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README.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="viewport" content="width=device-width, initial-scale=1">
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<p>29 JAN 2018</p>
<h1 id="readme">README</h1>
<p>The goal of functions in this repo is to semi automatically build Ordinary Least Squares (OLS) models on the basis of a set of declared variables. If the available data is time series, lagging and differencing is possible.</p>
<h3 id="short-description-of-the-functions">1. Short description of the functions</h3>
<ol>
<li><code>ols</code>: Function allows building one OLS model and performs statistical tests.</li>
<li><code>ols_summary</code>: Function allows building multiple OLS models and lets the user parallelization of computations (if required).</li>
<li><code>ncomb</code>: Allows all possible combinations of a set of variables (including the ones after differencing).</li>
<li><code>lags</code>: Allows lagging variables.</li>
<li><code>difs</code>: Allows differencing variables.</li>
<li><code>PRESS</code>: Computes PRESS statistic required to calculate predicted R-squared.</li>
<li><code>pred_r_squared</code>: Computes predicted R-squared.</li>
</ol>
<h3 id="tutorial">2. Tutorial</h3>
<p>This tutorial will teach you how to use above mentioned functions. After getting through below given examples, you'll be able to:</p>
<ol>
<li>Build one regression model and test it.</li>
<li>Visualize histogram of errors.</li>
<li>Obtaining additional statistic: predicted R-squared.</li>
<li>Difference and lag selected variables.</li>
<li>Build multiple regression models and test them.</li>
<li>Use parallelization while building multiple models.</li>
<li>Decide if utilizing parallelization actually shortens computation time.</li>
</ol>
<h3 id="required-packages">2.0 Required packages</h3>
<p>Before starting our tutorial, a few packages should be installed <em>a priori</em>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">install.packages</span>(<span class="st">"caret"</span>)
<span class="kw">install.packages</span>(<span class="st">"lmtest"</span>)
<span class="kw">install.packages</span>(<span class="st">"car"</span>)
<span class="kw">install.packages</span>(<span class="st">"nortest"</span>)
<span class="kw">install.packages</span>(<span class="st">"scales"</span>)
<span class="kw">install.packages</span>(<span class="st">"strucchange"</span>)
<span class="kw">install.packages</span>(<span class="st">"zoo"</span>)
<span class="kw">install.packages</span>(<span class="st">"lubridate"</span>)
<span class="kw">install.packages</span>(<span class="st">"nortest"</span>)
<span class="kw">install.packages</span>(<span class="st">"microbenchmark"</span>)
<span class="kw">install.packages</span>(<span class="st">"RcppEigen"</span>)</code></pre></div>
<h3 id="our-first-regression-model">2.1 Our first regression model</h3>
<p>Firstly, let's read the data. We will take advantage of <code>EuStockMarkets</code> from library <code>datasets</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(datasets)
<span class="kw">library</span>(RcppEigen)
<span class="kw">data</span>(EuStockMarkets)</code></pre></div>
<p>Let's take a look at a couple of rows:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">head</span>(EuStockMarkets)</code></pre></div>
<table>
<thead>
<tr class="header">
<th align="right">DAX</th>
<th align="right">SMI</th>
<th align="right">CAC</th>
<th align="right">FTSE</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="right">1628.75</td>
<td align="right">1678.1</td>
<td align="right">1772.8</td>
<td align="right">2443.6</td>
</tr>
<tr class="even">
<td align="right">1613.63</td>
<td align="right">1688.5</td>
<td align="right">1750.5</td>
<td align="right">2460.2</td>
</tr>
<tr class="odd">
<td align="right">1606.51</td>
<td align="right">1678.6</td>
<td align="right">1718.0</td>
<td align="right">2448.2</td>
</tr>
<tr class="even">
<td align="right">1621.04</td>
<td align="right">1684.1</td>
<td align="right">1708.1</td>
<td align="right">2470.4</td>
</tr>
<tr class="odd">
<td align="right">1618.16</td>
<td align="right">1686.6</td>
<td align="right">1723.1</td>
<td align="right">2484.7</td>
</tr>
<tr class="even">
<td align="right">1610.61</td>
<td align="right">1671.6</td>
<td align="right">1714.3</td>
<td align="right">2466.8</td>
</tr>
</tbody>
</table>
<p>The data set consists of 4 time series - stock indexes. In order to build our first OLS models, we can use the function <code>ols</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"SMI CAC FTSE"</span>)</code></pre></div>
<p>The first argument, <code>dset</code>, is the data set we want to use. <code>target</code> is our target variable; <code>vars</code> is a string containing variable names separated by single blanks (spaces). Let’s take a look at names of consecutive elements of <code>model1</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">names</span>(model1)</code></pre></div>
