fasster::useR2018

## Forecasting multiple seasonality with state switching

.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>
### 13 July 2018

### Slides @ [slides.mitchelloharawild.com/useR18/](https://slides.mitchelloharawild.com/useR18/)
]

---
class: center

.animated.fadeIn[
## Time-series data is changing

### More data, more often.

<hr>
]

---
class: center

## Time-series data is changing

### More data, more often.

<hr>

.animated.fadeIn[
## Complicated patterns emerge

.pull-left[
### Multiple seasonality
### Lots of data
]
.pull-right[
### Missing values
### Additional noise
]

<hr> 
]

---
class: center

## Time-series data is changing

### More data, more often.

<hr>

## Complicated patterns emerge

.pull-left[
### Multiple seasonality
### Lots of data
]
.pull-right[
### Missing values
### Additional noise
]

<hr>

.animated.fadeIn[
## New tools are needed
.sticker[![tsibble](resources/tsibble.svg)]
.sticker[![fable](resources/fable.svg)]
.sticker[![fasster](resources/fasster.png)]
]

---
class: inverse, center, top

.animated.fadeIn.shadowText[
# Electricity demand
]

---

# Electricity demand (Monthly)

---

# Electricity demand (Daily)

---

# Electricity demand (Half-hourly)

<video autoplay>
        <source src="resources/anim3.mp4" type="video/mp4">
      </video>
---

# Electricity demand (Half-hourly)

<video autoplay>
        <source src="resources/anim4.mp4" type="video/mp4">
      </video>
---

# Models for multiple seasonality
<div id="htmlwidget-ec46561ddba0dd3d0eb1" class="timevis html-widget" style="width:100%;height:250px;">
<div class="btn-group zoom-menu">
<button type="button" class="btn btn-default btn-lg zoom-in" title="Zoom in">+</button>
<button type="button" class="btn btn-default btn-lg zoom-out" title="Zoom out">-</button>
</div>
</div>
<script type="application/json" data-for="htmlwidget-ec46561ddba0dd3d0eb1">{"x":{"items":[{"id":"1","content":"MSARIMA","start":"1970","group":"ss"},{"id":"2","content":"DSHW","start":"2003","group":"ss"},{"id":"3","content":"TBATS","start":"2010","group":"ss"},{"id":"4","content":"MLR","start":"???","group":"reg"},{"id":"5","content":"GAM","start":"1990","group":"reg"},{"id":"6","content":"Prophet","start":"2017","group":"reg"}],"groups":[{"id":"ss","content":"State Space"},{"id":"reg","content":"Regression"}],"showZoom":false,"zoomFactor":0.5,"fit":true,"options":{"zoomable":false,"showCurrentTime":false},"height":"250px","api":[]},"evals":[],"jsHooks":[]}</script>

<table class="table">
  <thead>
    <tr>
      <th>Model</th>
      <th>Flexible</th>
      <th>Speed</th>
      <th>Exogenous Regressors</th>
      <th>Accuracy</th>
      <th>Decompose Components</th>
      <th>Evolving Terms</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>State&nbspSpace</td>
      <td class="danger">No</td>
      <td class="danger">Slow</td>
      <td class="warning">Depends</td>
      <td class="warning">Okay</td>
      <td class="success">Yes</td>
      <td class="success">Yes</td>
    </tr>
    <tr>
      <td>Regression</td>
      <td class="success">Yes</td>
      <td class="success">Fast</td>
      <td class="success">Yes</td>
      <td class="warning">Okay</td>
      <td class="warning">Depends</td>
      <td class="danger">No</td>
    </tr>
  </tbody>
</table>

---
class: inverse

### * **F**orecasting with **A**dditive **S**witching of **S**easonality, **T**rend & **E**xogenous **R**egressors*

<br>

### A state space model that is:
.pull-left[
* ### Flexible
]
.pull-right[
* ### Fast
]

<br>

### With support for:

---

# Extending fable

**fasster** is the first extension of fable.

<br>

This allows fasster models to work with other features from the fable package.

