document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135297>Question 1135297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let's directly calculate the 95% confidence intervals of our parameters. The formula for a given parameter is:\r<BR>\n" );
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document.write( "𝐶𝐼=(𝛽−𝑧⋅𝑠𝑛⎯⎯√,𝛽+𝑧⋅𝑠𝑛⎯⎯√)<BR>\n" );
document.write( "Where, 𝛽 is the coefficient, 𝑧 is the critical value(t-statistic required to obtain a probability less than the alpha significance level), and 𝑆𝐸𝑖,𝑖 is the Standard Error Matrix.\r<BR>\n" );
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document.write( "start = '2014-01-01'<BR>\n" );
document.write( "end = '2015-01-01'<BR>\n" );
document.write( "asset = get_pricing('KO', fields='price', start_date=start, end_date=end)<BR>\n" );
document.write( "benchmark = get_pricing('PEP', fields='price', start_date=start, end_date=end)\r<BR>\n" );
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document.write( "X = asset.pct_change()[1:]<BR>\n" );
document.write( "Y = benchmark.pct_change()[1:]\r<BR>\n" );
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document.write( "result = sm.OLS(Y,X).fit()\r<BR>\n" );
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document.write( "# Convert X to Matrix (adding columns of one)<BR>\n" );
document.write( "X = np.vstack((X, np.ones( X.size ) ))<BR>\n" );
document.write( "X = np.matrix( X )\r<BR>\n" );
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document.write( "# Matrix Multiplication and inverse calculation<BR>\n" );
document.write( "C = np.linalg.inv( X * X.T )<BR>\n" );
document.write( "C *= result.mse_resid<BR>\n" );
document.write( "SE = np.sqrt(C) # Calucaltion of Standart Error. \r<BR>\n" );
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document.write( "# Critical Values of the t-statistic<BR>\n" );
document.write( "N = result.nobs<BR>\n" );
document.write( "P = result.df_model<BR>\n" );
document.write( "dof = N - P - 1<BR>\n" );
document.write( "z = scipy.stats.t(dof).ppf(0.975)\r<BR>\n" );
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document.write( "i = 0<BR>\n" );
document.write( "## Your code goes here\r<BR>\n" );
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document.write( "# Fetch values of Beta and parameters of SE from the matrix<BR>\n" );
document.write( "beta = ## Your code goes here<BR>\n" );
document.write( "c = ## Your code goes here\r<BR>\n" );
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document.write( "print ## Your code goes here\r<BR>\n" );
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document.write( "## Instead of running the code above and calculate the CI step by step, <BR>\n" );
document.write( "## you can get the CI automatically from OLS table.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752879 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53937)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Nonsense.\r<BR>\n" );
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document.write( "Not an appropriate post/problem/request for this forum.\r<BR>\n" );
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document.write( "Do not spend your time for nothing posting such requests - they make no sense.\r<BR>\n" );
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document.write( "Have a nice day / afternoon / evening / night / morning etc.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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