<pre><code>## [1] "stats" "var.stats" "plot"
## [4] "output.residuals" "time.plot"</code></pre>
<p>We can see that the object consists of 5 elements. We will start our analysis with the first one, <code>stats</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1<span class="op">$</span>stats</code></pre></div>
<table>
<colgroup>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="1%"></col>
<col width="1%"></col>
<col width="25%"></col>
</colgroup>
<thead>
<tr class="header">
<th align="left">target</th>
<th align="left">vars</th>
<th align="right">R2</th>
<th align="right">adjusted.R2</th>
<th align="right">RMSE</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">F.stat</th>
<th align="right">F.p.value</th>
<th align="right">bp.stat</th>
<th align="right">bp.p.value</th>
<th align="right">bg.stat</th>
<th align="right">bg.p.value</th>
<th align="right">reset.stat</th>
<th align="right">reset.p.value</th>
<th align="right">ad.stat</th>
<th align="right">ad.p.value</th>
<th align="right">sw.stat</th>
<th align="right">sw.p.value</th>
<th align="right">chow.stat</th>
<th align="right">chow.p.value</th>
<th align="left">significance</th>
<th align="right">max.p.value</th>
<th align="right">max.vif</th>
<th align="left">tests</th>
<th align="right">n</th>
<th align="left">equation</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">DAX</td>
<td align="left">SMI CAC FTSE</td>
<td align="right">0.9898478</td>
<td align="right">0.9898314</td>
<td align="right">803.3033</td>
<td align="right">22749.55</td>
<td align="right">22777.19</td>
<td align="right">60320.47</td>
<td align="right">0</td>
<td align="right">243.397</td>
<td align="right">0</td>
<td align="right">1803.221</td>
<td align="right">0</td>
<td align="right">47.01741</td>
<td align="right">0</td>
<td align="right">10.44616</td>
<td align="right">0</td>
<td align="right">0.9862875</td>
<td align="right">0</td>
<td align="right">144.7465</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.4103735</td>
<td align="right">100.8572</td>
<td align="left">TRUE</td>
<td align="right">1860</td>
<td align="left">(Intercept)<em>(-175.945668313583)+SMI</em>(0.49277225460085)+CAC<em>(0.495653787472762)+FTSE</em>(-0.0172026329222922)</td>
</tr>
</tbody>
</table>
<p>The output presents a flat table, showing the target variable, the independent variables, statistics representing the model quality (R-Squared, adjusted R-Squared, RMSE) and some statistical tests:</p>
<ol>
<li><strong>AIC</strong>: Akaike Information Criterion comparable between different models; the smaller the AIC, the better the fit.</li>
<li><strong>BIC</strong>: Schwarz's Bayesian Criterion comparable between different models; the smaller the AIC, the better the fit. BIC is more restrictive than AIC: it penalizes more heavily models with greater number of parameters.</li>
<li><strong>F</strong>: significance test of all variables in the model.</li>
<li><strong>bp</strong>: Breusch-Pagan heteroscedasticity test.</li>
<li><strong>bg</strong>: Breusch-Godfrey autocorrelation test.</li>
<li><strong>reset</strong>: RESET specification test (informs whether the linear model can be applied for such target and independent variables).</li>
<li><strong>ad</strong>: Anderson-Darling normality of error term test.</li>
<li><strong>sw</strong>: Shapiro-Wilk normality of error term test (for small samples, n<20).</li>
<li><strong>chow</strong>: Chow test checking stability of coefficients in time.</li>
<li><strong>max.vif</strong>: Maximum VIF (Variance Inflation Factor) in the model.</li>
<li><strong>significance</strong>: point out whether all variable in a model are statistically significant at determined level (by default: 5%).</li>
<li><strong>max.p.value</strong>: shows the p.value of <em>the least significant</em> variable. 11. 11. <strong>tests</strong>: column informs whether the model complies with tests from points 2-7.</li>
<li><strong>n</strong>: number of observations, on which the model was built. The last column shows the equation of a given regression.</li>
</ol>
<p>Last but not least, the column <strong>equation</strong> presents model equation.</p>
<p>The table <code>var.stats</code> show statistics of regressors:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1<span class="op">$</span>var.stats</code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">var</th>
<th align="right">coef</th>
<th align="right">p.value</th>
<th align="right">vif</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">(Intercept)</td>
<td align="right">-175.9456683</td>
<td align="right">0.0000848</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="left">SMI</td>
