-
Notifications
You must be signed in to change notification settings - Fork 16
/
Copy pathTime-Series-Forecasting-With-R.html
343 lines (304 loc) · 18.1 KB
/
Time-Series-Forecasting-With-R.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
<!DOCTYPE html>
<html>
<head>
<title>Time Series Forecasting</title>
<meta charset="utf-8">
<meta name="Description" content="R Language Tutorials for Advanced Statistics">
<meta name="Keywords" content="R, Tutorial, Machine learning, Statistics, Data Mining, Analytics, Data science, Linear Regression, Logistic Regression, Time series, Forecasting">
<meta name="Distribution" content="Global">
<meta name="Author" content="Selva Prabhakaran">
<meta name="Robots" content="index, follow">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="shortcut icon" href="/screenshots/iconb-64.png" type="image/x-icon" />
<link href="www/bootstrap.min.css" rel="stylesheet">
<link href="www/highlight.css" rel="stylesheet">
<link href='http://fonts.googleapis.com/css?family=Inconsolata:400,700'
rel='stylesheet' type='text/css'>
<!-- Color Script -->
<style type="text/css">
a {
color: #3675C5;
color: rgb(25, 145, 248);
color: #4582ec;
color: #3F73D8;
}
li {
line-height: 1.65;
}
/* reduce spacing around math formula*/
.MathJax_Display {
margin: 0em 0em;
}
</style>
<!-- Add Google search -->
<script language="Javascript" type="text/javascript">
function my_search_google()
{
var query = document.getElementById("my-google-search").value;
window.open("http://google.com/search?q=" + query
+ "%20site:" + "http://r-statistics.co");
}
</script>
</head>
<body>
<div class="container">
<div class="masthead">
<!--
<ul class="nav nav-pills pull-right">
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">
Table of contents<b class="caret"></b>
</a>
<ul class="dropdown-menu pull-right" role="menu">
<li class="dropdown-header"></li>
<li class="dropdown-header">Tutorial</li>
<li><a href="R-Tutorial.html">R Tutorial</a></li>
<li class="dropdown-header">ggplot2</li>
<li><a href="ggplot2-Tutorial-With-R.html">ggplot2 Short Tutorial</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part1-With-R-Code.html">ggplot2 Tutorial 1 - Intro</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html">ggplot2 Tutorial 2 - Theme</a></li>
<li><a href="Top50-Ggplot2-Visualizations-MasterList-R-Code.html">ggplot2 Tutorial 3 - Masterlist</a></li>
<li><a href="ggplot2-cheatsheet.html">ggplot2 Quickref</a></li>
<li class="dropdown-header">Foundations</li>
<li><a href="Linear-Regression.html">Linear Regression</a></li>
<li><a href="Statistical-Tests-in-R.html">Statistical Tests</a></li>
<li><a href="Missing-Value-Treatment-With-R.html">Missing Value Treatment</a></li>
<li><a href="Outlier-Treatment-With-R.html">Outlier Analysis</a></li>
<li><a href="Variable-Selection-and-Importance-With-R.html">Feature Selection</a></li>
<li><a href="Model-Selection-in-R.html">Model Selection</a></li>
<li><a href="Logistic-Regression-With-R.html">Logistic Regression</a></li>
<li><a href="Environments.html">Advanced Linear Regression</a></li>
<li class="dropdown-header">Advanced Regression Models</li>
<li><a href="adv-regression-models.html">Advanced Regression Models</a></li>
<li class="dropdown-header">Time Series</li>
<li><a href="Time-Series-Analysis-With-R.html">Time Series Analysis</a></li>
<li><a href="Time-Series-Forecasting-With-R.html">Time Series Forecasting </a></li>
<li><a href="Time-Series-Forecasting-With-R-part2.html">More Time Series Forecasting</a></li>
<li class="dropdown-header">High Performance Computing</li>
<li><a href="Parallel-Computing-With-R.html">Parallel computing</a></li>
<li><a href="Strategies-To-Improve-And-Speedup-R-Code.html">Strategies to Speedup R code</a></li>
<li class="dropdown-header">Useful Techniques</li>
<li><a href="Association-Mining-With-R.html">Association Mining</a></li>
<li><a href="Multi-Dimensional-Scaling-With-R.html">Multi Dimensional Scaling</a></li>
<li><a href="Profiling.html">Optimization</a></li>
<li><a href="Information-Value-With-R.html">InformationValue package</a></li>
</ul>
</li>
</ul>
-->
<ul class="nav nav-pills pull-right">
<div class="input-group">
<form onsubmit="my_search_google()">
<input type="text" class="form-control" id="my-google-search" placeholder="Search..">