* Consistent output and graphics
* Usable in combination forecasts

<br>

Uses formula based model specification:

.panel.panel-default[.panel-body.largecode[
t(y) ~ *\{specials\}*
]]

---

# Supported specials for fasster

<table class="table" style="font-size: 26px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Function </th>
   <th style="text-align:left;"> Description </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> poly(n) </td>
   <td style="text-align:left;"> Polynomials </td>
  </tr>
  <tr>
   <td style="text-align:left;"> seas(s) </td>
   <td style="text-align:left;"> Seasonal factors </td>
  </tr>
  <tr>
   <td style="text-align:left;"> trig(s, q) </td>
   <td style="text-align:left;"> Seasonal fourier terms </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ARMA(ar, ma) </td>
   <td style="text-align:left;"> ARMA processes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> xreg </td>
   <td style="text-align:left;"> Exogenous regressors </td>
  </tr>
  <tr>
   <td style="text-align:left;"> custom() </td>
   <td style="text-align:left;"> Custom dlm matrices </td>
  </tr>
  <tr>
   <td style="text-align:left;"> %S% </td>
   <td style="text-align:left;"> State switching </td>
  </tr>
</tbody>
</table>

---

# Modelling with fasster

---

# Modelling with fasster

```r
elec_tr <- tsibbledata::elecdemand %>%
  filter(index < ymd("2014-03-01"))
```

```
#> # A tsibble: 2,832 x 4 [30MINUTE]
#>    index               Demand WorkDay Temperature
#>    <dttm>               <dbl>   <dbl>       <dbl>
#>  1 2014-01-01 00:00:00   3.91       0        18.2
#>  2 2014-01-01 00:30:00   3.67       0        17.9
#>  3 2014-01-01 01:00:00   3.50       0        17.6
#>  4 2014-01-01 01:30:00   3.34       0        16.8
#>  5 2014-01-01 02:00:00   3.20       0        16.3
#>  6 2014-01-01 02:30:00   3.10       0        16.6
#>  7 2014-01-01 03:00:00   3.04       0        16.6
#>  8 2014-01-01 03:30:00   3.01       0        16.7
#>  9 2014-01-01 04:00:00   3.02       0        16.2
#> 10 2014-01-01 04:30:00   3.03       0        16.6
#> # ... with 2,822 more rows
```

---

# Capturing seasonality

```r
Demand ~ poly(1) + trig(48, 16)
```

---

# Capturing seasonality

```r
Demand ~ DayType %S% (poly(1) + trig(48, 16))
```

---

# Using temperature information

```r
Demand ~ Temperature + I(Temperature^2)
# (huge simplification of the non-linear relationship)
```

* Strongly related non-linear relationship.
* Takes care of most annual seasonality.

---

# Estimating the model

```r
elec_fit <- elec_tr %>%
  fasster(
    log(Demand) ~ 
      WorkDay %S% (trig(48, 16) + poly(1)) + 
      Temperature + I(Temperature^2)
  )
```

```
#> # A mable: 1 model [30MINUTE]
#>   data                  model  
#>   <list>                <model>
#> 1 <tsibble [2,832 × 4]> FASSTER
```

<br>

* A log transformation is taken to stabalise the variance.
* Specials are combined additively.

---

# Components

```r
components(elec_fit)
```

```
#> # A tsibble: 2,832 x 7 [30MINUTE]
#>    index               `I(Temperature^2… Temperature `WorkDay_0/poly… `WorkDay_0/trig…
#>    <dttm>                          <dbl>       <dbl>            <dbl>            <dbl>
#>  1 2014-01-01 00:00:00          0.000512     -0.0189             1.55         -0.00826
#>  2 2014-01-01 00:30:00          0.000512     -0.0189             1.55         -0.0826 
#>  3 2014-01-01 01:00:00          0.000512     -0.0189             1.55         -0.118  
#>  4 2014-01-01 01:30:00          0.000512     -0.0189             1.55         -0.167  
#>  5 2014-01-01 02:00:00          0.000510     -0.0188             1.55         -0.198  
#>  6 2014-01-01 02:30:00          0.000509     -0.0186             1.54         -0.227  
#>  7 2014-01-01 03:00:00          0.000510     -0.0187             1.54         -0.244  
#>  8 2014-01-01 03:30:00          0.000509     -0.0187             1.53         -0.249  
#>  9 2014-01-01 04:00:00          0.000521     -0.0195             1.54         -0.250  
#> 10 2014-01-01 04:30:00          0.000505     -0.0184             1.52         -0.232  
#> # ... with 2,822 more rows, and 2 more variables: `WorkDay_1/poly(1)` <dbl>,
#> #   `WorkDay_1/trig(48, 16)` <dbl>
```