<td align="right">0.4927723</td>
<td align="right">0.0000000</td>
<td align="right">100.85721</td>
</tr>
<tr class="odd">
<td align="left">CAC</td>
<td align="right">0.4956538</td>
<td align="right">0.0000000</td>
<td align="right">12.47012</td>
</tr>
<tr class="even">
<td align="left">FTSE</td>
<td align="right">-0.0172026</td>
<td align="right">0.4103735</td>
<td align="right">64.68514</td>
</tr>
</tbody>
</table>
<p>The consecutive columns shows variable names, their coefficients, p.values and VIFs. We can see that VIFs of <code>SMI</code> and <code>FTSE</code> are way beyond 10 (one of many literature threshold for this indicator). We will cope with this problem later.</p>
<p>The default p-value for the regression is <code>alpha = 0.05</code>. This parameter can also be changed:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"SMI CAC FTSE"</span>,
<span class="dt">alpha =</span> <span class="fl">0.1</span>)
model1[<span class="st">"var.stats"</span>]</code></pre></div>
<pre><code>## $var.stats
## var coef p.value vif
## (Intercept) (Intercept) -175.94566831 8.479065e-05 NA
## SMI SMI 0.49277225 9.020895e-181 100.85721
## CAC CAC 0.49565379 2.999041e-180 12.47012
## FTSE FTSE -0.01720263 4.103735e-01 64.68514</code></pre>
<p>As mentioned above, multicollinearity was observed. In order to get rid of it, we can exclude the <code>SMI</code> index from the model:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model2 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"CAC FTSE"</span>)
model2<span class="op">$</span>var.stats</code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">var</th>
<th align="right">coef</th>
<th align="right">p.value</th>
<th align="right">vif</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">(Intercept)</td>
<td align="right">-1575.3045205</td>
<td align="right">0</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td align="left">CAC</td>
<td align="right">0.8479211</td>
<td align="right">0</td>
<td align="right">6.194059</td>
</tr>
<tr class="odd">
<td align="left">FTSE</td>
<td align="right">0.6217500</td>
<td align="right">0</td>
<td align="right">6.194059</td>
</tr>
</tbody>
</table>
<p>It is also possible to build a model without an intercept. Such an action is controlled by the parameter <code>intercept</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model3 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"CAC FTSE"</span>,
<span class="dt">intercept =</span> <span class="ot">FALSE</span>)</code></pre></div>
<pre><code>## Warning in vif.default(model.original): No intercept: vifs may not be
## sensible.</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model3<span class="op">$</span>var.stats</code></pre></div>
<table style="width:100%;">
<colgroup>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="4%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="4%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="4%"></col>
<col width="4%"></col>
<col width="4%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="15%"></col>
</colgroup>
<thead>
<tr class="header">
<th align="left">target</th>
<th align="left">vars</th>
<th align="right">R2</th>
<th align="right">adjusted.R2</th>
<th align="right">RMSE</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">F.stat</th>
<th align="right">F.p.value</th>
<th align="right">bg.stat</th>
<th align="right">bg.p.value</th>
<th align="right">reset.stat</th>
<th align="right">reset.p.value</th>
<th align="right">ad.stat</th>
<th align="right">ad.p.value</th>
<th align="right">sw.stat</th>
<th align="right">sw.p.value</th>
<th align="right">chow.stat</th>
<th align="right">chow.p.value</th>
<th align="left">significance</th>
<th align="right">max.p.value</th>
<th align="right">max.vif</th>
<th align="left">tests</th>
<th align="right">n</th>
<th align="left">equation</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">DAX</td>
<td align="left">CAC FTSE</td>
<td align="right">0.9769045</td>
<td align="right">0.9768796</td>
<td align="right">670.5558</td>
<td align="right">27740.15</td>
<td align="right">27756.73</td>
<td align="right">39295.28</td>
<td align="right">0</td>
<td align="right">1854.851</td>
<td align="right">0</td>
<td align="right">8859.123</td>
<td align="right">0</td>
<td align="right">138.9562</td>
<td align="right">0</td>
<td align="right">0.7871347</td>
<td align="right">0</td>
<td align="right">3803.564</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0</td>
<td align="right">88.15412</td>
<td align="left">TRUE</td>
<td align="right">1860</td>
<td align="left">CAC<em>(0.321755922999695)+FTSE</em>(0.536557076690009)</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr class="header">
<th align="left">var</th>
<th align="right">coef</th>
<th align="right">p.value</th>
