("year"))) %>%
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>% 
  forecast(h = "3 years")
```

### Extensible by design.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>% 
  group_by(Purpose) %>%
  summarise(Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")),
        ets_a = ETS(Trips ~ trend("A")),
        arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)), 
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
* mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>%
  forecast(h = "3 years")
```

### Natural interface for model combinations.

---
class: inverse

```r
library(fable)
library(tidyverse)
tsibble::tourism %>% 
  group_by(Purpose) %>%
  summarise(Trips = sum(Trips)) %>%
  model(ets_n = ETS(Trips ~ trend("N")),
        ets_a = ETS(Trips ~ trend("A")),
        arima = ARIMA(Trips),
        fasster = fasster::fasster(Trips ~ season("year") + poly(2)), 
        prophet = fable.prophet::prophet(Trips ~ season("year"))) %>% 
  mutate(combn = (ets_n + ets_a + arima + fasster)/4) %>%
* forecast(h = "3 years")
```

### Distributional forecasts in a data format.

---
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>]

.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.]
]

---
class: inverse, top

<br>

---
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.

---

# Comparing multiple models

### Forecast accuracy

```r
aus_travel %>% 
* 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(aus_travel) %>%
* arrange(MASE)
```
]
.right-plot[

```
#> # A tibble: 12 x 10
#>    .model Purpose  .type     ME  RMSE    MAE   MPE  MAPE  MASE    ACF1
#>    <chr>  <chr>    <chr>  <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>   <dbl>
#>  1 arima  Other    Test   -12.4  112.   76.3 -1.59  5.62 0.646 -0.133 
#>  2 ets_a  Other    Test   -43.9  101.   80.7 -3.66  6.03 0.683 -0.567 
#>  3 ets_n  Other    Test    71.4  129.  102.   4.62  7.10 0.863 -0.0743
#>  4 arima  Visiting Test   538.   686.  539.   6.18  6.20 1.30   0.281 
#>  5 ets_a  Holiday  Test   581.   700.  581.   5.36  5.36 1.46   0.304 
#>  6 ets_a  Visiting Test   612.   758.  612.   7.03  7.03 1.47   0.317 
#>  7 ets_a  Business Test   423.   573.  448.   7.66  8.27 1.51   0.505 
#>  8 ets_n  Visiting Test   652.   800.  652.   7.53  7.53 1.57   0.367 
#>  9 ets_n  Business Test   511.   645.  513.   9.50  9.55 1.73   0.569 
#> 10 ets_n  Holiday  Test   939.  1061.  939.   8.69  8.69 2.36   0.415 
#> 11 arima  Business Test   820.   968.  883.  15.1  16.6  2.97   0.233 
#> 12 arima  Holiday  Test  1261.  1380. 1261.  11.7  11.7  3.16   0.425
```
]

---
class: inverse, top

<br>

---

# Forecast reconciliation

<div id="htmlwidget-98dc638aec296b6b43a8" style="width:100%;height:550px;" class="collapsibleTree html-widget"></div>
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---

# 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
```

---

# 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, top

<br>

---

# Multivariate modelling

```r
lung_deaths <- cbind(mdeaths, fdeaths) %>% 
  as_tsibble(pivot_longer = FALSE)
```

```
#> # A tsibble: 72 x 3 [1M]
#>       index mdeaths fdeaths
#>       <mth>   <dbl>   <dbl>
#>  1 1974 Jan    2134     901
#>  2 1974 Feb    1863     689
#>  3 1974 Mar    1877     827
#>  4 1974 Apr    1877     677
#>  5 1974 May    1492     522
#>  6 1974 Jun    1249     406
#>  7 1974 Jul    1280     441
#>  8 1974 Aug    1131     393
#>  9 1974 Sep    1209     387
#> 10 1974 Oct    1492     582
#> # … with 62 more rows
```

---

# Multivariate modelling

```r
lung_deaths %>% 
* model(VAR(vars(mdeaths, fdeaths) ~ AR(3) + fourier("year", 4))) %>%
  forecast() %>% 
  autoplot(lung_deaths)
```