In the dataset of production.txt, it has the monthly industrial production (IP) of US from year 1990 to year 2014. The data is retrieved from the Federal Reserve Bank of St. Louis.

• Plot the time series of IP, ACF and PACF of IP. Test the stationary of the IP.
• Generate the difference of IP. Plot the time series of differenced IP, ACF and PACF of the differenced IP. Test the stationary of the differenced IP.
• Are there seasonal pattern in the series of IP?
• Use AIC or BIC to fit an appropriate ARIMA model for the time series. Fit an ARIMA model with seasonal lag for the time series. Compare the two models.
• Use Ljung-Box test to evaluate the serial correlation of residuals.
• Compute 12-months-ahead forecasts based on the fitted model of your choice.

observation_date\tIPGMFN 1990-01-01\t58.0675 1990-02-01\t59.9663 1990-03-01\t60.8556 1990-04-01\t59.8361 1990-05-01\t60.7942 1990-06-01\t62.4065 1990-07-01\t58.9195 1990-08-01\t61.3320 1990-09-01\t62.3798 1990-10-01\t61.7897 1990-11-01\t59.7225 1990-12-01\t57.9880 1991-01-01\t57.6173 1991-02-01\t58.1532 1991-03-01\t57.8848 1991-04-01\t58.5195 1991-05-01\t58.8722 1991-06-01\t60.8395 1991-07-01\t57.5694 1991-08-01\t60.1914 1991-09-01\t61.6242 1991-10-01\t61.5260 1991-11-01\t59.8859 1991-12-01\t58.3145 1992-01-01\t58.1976 1992-02-01\t59.8928 1992-03-01\t61.2782 1992-04-01\t60.8129 1992-05-01\t61.6853 1992-06-01\t63.2492 1992-07-01\t60.0608 1992-08-01\t62.6368 1992-09-01\t63.3181 1992-10-01\t63.9425 1992-11-01\t62.9319 1992-12-01\t61.4363 1993-01-01\t61.6671 1993-02-01\t63.1791 1993-03-01\t63.7860 1993-04-01\t63.3419 1993-05-01\t63.7435 1993-06-01\t65.0660 1993-07-01\t61.4606 1993-08-01\t64.1921 1993-09-01\t65.3718 1993-10-01\t65.9931 1993-11-01\t64.9620 1993-12-01\t63.7894 1994-01-01\t63.7228 1994-02-01\t65.1281 1994-03-01\t66.8915 1994-04-01\t66.7265 1994-05-01\t67.4424 1994-06-01\t69.2440 1994-07-01\t65.2051 1994-08-01\t69.0102 1994-09-01\t70.4195 1994-10-01\t70.9975 1994-11-01\t70.1964 1994-12-01\t69.4446 1995-01-01\t69.1597 1995-02-01\t70.5855 1995-03-01\t71.8696 1995-04-01\t70.1813 1995-05-01\t71.0056 1995-06-01\t73.2740 1995-07-01\t68.4365 1995-08-01\t72.4739 1995-09-01\t74.4219 1995-10-01\t73.9374 1995-11-01\t72.6585 1995-12-01\t71.4606 1996-01-01\t70.3240 1996-02-01\t72.9890 1996-03-01\t74.0231 1996-04-01\t73.6232 1996-05-01\t74.4606 1996-06-01\t77.3231 1996-07-01\t72.6655 1996-08-01\t76.8514 1996-09-01\t78.9755 1996-10-01\t78.3583 1996-11-01\t77.6667 1996-12-01\t76.5634 1997-01-01\t76.0947 1997-02-01\t78.8419 1997-03-01\t80.6270 1997-04-01\t80.0856 1997-05-01\t80.3935 1997-06-01\t82.5396 1997-07-01\t77.4122 1997-08-01\t82.8721 1997-09-01\t85.2707 1997-10-01\t85.8342 1997-11-01\t85.9420 1997-12-01\t84.8387 1998-01-01\t84.2599 1998-02-01\t86.4183 1998-03-01\t87.5873 1998-04-01\t85.7920 1998-05-01\t87.1869 1998-06-01\t87.7470 1998-07-01\t82.7629 1998-08-01\t88.4561 1998-09-01\t89.0932 1998-10-01\t90.5819 1998-11-01\t89.4717 1998-12-01\t88.5272 1999-01-01\t87.7792 1999-02-01\t90.2288 1999-03-01\t91.9569 1999-04-01\t90.4744 1999-05-01\t91.6394 1999-06-01\t93.3369 1999-07-01\t87.5000 1999-08-01\t92.7664 1999-09-01\t93.3064 1999-10-01\t95.1730 1999-11-01\t94.3190 1999-12-01\t93.2938 2000-01-01\t92.6503 2000-02-01\t94.5488 2000-03-01\t97.2280 2000-04-01\t96.0614 2000-05-01\t96.2810 2000-06-01\t98.9920 2000-07-01\t92.4177 2000-08-01\t96.6096 2000-09-01\t98.3345 2000-10-01\t98.0625 2000-11-01\t96.3427 2000-12-01\t94.3899 