<th align="right">vif</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">CAC</td>
<td align="right">0.3217559</td>
<td align="right">0</td>
<td align="right">88.15412</td>
</tr>
<tr class="even">
<td align="left">FTSE</td>
<td align="right">0.5365571</td>
<td align="right">0</td>
<td align="right">88.15412</td>
</tr>
</tbody>
</table>
<p>In such case Breusch-Pagan test won't be executed (it requires an intercept).</p>
<h3 id="visualizations">2.2 Visualizations</h3>
<p>We can output residuals of the regression by using the argument <code>output.residuals</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"SMI CAC FTSE"</span>,
<span class="dt">visualize =</span> <span class="ot">TRUE</span>,
<span class="dt">output.residuals =</span> <span class="ot">TRUE</span>)
<span class="kw">qplot</span>(model1[[<span class="st">"output.residuals"</span>]]) <span class="op">+</span>
<span class="st"> </span><span class="kw">theme_minimal</span>() <span class="op">+</span>
<span class="st"> </span><span class="kw">xlab</span>(<span class="st">''</span>) <span class="op">+</span>
<span class="st"> </span><span class="kw">ggtitle</span>(<span class="st">"Histogram of residuals"</span>) <span class="co"># plot</span></code></pre></div>
<pre><code>## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.</code></pre>
<p><img src="data:image/png;base64,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" /></p>
<p>The <code>EuStockMarkets</code> data set is an object of <code>mts</code> class. That means that it includes dates. We can take advantage of it and visualize predicted and observed values of <code>DAX</code> on one plot dependent on time. To do it,<code>time.series</code> and <code>visualize</code> arguments are used:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"CAC FTSE"</span>,
<span class="dt">visualize =</span> <span class="ot">TRUE</span>,
<span class="dt">time.series =</span> <span class="ot">TRUE</span>)
model1<span class="op">$</span>time.plot</code></pre></div>
<pre><code>## Don't know how to automatically pick scale for object of type yearmon. Defaulting to continuous.</code></pre>
<p><img src="data:image/png;base64,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" /></p>
<p>However, data usually comes in the form of data frames. In such case, <code>time.plot</code> can be produced as well by pointing out the time variable in the data set. Exemplyfing, we will obtain the time variable from <code>EuStockMarkets</code>,transform it to a data frame and add the extracted time:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(zoo)
date <-<span class="st"> </span><span class="kw">as.yearmon</span>(<span class="kw">time</span>(EuStockMarkets))
EuStockMarkets <-<span class="st"> </span><span class="kw">data.frame</span>(EuStockMarkets)
EuStockMarkets<span class="op">$</span>date <-<span class="st"> </span>date</code></pre></div>
<p>Now, let's build our model again, this time with calling the <code>time.var</code> argument and setting its value to previously obtained <code>date</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"CAC FTSE"</span>,
<span class="dt">visualize =</span> <span class="ot">TRUE</span>,
<span class="dt">time.var =</span> <span class="st">"date"</span>)
model1<span class="op">$</span>time.plot</code></pre></div>
<pre><code>## Don't know how to automatically pick scale for object of type yearmon. Defaulting to continuous.</code></pre>
<p><img src="data:image/png;base64,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" /> We can see that the plots are identical.</p>
<p>Last but not least, it is possible to plot predicted and observed value even for . The object is produced by <code>ols</code> when <code>visualize</code> is set to <code>TRUE</code> and is simply called <code>plot</code>. This time we will use <code>iris</code> data set:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model2 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> iris,
<span class="dt">target =</span> <span class="st">"Sepal.Length"</span>,
<span class="dt">vars =</span> <span class="st">"Sepal.Width Petal.Length"</span>,
<span class="dt">visualize =</span> <span class="ot">TRUE</span>)
model2<span class="op">$</span>plot</code></pre></div>
<p><img src="data:image/png;base64,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" /></p>
<h3 id="additional-statistic-predicted-r-squared">2.3 Additional statistic: predicted R-squared</h3>
<p>An additional statistic which can be optionally obtained is a predicted R-squared. It helps evaluating how well the model predicts new observations. The higher predicted R-squared, the better your model is at predictng new instances of the target variable. The method of its calculation is as follows:</p>
<ol>
<li>For every sample in the data set perform a Leave-One-Out Cross-Validation (LOOCV):</li>
</ol>
<ul>
