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| 35 | <td><a href="./../../overview.html?format=raw" title="Overview of library">Overview</a></td> |
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| 47 | <td><a href="./../../idldoc-index.html?format=raw" title="Index of files, routines, and parameters">Index</a></td> |
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| 72 | <div id="secondary_navbar"> |
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| 73 | |
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| 74 | <a href="a_correlate2d.html"><<prev file</a> | <a href="c_timecorrelate.html">next file >></a> <a href="a_timecorrelate.html" target="_TOP">view single page</a> | <a href="./../../index.html?format=raw" target="_TOP">view frames</a> summary: fields | <a href="#routine_summary">routine</a> details: <a href="#routine_details">routine</a> |
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| 78 | |
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| 79 | <div id="container"> |
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| 80 | |
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| 81 | <h1 class="directory"><a href="directory-overview.html?format=raw">ToBeReviewed/STATISTICS/</a></h1> |
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| 82 | <h2 class="pro_file">a_timecorrelate.pro</h2> |
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| 83 | |
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| 84 | <div id="file_attr"> |
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| 85 | <dl> |
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| 86 | </dl> |
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| 87 | </div> |
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| 88 | |
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| 89 | <div id="file_comments"></div> |
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| 90 | |
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| 92 | |
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| 93 | |
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| 94 | |
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| 95 | |
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| 96 | |
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| 97 | |
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| 98 | <div id="routine_summary"> |
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| 99 | <h2>Routine summary</h2> |
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| 100 | |
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| 101 | <dl> |
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| 102 | |
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| 103 | <dt><p><a href="#_TimeAuto_Cov"><span class="result">result = </span>TimeAuto_Cov(<span class="result">X, M, nT</span>, Double=<span class="result">Double</span>, zero2nan=<span class="result">zero2nan</span>)</a></p><dt> |
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| 104 | <dd> NAME: A_TIMECORRELATE PURPOSE: Same function as A_CORRELATE but accept array (until 4 dimension) for input and do the autocorrelation or the autocovariance along the time dimension which must be the last one of the input array.</dd> |
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| 105 | |
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| 106 | <dt><p><a href="#_A_TimeCorrelate"><span class="result">result = </span>A_TimeCorrelate(<span class="result">X, Lag</span>, COVARIANCE=<span class="result">COVARIANCE</span>, DOUBLE=<span class="result">DOUBLE</span>)</a></p><dt> |
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| 107 | <dd></dd> |
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| 108 | |
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| 109 | </dl> |
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| 110 | </div> |
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| 111 | |
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| 112 | |
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| 113 | <div id="routine_details"> |
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| 114 | |
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| 115 | |
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| 116 | <div class="routine_details" id="_TimeAuto_Cov"> |
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| 117 | |
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| 118 | <h2><a class="top" href="#container">top</a>TimeAuto_Cov </h2> |
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| 119 | |
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| 120 | <p class="header"> |
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| 121 | <span class="result">result = </span>TimeAuto_Cov(<span class="result"><a href="#_TimeAuto_Cov_param_X">X</a>, <a href="#_TimeAuto_Cov_param_M">M</a>, <a href="#_TimeAuto_Cov_param_nT">nT</a></span>, <a href="#_TimeAuto_Cov_keyword_Double">Double</a>=<span class="result">Double</span>, <a href="#_TimeAuto_Cov_keyword_zero2nan">zero2nan</a>=<span class="result">zero2nan</span>)</p> |
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| 122 | |
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| 123 | <div class="comments"> |
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| 124 | NAME: |
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| 125 | A_TIMECORRELATE |
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| 126 | |
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| 127 | PURPOSE: |
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| 128 | Same function as A_CORRELATE but accept array (until 4 |
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| 129 | dimension) for input and do the autocorrelation or the |
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| 130 | autocovariance along the time dimension which must be the last |
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| 131 | one of the input array. |
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| 132 | |
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| 133 | This function computes the autocorrelation Px(L) or autocovariance |
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| 134 | Rx(L) of a sample population X as a function of the lag (L). |
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| 135 | |
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| 136 | CATEGORY: |
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| 137 | Statistics. |
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| 138 | |
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| 139 | CALLING SEQUENCE: |
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| 140 | Result = a_timecorrelate(X, Lag) |
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| 141 | |
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| 142 | INPUTS: |
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| 143 | X: an Array which last dimension is the time dimension os |
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| 144 | size n. |
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| 145 | |
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| 146 | LAG: A scalar or n-element vector, in the interval [-(n-2), (n-2)], |
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| 147 | of type integer that specifies the absolute distance(s) between |
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| 148 | indexed elements of X. |
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| 149 | |
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| 150 | KEYWORD PARAMETERS: |
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| 151 | COVARIANCE: If set to a non-zero value, the sample autocovariance |
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| 152 | is computed. |
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| 153 | |
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| 154 | DOUBLE: If set to a non-zero value, computations are done in |
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| 155 | double precision arithmetic. |
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| 156 | |
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| 157 | EXAMPLE |
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| 158 | Define an n-element sample population. |
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| 159 | x = [3.73, 3.67, 3.77, 3.83, 4.67, 5.87, 6.70, 6.97, 6.40, 5.57] |
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| 160 | |
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| 161 | Compute the autocorrelation of X for LAG = -3, 0, 1, 3, 4, 8 |
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| 162 | lag = [-3, 0, 1, 3, 4, 8] |
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| 163 | result = a_correlate(x, lag) |