<form>
</div><!-- /input-group -->
</ul><!-- /.col-lg-6 -->
<h3 class="muted"><a href="/">r-statistics.co</a><small> by Selva Prabhakaran</small></h3>
<hr>
</div>
<div class="row">
<div class="col-xs-12 col-sm-3" id="nav">
<div class="well">
<li>
<ul class="list-unstyled">
<li class="dropdown-header"></li>
<li class="dropdown-header">Tutorial</li>
<li><a href="R-Tutorial.html">R Tutorial</a></li>
<li class="dropdown-header">ggplot2</li>
<li><a href="ggplot2-Tutorial-With-R.html">ggplot2 Short Tutorial</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part1-With-R-Code.html">ggplot2 Tutorial 1 - Intro</a></li>
<li><a href="Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html">ggplot2 Tutorial 2 - Theme</a></li>
<li><a href="Top50-Ggplot2-Visualizations-MasterList-R-Code.html">ggplot2 Tutorial 3 - Masterlist</a></li>
<li><a href="ggplot2-cheatsheet.html">ggplot2 Quickref</a></li>
<li class="dropdown-header">Foundations</li>
<li><a href="Linear-Regression.html">Linear Regression</a></li>
<li><a href="Statistical-Tests-in-R.html">Statistical Tests</a></li>
<li><a href="Missing-Value-Treatment-With-R.html">Missing Value Treatment</a></li>
<li><a href="Outlier-Treatment-With-R.html">Outlier Analysis</a></li>
<li><a href="Variable-Selection-and-Importance-With-R.html">Feature Selection</a></li>
<li><a href="Model-Selection-in-R.html">Model Selection</a></li>
<li><a href="Logistic-Regression-With-R.html">Logistic Regression</a></li>
<li><a href="Environments.html">Advanced Linear Regression</a></li>
<li class="dropdown-header">Advanced Regression Models</li>
<li><a href="adv-regression-models.html">Advanced Regression Models</a></li>
<li class="dropdown-header">Time Series</li>
<li><a href="Time-Series-Analysis-With-R.html">Time Series Analysis</a></li>
<li><a href="Time-Series-Forecasting-With-R.html">Time Series Forecasting </a></li>
<li><a href="Time-Series-Forecasting-With-R-part2.html">More Time Series Forecasting</a></li>
<li class="dropdown-header">High Performance Computing</li>
<li><a href="Parallel-Computing-With-R.html">Parallel computing</a></li>
<li><a href="Strategies-To-Improve-And-Speedup-R-Code.html">Strategies to Speedup R code</a></li>
<li class="dropdown-header">Useful Techniques</li>
<li><a href="Association-Mining-With-R.html">Association Mining</a></li>
<li><a href="Multi-Dimensional-Scaling-With-R.html">Multi Dimensional Scaling</a></li>
<li><a href="Profiling.html">Optimization</a></li>
<li><a href="Information-Value-With-R.html">InformationValue package</a></li>
</ul>
</li>
</div>
<div class="well">
<p>Stay up-to-date. <a href="https://docs.google.com/forms/d/1xkMYkLNFU9U39Dd8S_2JC0p8B5t6_Yq6zUQjanQQJpY/viewform">Subscribe!</a></p>
<p><a href="https://docs.google.com/forms/d/13GrkCFcNa-TOIllQghsz2SIEbc-YqY9eJX02B19l5Ow/viewform">Chat!</a></p>
</div>
<h4>Contents</h4>
<ul class="list-unstyled" id="toc"></ul>
<!--
<hr>
<p><a href="/contribute.html">How to contribute</a></p>
<p><a class="btn btn-primary" href="">Edit this page</a></p>
-->
</div>
<div id="content" class="col-xs-12 col-sm-8 pull-right">
<h1>Time Series Forecasting</h1>
<blockquote>
<p>This is a follow-up to the introduction to <a href="Time-Series-Analysis-With-R">time series analysis</a>, but focused more on forecasting rather than analysis.</p>
</blockquote>
<h2>Simple Moving Average</h2>
<p>Simple moving average can be calculated using <code>ma()</code> from forecast</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">sm <-<span class="st"> </span><span class="kw">ma</span>(ts, <span class="dt">order=</span><span class="dv">12</span>) <span class="co"># 12 month moving average</span>
<span class="kw">lines</span>(sm, <span class="dt">col=</span><span class="st">"red"</span>) <span class="co"># plot</span></code></pre></div>
<h2>Exponential Smoothing</h2>
<p>Simple, Double and Triple exponential smoothing can be performed using the HoltWinters() function. There are multiple implementations of the Holt Winters method – <code>hw()</code> {forecast} and <code>ets()</code>.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(forecast)
<span class="co"># Simple exponential smoothing: Level Only</span>