2001-01-01\t92.4652 2001-02-01\t94.0703 2001-03-01\t95.6729 2001-04-01\t92.3913 2001-05-01\t93.3058 2001-06-01\t94.8729 2001-07-01\t88.1760 2001-08-01\t92.3675 2001-09-01\t92.9760 2001-10-01\t92.3480 2001-11-01\t90.5904 2001-12-01\t89.0934 2002-01-01\t88.9081 2002-02-01\t90.8019 2002-03-01\t93.0531 2002-04-01\t92.4406 2002-05-01\t93.0065 2002-06-01\t96.3548 2002-07-01\t89.1767 2002-08-01\t94.5726 2002-09-01\t95.8445 2002-10-01\t95.2999 2002-11-01\t93.7972 2002-12-01\t91.4350 2003-01-01\t91.4840 2003-02-01\t93.7914 2003-03-01\t95.7567 2003-04-01\t93.2135 2003-05-01\t93.9127 2003-06-01\t96.4657 2003-07-01\t89.5855 2003-08-01\t94.9464 2003-09-01\t96.8499 2003-10-01\t96.4235 2003-11-01\t95.9070 2003-12-01\t93.6704 2004-01-01\t92.5225 2004-02-01\t95.8827 2004-03-01\t97.4063 2004-04-01\t95.7372 2004-05-01\t97.2909 2004-06-01\t98.8631 2004-07-01\t93.5522 2004-08-01\t98.5648 2004-09-01\t99.1640 2004-10-01\t100.1841 2004-11-01\t98.5328 2004-12-01\t97.3475 2005-01-01\t97.5139 2005-02-01\t100.1289 2005-03-01\t100.9693 2005-04-01\t100.9979 2005-05-01\t101.3544 2005-06-01\t104.0919 2005-07-01\t97.8374 2005-08-01\t102.6514 2005-09-01\t102.4431 2005-10-01\t103.4590 2005-11-01\t102.5961 2005-12-01\t101.0458 2006-01-01\t100.8319 2006-02-01\t102.4575 2006-03-01\t104.4037 2006-04-01\t102.5347 2006-05-01\t103.9560 2006-06-01\t106.8027 2006-07-01\t101.0063 2006-08-01\t105.8672 2006-09-01\t106.7613 2006-10-01\t105.7357 2006-11-01\t104.2187 2006-12-01\t104.1946 2007-01-01\t102.4760 2007-02-01\t104.5278 2007-03-01\t107.6548 2007-04-01\t106.9374 2007-05-01\t107.8803 2007-06-01\t110.6432 2007-07-01\t105.1823 2007-08-01\t109.1522 2007-09-01\t110.3087 2007-10-01\t109.0478 2007-11-01\t108.1093 2007-12-01\t106.4661 2008-01-01\t105.0175 2008-02-01\t105.6470 2008-03-01\t107.0959 2008-04-01\t105.8772 2008-05-01\t105.4167 2008-06-01\t107.3312 2008-07-01\t101.4988 2008-08-01\t103.6191 2008-09-01\t100.7990 2008-10-01\t99.3673 2008-11-01\t95.7552 2008-12-01\t91.3603 2009-01-01\t87.4489 2009-02-01\t88.4339 2009-03-01\t88.4696 2009-04-01\t86.3486 2009-05-01\t86.5737 2009-06-01\t88.0214 2009-07-01\t85.9846 2009-08-01\t89.6407 2009-09-01\t90.3865 2009-10-01\t90.5054 2009-11-01\t90.1490 2009-12-01\t88.7229 2010-01-01\t89.0179 2010-02-01\t90.0316 2010-03-01\t93.2191 2010-04-01\t93.0683 2010-05-01\t94.8271 2010-06-01\t96.8483 2010-07-01\t93.0320 2010-08-01\t96.4725 2010-09-01\t96.8515 2010-10-01\t96.6386 2010-11-01\t95.1025 2010-12-01\t94.4695 2011-01-01\t94.1086 2011-02-01\t94.9617 2011-03-01\t97.8004 2011-04-01\t96.0002 2011-05-01\t96.5772 2011-06-01\t98.9335 2011-07-01\t95.4499 2011-08-01\t98.6037 2011-09-01\t99.4738 2011-10-01\t99.3954 2011-11-01\t97.6869 2011-12-01\t97.4657 2012-01-01\t97.4915 2012-02-01\t99.0855 2012-03-01\t100.5449 2012-04-01\t99.8612 2012-05-01\t100.0506 2012-06-01\t102.4872 2012-07-01\t98.1944 2012-08-01\t101.0464 2012-09-01\t101.3844 2012-10-01\t100.5852 2012-11-01\t99.8587 2012-12-01\t99.4101 2013-01-01\t98.5668 2013-02-01\t100.0121 2013-03-01\t101.4019 2013-04-01\t101.0112 2013-05-01\t101.0059 2013-06-01\t103.3274 2013-07-01\t98.4237 2013-08-01\t102.4019 2013-09-01\t102.6802 2013-10-01\t102.6028 2013-11-01\t101.3195 2013-12-01\t100.0322 2014-01-01\t98.6621 2014-02-01\t101.0349 2014-03-01\t103.8628 2014-04-01\t103.1245 2014-05-01\t103.7433 2014-06-01\t106.3091 2014-07-01\t102.2674 2014-08-01\t105.8006 2014-09-01\t106.1037 2014-10-01\t105.9423 2014-11-01\t105.5887 2014-12-01\t104.3692