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| 164 | |
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| 165 | The result should be: |
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| 166 | [0.0146185, 1.00000, 0.810879, 0.0146185, -0.325279, -0.151684] |
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| 167 | |
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| 168 | PROCEDURE: |
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| 169 | |
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| 170 | |
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| 171 | n-L-1 |
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| 172 | sigma (X[k]-Xmean)(X[k+L]-Xmean) |
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| 173 | k=0 |
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| 174 | correlation(X,L)=---------------------------------------- |
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| 175 | n-1 |
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| 176 | sigma (X[k]-Xmean)^2 |
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| 177 | k=0 |
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| 178 | |
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| 179 | |
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| 180 | |
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| 181 | n-L-1 |
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| 182 | sigma (X[k]-Xmean)(X[k+L]-Xmean) |
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| 183 | k=0 |
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| 184 | covariance(X,L)=------------------------------------------- |
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| 185 | n |
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| 186 | |
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| 187 | Where Xmean is the Time mean of the sample population |
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| 188 | x=(x[t=0],x[t=1],...,x[t=n-1]) |
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| 189 | |
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| 190 | |
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| 191 | REFERENCE: |
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| 192 | INTRODUCTION TO STATISTICAL TIME SERIES |
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| 193 | Wayne A. Fuller |
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| 194 | ISBN 0-471-28715-6 |
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| 195 | |
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| 196 | MODIFICATION HISTORY:</div> |
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| 197 | |
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| 198 | |
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| 199 | |
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| 200 | |
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| 201 | <h3>Parameters</h3> |
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| 202 | |
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| 203 | |
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| 204 | <h4 id="_TimeAuto_Cov_param_X">X |
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| 212 | |
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| 213 | </h4> |
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| 214 | |
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| 215 | <div class="comments"></div> |
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| 216 | |
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| 217 | <h4 id="_TimeAuto_Cov_param_M">M |
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| 225 | |
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| 226 | </h4> |
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| 227 | |
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| 228 | <div class="comments"></div> |
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| 229 | |
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| 230 | <h4 id="_TimeAuto_Cov_param_nT">nT |
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| 239 | </h4> |
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| 241 | <div class="comments"></div> |
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| 247 | |
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| 248 | <h3>Keywords</h3> |
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| 249 | |
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| 250 | <h4 id="_TimeAuto_Cov_keyword_Double">Double |
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| 259 | </h4> |
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| 260 | |
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| 261 | <div class="comments"></div> |
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| 262 | |
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| 263 | <h4 id="_TimeAuto_Cov_keyword_zero2nan">zero2nan |
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| 272 | </h4> |
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| 273 | |
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| 274 | <div class="comments"></div> |
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| 300 | |
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| 301 | </div> |
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| 302 | |
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| 303 | |
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| 304 | <div class="routine_details" id="_A_TimeCorrelate"> |
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| 305 | |
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| 306 | <h2><a class="top" href="#container">top</a>A_TimeCorrelate </h2> |
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| 307 | |
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| 308 | <p class="header"> |
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| 309 | <span class="result">result = </span>A_TimeCorrelate(<span class="result"><a href="#_A_TimeCorrelate_param_X">X</a>, <a href="#_A_TimeCorrelate_param_Lag">Lag</a></span>, <a href="#_A_TimeCorrelate_keyword_COVARIANCE">COVARIANCE</a>=<span class="result">COVARIANCE</span>, <a href="#_A_TimeCorrelate_keyword_DOUBLE">DOUBLE</a>=<span class="result">DOUBLE</span>)</p> |
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| 310 | |
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| 311 | <div class="comments"></div> |
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| 312 | |
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| 313 | |
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| 314 | |
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| 315 | |
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| 316 | <h3>Parameters</h3> |
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| 317 | |
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| 318 | |
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| 319 | <h4 id="_A_TimeCorrelate_param_X">X |
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| 328 | </h4> |
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| 329 | |
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| 330 | <div class="comments"></div> |
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| 331 | |
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| 332 | <h4 id="_A_TimeCorrelate_param_Lag">Lag |
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| 333 | |
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| 341 | </h4> |
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| 343 | <div class="comments"></div> |
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| 344 | |
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| 349 | |
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| 350 | <h3>Keywords</h3> |
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| 351 | |
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| 352 | <h4 id="_A_TimeCorrelate_keyword_COVARIANCE">COVARIANCE |
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| 361 | </h4> |
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| 362 | |
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| 363 | <div class="comments"></div> |
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| 364 | |
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| 365 | <h4 id="_A_TimeCorrelate_keyword_DOUBLE">DOUBLE |
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| 403 | </div> |
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| 404 | |
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| 405 | </div> |
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| 409 | <div id="tagline">Produced by IDLdoc 2.0.</div> |
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| 411 | </div> |
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| 414 | </html> |
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