<li>Predict the left out in a given run target value on the basis of the model built without this value.</li>
</ul>
<ol>
<li>Compute the sum of squared differences between predicted and observed values obtained in .): it is so called <code>PRESS</code> statistic.</li>
<li>Compute the ratio: <code>PRESS/TSS</code> (<code>TSS</code> = Tota Sum of Squared, i.e. the sum of squared differences between the target values and their average).</li>
<li>Compute predicted R-squared: <code>1 - PRESS/TSS</code>.</li>
</ol>
<p>If you're interested in more details, they can be found <a href="https://rpubs.com/RatherBit/102428">here</a>.</p>
<p>Let's not jump to the example. Again, we will use the <code>EuStockMarkets</code> data set. It is worth mentioning that for the needs of calculation of this statistic the <strong>data set have to be a data frame</strong> (not a <code>mts</code> object). However, in this example we don't have to worry about that since we transformed it earlier. The parameter controlling the output of this statistic is called <code>pred.R2</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">model4 <-<span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"CAC FTSE"</span>,
<span class="dt">pred.R2 =</span> <span class="ot">TRUE</span>)
model4<span class="op">$</span>stats</code></pre></div>
<table style="width:100%;">
<colgroup>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="1%"></col>
<col width="1%"></col>
<col width="20%"></col>
</colgroup>
<thead>
<tr class="header">
<th align="left">target</th>
<th align="left">vars</th>
<th align="right">R2</th>
<th align="right">adjusted.R2</th>
<th align="right">RMSE</th>
<th align="right">pred.R2</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">F.stat</th>
<th align="right">F.p.value</th>
<th align="right">bp.stat</th>
<th align="right">bp.p.value</th>
<th align="right">bg.stat</th>
<th align="right">bg.p.value</th>
<th align="right">reset.stat</th>
<th align="right">reset.p.value</th>
<th align="right">ad.stat</th>
<th align="right">ad.p.value</th>
<th align="right">sw.stat</th>
<th align="right">sw.p.value</th>
<th align="right">chow.stat</th>
<th align="right">chow.p.value</th>
<th align="left">significance</th>
<th align="right">max.p.value</th>
<th align="right">max.vif</th>
<th align="left">tests</th>
<th align="right">n</th>
<th align="left">equation</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">DAX</td>
<td align="left">CAC FTSE</td>
<td align="right">0.9841894</td>
<td align="right">0.9841724</td>
<td align="right">708.3813</td>
<td align="right">0.9841277</td>
<td align="right">23571.5</td>
<td align="right">23593.62</td>
<td align="right">57798.07</td>
<td align="right">0</td>
<td align="right">301.2286</td>
<td align="right">0</td>
<td align="right">1802.022</td>
<td align="right">0</td>
<td align="right">146.4167</td>
<td align="right">0</td>
<td align="right">4.530819</td>
<td align="right">0</td>
<td align="right">0.9935889</td>
<td align="right">3e-07</td>
<td align="right">256.8144</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0</td>
<td align="right">6.194059</td>
<td align="left">TRUE</td>
<td align="right">1860</td>
<td align="left">(Intercept)<em>(-1575.30452045062)+CAC</em>(0.847921086750325)+FTSE*(0.621750000476402)</td>
</tr>
</tbody>
</table>
<p>As we can see, the predicted R-squared is lower then both R-squared and adjusted R-squared.</p>
<p>Calculation of the predicted R-squared is turned off by default since it's really time consuming. Performing LOOCV translates to computing additional <code>n</code> models (where <code>n</code> is the number of observations in your data set). In the example above it was 1860 additional OLS models. Let's check how it influences computation time We will use the <code>microbenchmark</code> library. Each function was ran 100 times and on the basis of the results, basis statistics were obtained.</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(microbenchmark)
mbm.pred.R2 <-<span class="st"> </span><span class="kw">microbenchmark</span>(
<span class="st">"pred.R2"</span> =<span class="st"> </span>{model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"SMI CAC FTSE"</span>,
<span class="dt">pred.R2 =</span> <span class="ot">TRUE</span>)},
<span class="st">"no.pred.R2"</span> =<span class="st"> </span>{model1 <-<span class="st"> </span><span class="kw">ols</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">target =</span> <span class="st">"DAX"</span>,
<span class="dt">vars =</span> <span class="st">"SMI CAC FTSE"</span>,
<span class="dt">pred.R2 =</span> <span class="ot">FALSE</span>)})
mbm.pred.R2</code></pre></div>
<table>
<thead>
<tr class="header">
<th align="left">expr</th>
<th align="right">min</th>
<th align="right">lq</th>
<th align="right">mean</th>
<th align="right">median</th>
