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  <title>Forecasting</title>
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  <meta name="author" content="Jeffrey Leek, Assistant Professor of Biostatistics">
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        <h1>Forecasting</h1>
        <h2></h2>
        <p>Jeffrey Leek, Assistant Professor of Biostatistics<br/>Johns Hopkins Bloomberg School of Public Health</p>
      </hgroup>
          </slide>
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      <slide class="" id="slide-1" style="background:;">
    <h2>Time series data</h2>
  </hgroup>
  <article>
    <p><img class=center src=../../assets/img/08_PredictionAndMachineLearning/GOOG.png height=450></p>
<p><a href="https://www.google.com/finance">https://www.google.com/finance</a></p>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-2" style="background:;">
    <h2>What is different?</h2>
  </hgroup>
  <article>
<li>Data are dependent over time</li>
<li>Specific pattern types
<li>Trends - long term increase or decrease</li>
<li>Seasonal patterns - patterns related to time of week, month, year, etc.</li>
<li>Cycles - patterns that rise and fall periodically</li>
<li>Subsampling into training/test is more complicated</li>
<li>Similar issues arise in spatial data 
<li>Dependency between nearby observations</li>
<li>Location specific effects</li>
<li>Typically goal is to predict one or more observations into the future. </li>
<li>All standard predictions can be used (with caution!)</li>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-3" style="background:;">
    <h2>Beware spurious correlations!</h2>
  </hgroup>
  <article>
    <p><img class=center src=../../assets/img/08_PredictionAndMachineLearning/spurious.jpg height=450></p>
<p><a href="http://www.google.com/trends/correlate">http://www.google.com/trends/correlate</a></p>
<p><a href="http://www.newscientist.com/blogs/onepercent/2011/05/google-correlate-passes-our-we.html">http://www.newscientist.com/blogs/onepercent/2011/05/google-correlate-passes-our-we.html</a></p>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-4" style="background:;">
    <h2>Also common in geographic analyses</h2>
  </hgroup>
  <article>
    <p><img class=center src=../../assets/img/08_PredictionAndMachineLearning/heatmap.png height=450></p>
<p><a href="http://xkcd.com/1138/">http://xkcd.com/1138/</a></p>
  </article>
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      <slide class="" id="slide-5" style="background:;">
    <h2>Beware extrapolation!</h2>
  </hgroup>
  <article>
    <p><img class=center src=../../assets/img/08_PredictionAndMachineLearning/extrapolation.jpg height=450></p>
<p><a href="http://www.nature.com/nature/journal/v431/n7008/full/431525a.html">http://www.nature.com/nature/journal/v431/n7008/full/431525a.html</a></p>
  </article>
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      <slide class="" id="slide-6" style="background:;">
    <h2>Google data</h2>
  </hgroup>
  <article>
    <pre><code class="r">library(quantmod)
from.dat &lt;- as.Date(&quot;01/01/08&quot;, format=&quot;%m/%d/%y&quot;)
to.dat &lt;- as.Date(&quot;12/31/13&quot;, format=&quot;%m/%d/%y&quot;)
getSymbols(&quot;GOOG&quot;, src=&quot;google&quot;, from = from.dat, to = to.dat)
</code></pre>
<pre><code>[1] &quot;GOOG&quot;
</code></pre>
<pre><code class="r">head(GOOG)
</code></pre>
<pre><code>           GOOG.Open GOOG.High GOOG.Low GOOG.Close GOOG.Volume
</code></pre>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-7" style="background:;">
    <h2>Summarize monthly and store as time series</h2>
  </hgroup>
  <article>
    <pre><code class="r">mGoog &lt;- to.monthly(GOOG)
googOpen &lt;- Op(mGoog)
ts1 &lt;- ts(googOpen,frequency=12)
plot(ts1,xlab=&quot;Years+1&quot;, ylab=&quot;GOOG&quot;)
</code></pre>
