class: center, middle, inverse, title-slide # Modelling and forecasting time series in R ### <strong>Dr Matt Ashby</strong> | UCL Jill Dando Institute | October 2021 --- class: animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-generic-time-series-1-1.png" width="100%" /> --- class: animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-generic-time-series-2-1.png" width="100%" /> --- class: animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-generic-time-series-3-1.png" width="100%" /> --- class: animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-generic-time-series-4-1.png" width="100%" /> --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-different-trends-1-1.png" width="100%" /> --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-different-trends-2-1.png" width="100%" /> --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-multiple-seasons-1-1.png" width="100%" /> --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/chart-multiple-seasons-2-1.png" width="100%" /> --- class: big-text, middle, center, animated, fadeIn time-series data typically violate<br>the assumptions of regression models --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/acf-norm-1.png" width="100%" /> --- class: big-text, animated, fadeIn <img src="forecasting-time-series-in-r_files/figure-html/acf-ts-1.png" width="100%" /> --- class: big-text, middle, center, animated, fadeIn there are *many* ways of<br>modelling time-series data --- class: big-text, middle, animated, fadeIn **ARIMA** models combine one or more: 1. **auto-regression**: *lagged* values of the DV 2. **integration**: *differenced* values of the DV 3. **moving-average** values of the DV --- class: big-text, middle, animated, fadeIn `arima()` in the `stats` package `Arima()` in the `forecast` package `auto.arima()` in the `forecast` package **`ARIMA()` in the `fable` package** `stan_sarima()` in the `bayesforecast` package --- class: middle, center, animated, fadeIn <span style="font-size: 750%"><svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#0097A9;overflow:visible;position:relative;"><path d="M190.5 66.9l22.2-22.2c9.4-9.4 24.6-9.4 33.9 0L441 239c9.4 9.4 9.4 24.6 0 33.9L246.6 467.3c-9.4 9.4-24.6 9.4-33.9 0l-22.2-22.2c-9.5-9.5-9.3-25 .4-34.3L311.4 296H24c-13.3 0-24-10.7-24-24v-32c0-13.3 10.7-24 24-24h287.4L190.9 101.2c-9.8-9.3-10-24.8-.4-34.3z"/></svg> &nbsp; <svg aria-hidden="true" role="img" viewBox="0 0 581 512" style="height:1em;width:1.13em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#002855;overflow:visible;position:relative;"><path d="M581 226.6C581 119.1 450.9 32 290.5 32S0 119.1 0 226.6C0 322.4 103.3 402 239.4 418.1V480h99.1v-61.5c24.3-2.7 47.6-7.4 69.4-13.9L448 480h112l-67.4-113.7c54.5-35.4 88.4-84.9 88.4-139.7zm-466.8 14.5c0-73.5 98.9-133 220.8-133s211.9 40.7 211.9 133c0 50.1-26.5 85-70.3 106.4-2.4-1.6-4.7-2.9-6.4-3.7-10.2-5.2-27.8-10.5-27.8-10.5s86.6-6.4 86.6-92.7-90.6-87.9-90.6-87.9h-199V361c-74.1-21.5-125.2-67.1-125.2-119.9zm225.1 38.3v-55.6c57.8 0 87.8-6.8 87.8 27.3 0 36.5-38.2 28.3-87.8 28.3zm-.9 72.5H365c10.8 0 18.9 11.7 24 19.2-16.1 1.9-33 2.8-50.6 2.9v-22.1z"/></svg></span> --- class: big-text, middle, animated, fadeIn # Thanks! These slides:<br>**lesscrime.info/slides/time-series-models-nscr** <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> **matthew.ashby@ucl.ac.uk** <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#1DA1F2;overflow:visible;position:relative;"><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> **@LessCrime** <p style="font-size: 90%;">Cover photo by <a href="https://unsplash.com/@qrenep?utm_source=unsplash&utm_medium=referral&utm_content=creditCopyText">Rene Böhmer</a> on <a href="https://unsplash.com/s/photos/data?utm_source=unsplash&utm_medium=referral&utm_content=creditCopyText">Unsplash</a></p>