<th align="right">uq</th>
<th align="right">max</th>
<th align="right">neval</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left">pred.R2</td>
<td align="right">4671.14071</td>
<td align="right">4875.92802</td>
<td align="right">5141.06066</td>
<td align="right">5069.80760</td>
<td align="right">5291.08432</td>
<td align="right">6752.8239</td>
<td align="right">100</td>
</tr>
<tr class="even">
<td align="left">no.pred.R2</td>
<td align="right">43.77589</td>
<td align="right">45.09869</td>
<td align="right">49.16099</td>
<td align="right">47.61333</td>
<td align="right">50.61435</td>
<td align="right">87.3956</td>
<td align="right">100</td>
</tr>
</tbody>
</table>
<p>As we can see, the computation time rockets on average by 104.576016 times from 0.049161 to 5.1410607 seconds!</p>
<h3 id="differencing-and-lagging-variables">2.4 Differencing and lagging variables</h3>
<p>Now we will proceed to building multiple models. At the moment objects of class <code>mts</code> are not handled, so at first our data set should be converted into a data frame (if it hasn't been done earlier). Then we can add some lagged variables. To lag regressors, we can use <code>lag</code> function:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">EuStockMarkets <-<span class="st"> </span><span class="kw">data.frame</span>(EuStockMarkets)
EuStockMarkets <-<span class="st"> </span><span class="kw">lags</span>(<span class="dt">dset =</span> EuStockMarkets,
<span class="dt">vars =</span> <span class="kw">c</span>(<span class="st">"SMI"</span>, <span class="st">"CAC"</span>, <span class="st">"FTSE"</span>),
<span class="dt">lag.vec =</span> <span class="dv">1</span><span class="op">:</span><span class="dv">4</span>)</code></pre></div>
<p><code>dset</code> is the data set, in which variables can be found. The argument<code>vars</code> selects variables, which should be lagged. <code>lag.vec</code> is a vector of lags which should be executed. In this case, there are four lags: the minimum lag is <code>1</code>, and the maximum is <code>4</code>. Lagged variables have a suffix <code>.<lag.order.</code>, e.g. the <code>SME</code> index lagged by with a lag of three periods is called <code>SMI.3</code>.</p>
<p>Having lagged variables, we can proceed to obtaining vectors of all the possible combinations of lagged (and unlagged) regressors. To do this, we will use the function <code>ncomb</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">vars <-<span class="st"> </span><span class="kw">ncomb</span>(<span class="dt">vec =</span> <span class="kw">c</span>(<span class="st">"SMI"</span>, <span class="st">"CAC"</span>, <span class="st">"FTSE"</span>),
<span class="dt">m =</span> <span class="dv">1</span>,
<span class="dt">n =</span> <span class="dv">3</span>,
<span class="dt">max.lag =</span> <span class="dv">4</span>)</code></pre></div>
<p>The vector <code>vec</code> indicates, which variables should be taken into consideration when making combinations. <code>m</code> is a minimum number in combination and <code>n</code> is maximum number of variables in combination. <code>max.lag</code> indicates maximum lag of variables, which should be used when making combinations.</p>
<p>Let's see the result of <code>ncomb</code>:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">head</span>(vars, <span class="dv">10</span>)</code></pre></div>
<pre><code>## [1] "SMI.1" "SMI.2" "SMI.3" "SMI.4" "SMI" "CAC.1" "CAC.2" "CAC.3"
## [9] "CAC.4" "CAC"</code></pre>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">tail</span>(vars, <span class="dv">10</span>)</code></pre></div>
<pre><code>## [1] "SMI.1 CAC.4 FTSE" "SMI.2 CAC.4 FTSE" "SMI.3 CAC.4 FTSE"
## [4] "SMI.4 CAC.4 FTSE" "SMI CAC.4 FTSE" "SMI.1 CAC FTSE"
## [7] "SMI.2 CAC FTSE" "SMI.3 CAC FTSE" "SMI.4 CAC FTSE"
## [10] "SMI CAC FTSE"</code></pre>
<p>and the number of produced combinations</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">n.models <-<span class="st"> </span><span class="kw">length</span>(vars)
n.models</code></pre></div>
<pre><code>## [1] 215</code></pre>
<h3 id="creating-multiple-regression-models">2.5 Creating multiple regression models</h3>
<p>As we can see, in a moment we will build 215 OLS models. To obtain them in one command, <code>ols_summary</code> function will be used:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">models <-<span class="st"> </span><span class="kw">ols_summary</span>(<span class="dt">dset.sum =</span> EuStockMarkets,
<span class="dt">target.sum =</span> <span class="kw">rep</span>(<span class="st">"DAX"</span>, n.models),
<span class="dt">vars.sum =</span> vars)</code></pre></div>
<p><code>dset.sum</code> is our converted data set, <code>target.sum</code> is target variable repeated <code>n.models</code> times (since we want to build such a number of regressions) and <code>vars.sum</code> is a vector of all combinations of regressors produced by <code>ncomb</code> function.</p>