---

# Components (Seasonality)

---

# Forecasts

```r
elec_fc <- elec_fit %>% 
  forecast(newdata = elec_ts)
```

```
#> # A fable: 1 forecast [30MINUTE]
#>   data                  model   forecast     
#>   <list>                <model> <fc>         
#> 1 <tsibble [2,832 × 4]> FASSTER ~t(N) [h=672]
```

```r
elec_ts
```

```
#> # A tsibble: 672 x 3 [30MINUTE]
#>   index               WorkDay Temperature
#>   <dttm>                <dbl>       <dbl>
#> 1 2014-03-01 00:00:00       0        16.9
#> 2 2014-03-01 00:30:00       0        16.5
#> 3 2014-03-01 01:00:00       0        16.3
#> 4 2014-03-01 01:30:00       0        16.4
#> 5 2014-03-01 02:00:00       0        16.3
#> 6 2014-03-01 02:30:00       0        16.3
#> # ... with 666 more rows
```

---

# Forecasts

---

# Forecasts
<img src="figure/elecfcplotint-1.svg" style="display: block; margin: auto;" />
---

# Forecasts
<img src="figure/elecfcplotintactual-1.svg" style="display: block; margin: auto;" />

---
 
# Interpolation 
 
<img src="figure/elecmissing-1.svg" style="display: block; margin: auto;" />

```r
elec_misfit <- elecdemand_missing %>% 
  fasster(log(Demand) ~ WorkDay %S% (trig(48, 16) + poly(1)) +  
                        Temperature + Temperature^2)
```

---

# Interpolation 
<img src="figure/interpolated-1.svg" style="display: block; margin: auto;" />

```r
elec_misfit %>%
  interpolate
```

---

# Streaming data

---

# Streaming data

```r
elec_stream
```

---

# Streaming data

```r
elec_fit %>%
  stream(elec_stream) %>%
  forecast(newdata = elec_stream_future)
```

---
class: inverse, top

.larger[
Features:
.pull-left[
* Component extraction
* Forecasting
]
.pull-right[
* Interpolation
* Streaming
]
]

<br>

<table class="table">
  <thead>
    <tr>
      <th>Model</th>
      <th>Flexible</th>
      <th>Speed</th>
      <th>Exogenous Regressors</th>
      <th>Accuracy</th>
      <th>Decompose Components</th>
      <th>Evolving Terms</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>TBATS</td>
      <td class="danger">No</td>
      <td class="danger">Slow</td>
      <td class="danger">No</td>
      <td class="warning">Okay</td>
      <td class="success">Yes</td>
      <td class="success">Yes</td>
    </tr>
    <tr>
      <td>Prophet</td>
      <td class="warning">Okay</td>
      <td class="warning">Okay</td>
      <td class="success">Yes</td>
      <td class="success">Good</td>
      <td class="success">Yes</td>
      <td class="danger">No</td>
    </tr>
    <tr>
      <td>fasster</td>
      <td class="success">Yes</td>
      <td class="warning">Okay</td>
      <td class="success">Yes</td>
      <td class="success">Good</td>
      <td class="success">Yes</td>
      <td class="success">Yes</td>
    </tr>
  </tbody>
</table>

---

.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="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> Learn more on GitHub: [tidyverts/fasster](https://github.com/tidyverts/fasster)

<br>

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: center

## Corticosteroid drug sales
.thesisplot[
![](resources/thesisp1.png)
]
![](resources/thesist1.png)

---
class: center

## Pedestrian counts
.thesisplot[
![](resources/thesisp2.png)
]
![](resources/thesist2.png)

---
class: center

## Electricity demand
.thesisplot[
![](resources/thesisp3.png)
]
![](resources/thesist3.png)