model <-<span class="st"> </span><span class="kw">hw</span>(trainingData, <span class="dt">initial =</span> “optimal”, <span class="dt">h=</span>(forecastPeriodLen), <span class="dt">beta=</span><span class="ot">NULL</span>, <span class="dt">gamma=</span><span class="ot">NULL</span>) <span class="co"># h is the no. periods to forecast</span>
<span class="co"># Double Exponential smoothing: Level and Trend components</span>
model <-<span class="st"> </span><span class="kw">hw</span>(trainingData, <span class="dt">initial =</span> “optimal”, <span class="dt">h=</span>(forecastPeriodLen), <span class="dt">gamma=</span><span class="ot">NULL</span>)
<span class="co"># Holt Winters: Level, Trend and Seasonality</span>
model <-<span class="st"> </span><span class="kw">hw</span>(trainingData, <span class="dt">initial =</span> “optimal”, <span class="dt">h=</span>(forecastPeriodLen))
<span class="kw">plot</span>(model)
<span class="kw">accuracy</span>(model) <span class="co"># calculate accuracy measures</span></code></pre></div>
<h2>ARIMA</h2>
<p>The forecast package offers auto.arima() function to fit ARIMA models. It can also be manually fit using Arima(). A caveat with ARIMA models in R is that it does not have the functionality to fit long seasonality of more than 350 periods eg: 365 days for daily data or 24 hours for 15 sec data.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="co"># Fit and forecast with auto.arima()</span>
autoArimaFit <-<span class="st"> </span><span class="kw">auto.arima</span>(tsData)
<span class="kw">plot</span>(<span class="kw">forecast</span>(autoArimaFit, <span class="dt">h=</span><span class="dv">20</span>))
<span class="co"># Fit and forecast with Arima()</span>
arimaFit <-<span class="st"> </span><span class="kw">Arima</span>(tsData,<span class="dt">order=</span><span class="kw">c</span>(<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">0</span>))
<span class="kw">plot</span>(<span class="kw">forecast</span>(arimafit,<span class="dt">h=</span><span class="dv">20</span>))</code></pre></div>
<h2>How To Forecast ARIMA Models With Long Seasonality (Greater Than 350 Periods)?</h2>
<p>Upon plotting your Arima() forecast, you find a more or less flat forecast, it could be because of long seasonality. In such case, you can feed in the seasonality as an external regressor through the ‘xreg’ argument.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">Fit <-<span class="st"> </span><span class="kw">Arima</span>(tsData,<span class="dt">order=</span><span class="kw">c</span>(<span class="dv">3</span>,<span class="dv">1</span>,<span class="dv">0</span>)) <span class="co"># fit Arima model</span>
Fit <-<span class="st"> </span><span class="kw">auto.arima</span>(tsData, <span class="dt">seasonal=</span><span class="ot">FALSE</span>, <span class="dt">xreg=</span><span class="kw">fourier</span>(tsData,<span class="dv">4</span>)) <span class="co"># fit auto.arima model</span>
<span class="kw">plot</span>(<span class="kw">forecast</span>(Fit,<span class="dt">h=</span><span class="dv">20</span>))
pred <-<span class="st"> </span><span class="kw">predict</span> (Fit, <span class="dt">newxreg=</span>newXregVar) <span class="co"># alternate way to forecast</span>
<span class="kw">plot</span>(<span class="kw">forecast</span>(fit, <span class="dt">h=</span>h, <span class="dt">xreg=</span><span class="kw">fourierf</span>(tsData,<span class="dv">4</span>,h))) <span class="co"># h is number of forecasts</span></code></pre></div>
<p>If you are using a numeric vector as an external regressor (xreg), make sure you change it to a data.frame() before feeding it as an xreg parameter to auto.arima(). You can also use multiple external regressors by binding them together as a data.frame().</p>
<h2>Some Useful External Regressors For Arima() and auto.arima()</h2>
<p>Any dataframe with as many rows as length of ts data can be used as ‘xreg’ argument. A couple of common ‘xreg’s that are used to model seasonal effects are below.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">Xreg1 <-<span class="st"> </span><span class="kw">seasonaldummy</span>(tsData) <span class="co"># creates dummy binary variable for each period in a season.</span>