<p>The results are of the same structure as in case of our first model (obtained from <code>ols</code> function). The only additional column we get is <code>model.num</code>, which is a model number:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">models.stats <-<span class="st"> </span>models<span class="op">$</span>stats
models.stats<span class="op">$</span>model.num</code></pre></div>
<pre><code>## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
## [18] 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
## [35] 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
## [52] 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
## [69] 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
## [86] 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## [103] 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119
## [120] 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
## [137] 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153
## [154] 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
## [171] 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
## [188] 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
## [205] 205 206 207 208 209 210 211 212 213 214 215</code></pre>
<p>Let's see six best models in terms of adjusted R-Squared:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r"><span class="kw">head</span>(models.stats[<span class="kw">order</span>(models.stats<span class="op">$</span>adjusted.R2, <span class="dt">decreasing =</span> T),])</code></pre></div>
<table>
<colgroup>
<col width="1%"></col>
<col width="1%"></col>
<col width="4%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="1%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="2%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="3%"></col>
<col width="2%"></col>
<col width="1%"></col>
<col width="24%"></col>
<col width="2%"></col>
<col width="2%"></col>
</colgroup>
<thead>
<tr class="header">
<th></th>
<th align="left">target</th>
<th align="left">vars</th>
<th align="right">R2</th>
<th align="right">adjusted.R2</th>
<th align="right">RMSE</th>
<th align="right">pred.R2</th>
<th align="right">AIC</th>
<th align="right">BIC</th>
<th align="right">F.stat</th>
<th align="right">F.p.value</th>
<th align="right">bp.stat</th>
<th align="right">bp.p.value</th>
<th align="right">bg.stat</th>
<th align="right">bg.p.value</th>
<th align="right">reset.stat</th>
<th align="right">reset.p.value</th>
<th align="right">ad.stat</th>
<th align="right">ad.p.value</th>
<th align="right">sw.stat</th>
<th align="right">sw.p.value</th>
<th align="right">chow.stat</th>
<th align="left">chow.p.value</th>
<th align="right">significance</th>
<th align="right">max.p.value</th>
<th align="left">max.vif</th>
<th align="right">tests</th>
<th align="left">n</th>
<th align="left">equation</th>
<th align="right">model.num</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>185</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4 FTSE.4</td>
<td align="right">0.9899472</td>
<td align="right">0.9899309</td>
<td align="right">803.4522</td>
<td align="right">22683.54</td>
<td align="right">22711.17</td>
<td align="right">60791.90</td>
<td align="right">0</td>
<td align="right">204.6968</td>
<td align="right">0</td>
<td align="right">1761.647</td>
<td align="right">0</td>
<td align="right">45.56233</td>
<td align="right">0</td>
<td align="right">10.304760</td>
<td align="right">0</td>
<td align="right">0.9867456</td>
<td align="right">0</td>
<td align="right">134.6473</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.0348734</td>
<td align="right">85.364357</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-127.626973618169)+SMI</em>(0.513114108395759)+CAC.4<em>(0.482952957049387)+FTSE.4</em>(-0.0416017513798577)</td>
<td align="left">DAX</td>
<td align="right">185</td>
</tr>
<tr class="even">
<td>160</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4 FTSE.3</td>
<td align="right">0.9899393</td>
<td align="right">0.9899230</td>
<td align="right">803.9688</td>
<td align="right">22684.99</td>
<td align="right">22712.62</td>
<td align="right">60743.76</td>
<td align="right">0</td>
<td align="right">206.9403</td>
<td align="right">0</td>
<td align="right">1758.698</td>
<td align="right">0</td>
<td align="right">47.30768</td>
<td align="right">0</td>
<td align="right">10.094337</td>
<td align="right">0</td>
<td align="right">0.9869969</td>
<td align="right">0</td>
<td align="right">133.6170</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.0832867</td>
<td align="right">89.611317</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-140.068438037302)+SMI</em>(0.50873290702042)+CAC.4<em>(0.484290355238345)+FTSE.3</em>(-0.034770345076648)</td>
