In the price_data dataset, you will see three series of historical monthly price data: corn price (US$/bushel), crude oil price (US$/gallon), and ethanol price (US$/gallon). Please refer to the metadata sheet for descriptions about these prices. The corn and oil prices cover the period from January 2003 to September 2020, and the ethanol price covers from November 2005 to March 2018. First, transform the price data to logarithmic level (to ease the empirical analysis). You can use the LOG() function in Excel. So, we create the following new price variables by taking the logarithm of the prices and multiplying by 100. (Data transformation worth 5 points.) .com = log(P)*100 poi = log(P)*100 potreino! = log(Pethenol)*100 All the empirical analysis below will use these new (log) price variables. In the questions below, please clearly describe your process (for example, the steps you followed to perform the analysis, the functions used in R and/or Excel), so that I can replicate your work/results if needed. Part I: risk assessment. (20 points in total, 5 pints each) a) Visualize your price variables (i.e., draw a time series chart for pcorn, poil, pethanol). Describe any particular patterns/trends that are apparent in prices. b) Calculate the constant volatility, CV for each market (i.e., for pcorn, poil, pethanol), and compare the risk levels between these markets. c) Divide the sample into three subsamples: before Jan 2007, from Jan 2007 to Dec 2013, and from Jan 2014 to the end. Do the same assessment as the question (b) for each subsample. Compare (e.g., different periods within a market and same period across markets) and comment on your results. d) Calculate the moving average volatility and CV for each market (i.e., for pcorn, poil, pethanol). Choose two different windows (for example, n=24 and 36) for your calculation. Make one or more graphs to visualize your results. Compare and comment on your results. You may use the TTR package (runSDO, run Mean() and other functions) in R You can comment/discuss in the following areas: overall market volatility, any trend, characteristics of specific periods, comparison between markets, and so on. 2 Part II: Market interdependence. (15 points in total, 5 pints each) e) Draw a scatter plot and calculate correlation coefficients for each pair of price data (i.e., three correlation coefficients in total). Comment on your results (for example, which two markets are most connected and which two markets are the least connected). f) Calculate the dynamic correlation coefficient for each pair of price data. You can either do it using the moving average approach or you can do it by dividing your data into subsamples as we did in question (c). Make one or more graphs to visualize your results. Compare and comment on your results. g) Run the following four simple linear regressions. Interpret and discuss your results. (hint: B measures the response of y variable to x variable. For example, in Equation (1) below, the B measures the percentage change in corn prices relative to the 1% change in oil prices.) (1) porn = a + b* poi + E (2) porn = a + * p* etiana (3) pethanol = a + b* poil + E = a + * pethanol + E + (4) pol 0 1 2 3 4 3 5 7 3 0 1 2 3 4 3 06/30/2003 07/31/2003 08/31/2003 09/30/2003 10/31/2003 11/30/2003 12/31/2003 01/31/2004 02/29/2004 03/31/2004 [04/30/2004 05/31/2004 06/30/2004 07/31/2004 08/312004 09/30/2004 10/31/2004 11/30/2004 12/31/2004 01/31/2005 [02/28/2005 03/31/2005 04/30/2005 05/31/2005 106/30/2005 07/31/2005 08/31/2005 09/30/2005 10/31/2005 11/30/2005 12/31/2005 01/31/2006 02/28/2006 03/31/2006 04/30/2006 [05/31/2006 