<div class="rimage center"><img src="fig/tseries.png" title="plot of chunk tseries" alt="plot of chunk tseries" class="plot" /></div>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-8" style="background:;">
    <h2>Example time series decomposition</h2>
  </hgroup>
  <article>
<li><strong>Trend</strong>  - Consistently increasing pattern over time </li>
<li><strong>Seasonal</strong> -  When there is a pattern over a fixed period of time that recurs.</li>
<li><strong>Cyclic</strong> -  When data rises and falls over non fixed periods</li>
<p><a href="https://www.otexts.org/fpp/6/1">https://www.otexts.org/fpp/6/1</a></p>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-9" style="background:;">
    <h2>Decompose a time series into parts</h2>
  </hgroup>
  <article>
    <pre><code class="r">plot(decompose(ts1),xlab=&quot;Years+1&quot;)
</code></pre>
<div class="rimage center"><img src="fig/unnamed-chunk-1.png" title="plot of chunk unnamed-chunk-1" alt="plot of chunk unnamed-chunk-1" class="plot" /></div>
  </article>
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      <slide class="" id="slide-10" style="background:;">
    <h2>Training and test sets</h2>
  </hgroup>
  <article>
    <pre><code class="r">ts1Train &lt;- window(ts1,start=1,end=5)
ts1Test &lt;- window(ts1,start=5,end=(7-0.01))
</code></pre>
<pre><code>    Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
</code></pre>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-11" style="background:;">
    <h2>Simple moving average</h2>
  </hgroup>
  <article>
    <p>\[ Y_{t}=\frac{1}{2*k+1}\sum_{j=-k}^k {y_{t+j}}\]</p>
<pre><code class="r">plot(ts1Train)
lines(ma(ts1Train,order=3),col=&quot;red&quot;)
</code></pre>
<div class="rimage center"><img src="fig/unnamed-chunk-2.png" title="plot of chunk unnamed-chunk-2" alt="plot of chunk unnamed-chunk-2" class="plot" /></div>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-12" style="background:;">
    <h2>Exponential smoothing</h2>
  </hgroup>
  <article>
    <p><strong>Example - simple exponential smoothing</strong>
\[\hat{y}_{t+1} = \alpha y_t + (1-\alpha)\hat{y}_{t-1}\]</p>
<p><img class=center src=../../assets/img/08_PredictionAndMachineLearning/expsmooth.png height=300></p>
<p><a href="https://www.otexts.org/fpp/7/6">https://www.otexts.org/fpp/7/6</a></p>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-13" style="background:;">
    <h2>Exponential smoothing</h2>
  </hgroup>
  <article>
    <pre><code class="r">ets1 &lt;- ets(ts1Train,model=&quot;MMM&quot;)
fcast &lt;- forecast(ets1)
plot(fcast); lines(ts1Test,col=&quot;red&quot;)
</code></pre>
<div class="rimage center"><img src="fig/ets.png" title="plot of chunk ets" alt="plot of chunk ets" class="plot" /></div>
  </article>
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      <slide class="" id="slide-14" style="background:;">
    <h2>Get the accuracy</h2>
  </hgroup>
  <article>
    <pre><code class="r">accuracy(fcast,ts1Test)
</code></pre>
<pre><code>                   ME   RMSE    MAE     MPE   MAPE   MASE    ACF1 Theil&#39;s U
Training set   0.9464  48.78  39.35 -0.3297  7.932 0.3733 0.07298        NA
</code></pre>
  </article>
  <!-- Presenter Notes -->
      <slide class="" id="slide-15" style="background:;">
    <h2>Notes and further resources</h2>
  </hgroup>
  <article>
<li><a href="http://en.wikipedia.org/wiki/Forecasting">Forecasting and timeseries prediction</a> is an entire field</li>
<li>Rob Hyndman&#39;s <a href="https://www.otexts.org/fpp/">Forecasting: principles and practice</a> is a good place to start</li>
<li>Cautions
<li>Be wary of spurious correlations</li>
<li>Be careful how far you predict (extrapolation)</li>
<li>Be wary of dependencies over time</li>
<li>See <a href="http://cran.r-project.org/web/packages/quantmod/quantmod.pdf">quantmod</a> or <a href="http://www.quandl.com/help/packages/r">quandl</a> packages for finance-related problems.</li>
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