Xreg2 <-<span class="st"> </span><span class="kw">model.matrix</span>(~<span class="st"> </span><span class="kw">as.factor</span>(weekday) +<span class="st"> </span><span class="dv">0</span>)<span class="er">)</span> <span class="co"># weekday could be a monthday, hour-of-day, holiday indicator etc .. </span></code></pre></div>
<h2>How To Model Time Series With Complex Seasonality Pattern?</h2>
<p>Use the tbats() in forecast package. Time series with multiple-seasonality can be modelled with this method. Since this is a computationally intensive procedure, the in-built parallel processing facility may be leveraged.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">tbatsFit <-<span class="st"> </span><span class="kw">tbats</span>(tsData, <span class="dt">use.parallel=</span><span class="ot">TRUE</span>, <span class="dt">num.cores =</span> <span class="dv">2</span>) <span class="co"># fit tbats model</span>
<span class="kw">plot</span>(<span class="kw">forecast</span>(fit)) <span class="co"># plot</span>
components <-<span class="st"> </span><span class="kw">tbats.components</span>(tbatsFit)
<span class="kw">plot</span>(components)</code></pre></div>
<h2>How To Find Confidence Intervals For My Forecasts?</h2>
<p>The predict() function has the facility. By providing the argument ‘prediction.interval=TRUE’ and ‘level = n’, the prediction intervals for a given confidence is calculated. Below is a general format of the code.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model <-<span class="st"> </span><span class="kw">HoltWinters</span>(TS) <span class="kw">predict</span>(model, <span class="dv">50</span>, <span class="dt">prediction.interval =</span> <span class="ot">TRUE</span>, <span class="dt">level=</span> <span class="fl">0.99</span>) <span class="co"># prediction.interval = TRUE</span></code></pre></div>
<h2>More Useful Functions Related To Time Series</h2>
<table>
<thead>
<tr class="header">
<th align="left">Functions</th>
<th align="left">Description</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">accuracy()</td>
<td align="left">accuracy measures of forecast</td>
</tr>
<tr class="even">
<td align="left">BoxCox, invBoxCox()</td>
<td align="left">Box-Cox transformation</td>
</tr>
<tr class="odd">
<td align="left">decompose()</td>
<td align="left">Decompose time series data into components</td>
</tr>
<tr class="even">
<td align="left">dm.test()</td>
<td align="left">Diebold-Mariano test compares the forecast accuracy</td>
</tr>
<tr class="odd">
<td align="left">monthdays()</td>
<td align="left">number of days in seasonal series</td>
</tr>
<tr class="even">
<td align="left">na.interp()</td>
<td align="left">interpolate missing values</td>
</tr>
<tr class="odd">
<td align="left">seasadj()</td>
<td align="left">Remove the seasonal components from a time series</td>
</tr>
<tr class="even">
<td align="left">seasonaldummy()</td>
<td align="left">create matrix of seasonal indicator variables</td>
</tr>
<tr class="odd">
<td align="left">seasonplot()</td>
<td align="left">Plot seasonal effects</td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="footer">
<hr>
<p>© 2016-17 Selva Prabhakaran. Powered by <a href="http://jekyllrb.com/">jekyll</a>,
<a href="http://yihui.name/knitr/">knitr</a>, and
<a href="http://johnmacfarlane.net/pandoc/">pandoc</a>.
This work is licensed under the <a href="http://creativecommons.org/licenses/by-nc/3.0/">Creative Commons License.</a>
</p>
</div>
</div> <!-- /container -->
<script src="//code.jquery.com/jquery.js"></script>
<script src="www/bootstrap.min.js"></script>
<script src="www/toc.js"></script>
<!-- MathJax Script -->
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
});
</script>
<script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<!-- Google Analytics Code -->
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-69351797-1', 'auto');
ga('send', 'pageview');
</script>
<style type="text/css">
/* reduce spacing around math formula*/
.MathJax_Display {
margin: 0em 0em;
}
body {
font-family: 'Helvetica Neue', Roboto, Arial, sans-serif;
font-size: 16px;
line-height: 27px;
font-weight: 400;
}
blockquote p {
line-height: 1.75;
color: #717171;
}
.well li{
line-height: 28px;
}
li.dropdown-header {
display: block;
padding: 0px;
font-size: 14px;
}
</style>
</body>
</html>