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<title>Superb AR(1) Model: Global Temperature Linear Part</title>
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<h1 class="title">Superb AR(1) Model: Global Temperature Linear Part</h1>
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<div class="cell">
<details>
<summary>Show the code</summary>
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>temps_ts <span class="ot"><-</span> rio<span class="sc">::</span><span class="fu">import</span>(<span class="st">"data/global_temparature.csv"</span>) <span class="sc">|></span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">as_tsibble</span>(<span class="at">index =</span> year) <span class="sc">|></span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(year <span class="sc">>=</span> <span class="dv">1970</span>)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>temps_ts <span class="sc">|></span> <span class="fu">autoplot</span>(<span class="at">.vars =</span> change) <span class="sc">+</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">labs</span>(</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> <span class="at">x =</span> <span class="st">"Year"</span>,</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> <span class="st">"Temperature Change (Celsius)"</span>,</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> <span class="at">title =</span> <span class="fu">paste0</span>(<span class="st">"Change in Mean Annual Global Temperature ("</span>, <span class="fu">min</span>(temps_ts<span class="sc">$</span>year), <span class="st">"-"</span>, <span class="fu">max</span>(temps_ts<span class="sc">$</span>year), <span class="st">")"</span>)</span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> ) <span class="sc">+</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme_minimal</span>() <span class="sc">+</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">theme</span>(</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a> <span class="at">plot.title =</span> <span class="fu">element_text</span>(<span class="at">hjust =</span> <span class="fl">0.5</span>)</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a> ) <span class="sc">+</span> </span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_smooth</span>(<span class="at">method=</span><span class="st">'lm'</span>, <span class="at">formula=</span> y<span class="sc">~</span>x)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div id="fig-globalTempTimePlot" class="quarto-figure quarto-figure-center anchored">
<figure class="figure">
<p><img src="_ch6_lesson2_global_temps_files/figure-html/fig-globalTempTimePlot-1.png" class="img-fluid figure-img" width="672"></p>
<figcaption class="figure-caption">Figure 1: Time plot of the mean annual temperature globally for select years.</figcaption>
</figure>
</div>
</div>
</div>
<div class="cell">
<details>
<summary>Show the code</summary>
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>global <span class="ot"><-</span> <span class="fu">tibble</span>(<span class="at">x =</span> <span class="fu">scan</span>(<span class="st">"data/global.dat"</span>)) <span class="sc">|></span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> <span class="at">date =</span> <span class="fu">seq</span>(</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">ymd</span>(<span class="st">"1856-01-01"</span>),</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> <span class="at">by =</span> <span class="st">"1 months"</span>,</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> <span class="at">length.out =</span> <span class="fu">n</span>()),</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="at">year =</span> <span class="fu">year</span>(date),</span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> <span class="at">year_month =</span> tsibble<span class="sc">::</span><span class="fu">yearmonth</span>(date),</span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="at">stats_time =</span> year <span class="sc">+</span> <span class="fu">c</span>(<span class="dv">0</span><span class="sc">:</span><span class="dv">11</span>)<span class="sc">/</span><span class="dv">12</span>)</span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>global_ts <span class="ot"><-</span> global <span class="sc">|></span></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">as_tsibble</span>(<span class="at">index =</span> year_month)</span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>temp_tidy <span class="ot"><-</span> global_ts <span class="sc">|></span> <span class="fu">filter</span>(year <span class="sc">>=</span> <span class="dv">1970</span>)</span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a>temp_lm <span class="ot"><-</span> temp_tidy <span class="sc">|></span></span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">model</span>(<span class="at">lm =</span> <span class="fu">TSLM</span>(x <span class="sc">~</span> stats_time ))</span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a><span class="co"># tidy(temp_lm) |> pull(estimate)</span></span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a><span class="fu">tidy</span>(temp_lm) <span class="sc">|></span></span>
<span id="cb2-20"><a href="#cb2-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span>
<span id="cb2-21"><a href="#cb2-21" aria-hidden="true" tabindex="-1"></a> <span class="at">lower =</span> estimate <span class="sc">+</span> <span class="fu">qnorm</span>(<span class="fl">0.025</span>) <span class="sc">*</span> std.error,</span>
<span id="cb2-22"><a href="#cb2-22" aria-hidden="true" tabindex="-1"></a> <span class="at">upper =</span> estimate <span class="sc">+</span> <span class="fu">qnorm</span>(<span class="fl">0.975</span>) <span class="sc">*</span> std.error</span>
<span id="cb2-23"><a href="#cb2-23" aria-hidden="true" tabindex="-1"></a> ) <span class="sc">|></span></span>
<span id="cb2-24"><a href="#cb2-24" aria-hidden="true" tabindex="-1"></a> <span class="fu">display_table</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output-display">
<div id="tbl-globalTempsEstParams" class="anchored">
<table class="table table-striped table-sm small" data-quarto-postprocess="true">
<caption>Table 1: Parameter estimates for the fitted global temperature time series.</caption>
<thead>
<tr class="header">
<th style="text-align: center;" data-quarto-table-cell-role="th">.model</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">term</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">estimate</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">std.error</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">statistic</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">p.value</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">lower</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">upper</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: center; min-width: 0in;">lm</td>
<td style="text-align: center; min-width: 0in;">(Intercept)</td>
<td style="text-align: center; min-width: 0in;">-34.920409</td>