<td align="left">DAX</td>
<td align="right">160</td>
</tr>
<tr class="odd">
<td>135</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4 FTSE.2</td>
<td align="right">0.9899310</td>
<td align="right">0.9899147</td>
<td align="right">804.4874</td>
<td align="right">22686.53</td>
<td align="right">22714.16</td>
<td align="right">60693.01</td>
<td align="right">0</td>
<td align="right">209.3146</td>
<td align="right">0</td>
<td align="right">1758.335</td>
<td align="right">0</td>
<td align="right">49.77853</td>
<td align="right">0</td>
<td align="right">9.865628</td>
<td align="right">0</td>
<td align="right">0.9872799</td>
<td align="right">0</td>
<td align="right">133.0109</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.2257422</td>
<td align="right">94.180270</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-158.998174628224)+SMI</em>(0.502095876874254)+CAC.4<em>(0.486880719902912)+FTSE.2</em>(-0.0247679406452226)</td>
<td align="left">DAX</td>
<td align="right">135</td>
</tr>
<tr class="even">
<td>35</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4</td>
<td align="right">0.9899230</td>
<td align="right">0.9899121</td>
<td align="right">700.2205</td>
<td align="right">22686.00</td>
<td align="right">22708.10</td>
<td align="right">91015.77</td>
<td align="right">0</td>
<td align="right">211.9794</td>
<td align="right">0</td>
<td align="right">1755.853</td>
<td align="right">0</td>
<td align="right">45.51831</td>
<td align="right">0</td>
<td align="right">9.365358</td>
<td align="right">0</td>
<td align="right">0.9878405</td>
<td align="right">0</td>
<td align="right">170.6485</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.0000000</td>
<td align="right">9.181714</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-207.684673377669)+SMI</em>(0.485097308509324)+CAC.4*(0.494904389563161)</td>
<td align="left">DAX</td>
<td align="right">35</td>
</tr>
<tr class="odd">
<td>110</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4 FTSE.1</td>
<td align="right">0.9899247</td>
<td align="right">0.9899083</td>
<td align="right">804.9980</td>
<td align="right">22687.70</td>
<td align="right">22715.33</td>
<td align="right">60654.42</td>
<td align="right">0</td>
<td align="right">211.9374</td>
<td align="right">0</td>
<td align="right">1757.695</td>
<td align="right">0</td>
<td align="right">53.06066</td>
<td align="right">0</td>
<td align="right">9.579326</td>
<td align="right">0</td>
<td align="right">0.9876018</td>
<td align="right">0</td>
<td align="right">133.3751</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.5827608</td>
<td align="right">98.990796</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-184.955738670181)+SMI</em>(0.493022354676854)+CAC.4<em>(0.490983988133413)+FTSE.1</em>(-0.0114386271974997)</td>
<td align="left">DAX</td>
<td align="right">110</td>
</tr>
<tr class="even">
<td>210</td>
<td align="left">DAX</td>
<td align="left">SMI CAC.4 FTSE</td>
<td align="right">0.9899234</td>
<td align="right">0.9899070</td>
<td align="right">805.5190</td>
<td align="right">22687.94</td>
<td align="right">22715.57</td>
<td align="right">60646.48</td>
<td align="right">0</td>
<td align="right">214.9618</td>
<td align="right">0</td>
<td align="right">1755.931</td>
<td align="right">0</td>
<td align="right">57.17214</td>
<td align="right">0</td>
<td align="right">9.268893</td>
<td align="right">0</td>
<td align="right">0.9879479</td>
<td align="right">0</td>
<td align="right">134.8465</td>
<td align="right">0</td>
<td align="left">TRUE</td>
<td align="right">0.8036974</td>
<td align="right">103.232524</td>
<td align="left">TRUE</td>
<td align="right">1856</td>
<td align="left">(Intercept)<em>(-218.221847587644)+SMI</em>(0.481427677619494)+CAC.4<em>(0.496796260977783)+FTSE</em>(0.00525002049348799)</td>
<td align="left">DAX</td>
<td align="right">210</td>
</tr>
</tbody>
</table>
<p>As it can be noticed, the best model was the 185th one. We can see it by looking it up in <code>vars.stats</code> list:</p>
<div class="sourceCode"><pre class="sourceCode r"><code class="sourceCode r">vars.stats <-<span class="st"> </span>models<span class="op">$</span>vars.stats
vars.stats[[<span class="dv">185</span>]]</code></pre></div>
<table>
<thead>
<tr class="header">
<th></th>
<th align="left">var</th>
<th align="right">coef</th>
<th align="right">p.value</th>
<th align="right">vif</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>(Intercept)</td>
<td align="left">(Intercept)</td>
<td align="right">-127.6269736</td>
<td align="right">0.0019513</td>
<td align="right">NA</td>
</tr>
<tr class="even">
<td>SMI</td>
<td align="left">SMI</td>
<td align="right">0.5131141</td>
<td align="right">0.0000000</td>
<td align="right">85.36436</td>
</tr>
<tr class="odd">
<td>CAC.4</td>
<td align="left">CAC.4</td>
<td align="right">0.4829530</td>