<td style="text-align: center; min-width: 0in;">1.164899</td>
<td style="text-align: center; min-width: 0in;">-29.97721</td>
<td style="text-align: center; min-width: 0in;">0</td>
<td style="text-align: center; min-width: 0in;">-37.2035680</td>
<td style="text-align: center; min-width: 0in;">-32.6372500</td>
</tr>
<tr class="even">
<td style="text-align: center; min-width: 0in;">lm</td>
<td style="text-align: center; min-width: 0in;">stats_time</td>
<td style="text-align: center; min-width: 0in;">0.017654</td>
<td style="text-align: center; min-width: 0in;">0.000586</td>
<td style="text-align: center; min-width: 0in;">30.12786</td>
<td style="text-align: center; min-width: 0in;">0</td>
<td style="text-align: center; min-width: 0in;">0.0165055</td>
<td style="text-align: center; min-width: 0in;">0.0188025</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="cell">
<div class="cell-output-display">
<div id="tbl-globalTempsResidACF" class="anchored">
<table class="table table-striped table-sm small" data-quarto-postprocess="true">
<caption>Table 2: Autocorrelation function of the residuals for the global temperature time series.</caption>
<thead>
<tr class="header">
<th style="text-align: center;" data-quarto-table-cell-role="th">1M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">2M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">3M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">4M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">5M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">6M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">7M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">8M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">9M</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">10M</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: center; min-width: 0.5in;">0.706</td>
<td style="text-align: center; min-width: 0.5in;">0.638</td>
<td style="text-align: center; min-width: 0.5in;">0.5</td>
<td style="text-align: center; min-width: 0.5in;">0.447</td>
<td style="text-align: center; min-width: 0.5in;">0.375</td>
<td style="text-align: center; min-width: 0.5in;">0.307</td>
<td style="text-align: center; min-width: 0.5in;">0.254</td>
<td style="text-align: center; min-width: 0.5in;">0.206</td>
<td style="text-align: center; min-width: 0.5in;">0.12</td>
<td style="text-align: center; min-width: 0.5in;">0.078</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Load additional packages</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>pacman<span class="sc">::</span><span class="fu">p_load</span>(tidymodels, multilevelmod,</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> nlme, broom.mixed)</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>temp_spec <span class="ot"><-</span> <span class="fu">linear_reg</span>() <span class="sc">|></span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">set_engine</span>(<span class="st">"gls"</span>, <span class="at">correlation =</span> nlme<span class="sc">::</span><span class="fu">corAR1</span>(<span class="fl">0.706</span>))</span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>temp_gls <span class="ot"><-</span> temp_spec <span class="sc">|></span></span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">fit</span>(x <span class="sc">~</span> stats_time, <span class="at">data =</span> global_ts)</span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a><span class="fu">tidy</span>(temp_gls) <span class="sc">|></span></span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(</span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a> <span class="at">lower =</span> estimate <span class="sc">+</span> <span class="fu">qnorm</span>(<span class="fl">0.025</span>) <span class="sc">*</span> std.error,</span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a> <span class="at">upper =</span> estimate <span class="sc">+</span> <span class="fu">qnorm</span>(<span class="fl">0.975</span>) <span class="sc">*</span> std.error</span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a> )</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div class="cell">
<div class="cell-output-display">
<div id="tbl-globalTempsGLS" class="anchored">
<table class="table table-striped table-sm small" data-quarto-postprocess="true">
<caption>Table 3: Parameter estimates for the Generalized Least Squares estimates of the fit for the global temperature time series.</caption>
<thead>
<tr class="header">
<th style="text-align: center;" data-quarto-table-cell-role="th">term</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">estimate</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">std.error</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">statistic</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">p.value</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">lower</th>
<th style="text-align: center;" data-quarto-table-cell-role="th">upper</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td style="text-align: center; min-width: 0in;">(Intercept)</td>
<td style="text-align: center; min-width: 0in;">-9.1361773</td>
<td style="text-align: center; min-width: 0in;">0.4547490</td>
<td style="text-align: center; min-width: 0in;">-20.09059</td>
<td style="text-align: center; min-width: 0in;">0</td>
<td style="text-align: center; min-width: 0in;">-10.0274689</td>
<td style="text-align: center; min-width: 0in;">-8.2448856</td>
</tr>
<tr class="even">
<td style="text-align: center; min-width: 0in;">stats_time</td>
<td style="text-align: center; min-width: 0in;">0.0046599</td>
<td style="text-align: center; min-width: 0in;">0.0002354</td>
<td style="text-align: center; min-width: 0in;">19.79209</td>
<td style="text-align: center; min-width: 0in;">0</td>
<td style="text-align: center; min-width: 0in;">0.0041985</td>
<td style="text-align: center; min-width: 0in;">0.0051214</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="cell">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>temp_lm <span class="sc">|></span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">residuals</span>() <span class="sc">|></span></span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">acf</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img src="_ch6_lesson2_global_temps_files/figure-html/unnamed-chunk-8-1.png" class="img-fluid" width="672"></p>
</div>
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>temp_lm <span class="sc">|></span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">residuals</span>() <span class="sc">|></span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">pacf</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<p><img src="_ch6_lesson2_global_temps_files/figure-html/unnamed-chunk-8-2.png" class="img-fluid" width="672"></p>
</div>
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a> <span class="co"># model(arima = ARIMA(.resid ~ 1 + pdq(0,0,3) + PDQ(0, 0, 0))) </span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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