06/30/2006 07/31/2006 08/31/2006 09/30/2006 10/31/2006 11/30/2006 12/31/2006 01/31/2007 02/28/2007 03/31/2007 04/30/2007 05/31/2007 06/30/2007 07/31/2007 08/31/2007 09/30/2007 10/31/2007 11/30/2007 12/31/2007 01/31/2008 02/29/2008 03/31/2008 04/30/2008 05/31/2008 06/30/2008 07/31/2008 08/31/2008 09/30/2008 10/31/2008 11/30/2008 12/31/2008 01/31/2009 02/28/2009 03/31/2009 [04/30/2009 05/31/2009 06/30/2009 07/31/2009 08/312009 09/30/2009 10/31/2009 11/30/2009 12/31/2009 01/31/2010 [02/28/2010 03/31/2010 04/30/2010 05/31/2010 06/30/2010 07/31/2010 08/31/2010 09/30/2010 10/31/2010 11/30/2010 12/31/2010 01/31/2011 02/28/2011 03/31/2011 04/30/2011 05/31/2011 06/30/2011 07/31/2011 08/31/2011 09/30/2011 10/31/2011 11/30/2011 12/31/2011 01/31/2012 02/29/2012 03/31/2012 04/30/2012 05/31/2012 06/30/2012 07/31/2012 3/31/2012 09/30/2012 10/31/2012 11/30/2012 12/31/2012 01/31/2013 02/28/2013 03/31/2013 04/30/2013 [05/31/2013 106/30/2013 07/31/2013 08/31/2013 09/30/2013 10/31/2013 11/30/2013 12/31/2013 01/31/2014 02/28/2014 03/31/2014 04/30/2014 05/31/2014 06/30/2014 07/31/2014 08/31/2014 09/30/2014 10/31/2014 11/30/2014 12/31/2014 01/31/2015 02/28/2015 03/31/2015 04/30/2015 05/31/2015 06/30/2015 07/31/2015 08/31/2015 09/30/2015 10/31/2015 11/30/2015 12/31/2015 01/31/2016 02/29/2016 03/31/2016 04/30/2016 05/31/2016 06/30/2016 07/31/2016 08/31/2016 09/30/2016 10/31/2016 11/30/2016 12/31/2016 01/31/2017 02/28/2017 [03/31/2017 04/30/2017 05/31/2017 06/30/2017 07/31/2017 08/31/2017 09/30/2017 10/31/2017 11/30/2017 12/31/2017 01/31/2018 02/28/2018 03/31/2018 04/30/2018 05/31/2018 106/30/2018 07/31/2018 08/31/2018 09/30/2018 10/31/2018 11/30/2018 12/31/2018 01/31/2019 02/28/2019 03/31/2019 04/30/2019 05/31/2019 06/30/2019 07/31/2019 08/31/2019 09/30/2019 10/31/2019 11/30/2019 12/31/2019 01/31/2020 [02/29/2020 03/31/2020 04/30/2020 [05/31/2020 06/30/2020 07/31/2020 08/31/2020 09/30/2020 2.31 0.73 206 10.732380952 2.32 0.751666667 21 0674047619 242 0.722380952 2.49 0740714286 246 0765 26 0.816904762 2.8 0.825952381 3.09 0.874761905 3.06 0875 2.89 0.959047619 2.43 0.90547619 202 0970952381 218 1.069047619 1.76 1.093809524 1.76 1.268571429 1.74 1.154047619 1.8 1.027380952 1.77 1.115238095 1.98 1.146428571 1.91 1.290238095 19 1.261428571 2.02 1.186428571 1.94 1.341666667 212 1.404761905 1.77 1.547380952 1.74 1.561666667 1.61 1.482380952 1.62 1.388571429 1.9643333 1.91 1.41452381 2.0277419 1.99 1.559285714 2.3406452 2.08 1.467380952 2.41 2008 1.492619048 2.4312903 2.18 1.653333333 26336667 226 1.686666667 2.9925806 216 1.689285714 3.1733333 218 1.771666667 2.9741935 216 1.739047619 2.4890323 243 1.519047619 1.9056667 3.11 1.402142857 1.8332258 3.67 1.406666667 2.1936667 3.68 1.475238095 2.3445161 3.87 1.297857143 2.093871 4.14 1.411428571 2.0953571 3.55 1.439047619 2.3325806 3.44 1.523333333 2.1936667 3.75 1.510952381 2.2490323 3.3 1.606904762 2.083 3.26 1.764761905 20064516 32 1.722857143 1.8080645 3.5 1.902857143 1.5786667 3.56 2.042857143 1.6583871 3.75 2.256428571 1.9086667 4.41 2.183095238 2.1851613 4.89 2.213571429 2.2441935 5.36 2271190476 22844828 5.45 2.510714286 2.4732258 5.78 2.68047619 2.548 5.74 2.985714286 2.5193548 7.08 3.187619048 2764 5.63 3.17547619 26225806 5.58 2.777857143 2.3006452 4.63 2478809524 2.1893333 3.94 1.824047619 1.7903226 3.49 1.36452381 1.6836667 4 0.979047619 1.5435484 3.74 0.993095238 1.6041935 3.51 0930714286 1.5696429 4.01 1.141428571 1.5751613 3.4 1.182142857 1.6126667 421 1.40547619 1.7277419 3.33 1.658095238 1.7753333 3.21 1.527380952 17 3.16 1.691666667 1.6054839 3.19 1.652619048 1.697 3.43 1.802857143 1.8851613 3.73 1.856904762 21196667 39 1.773095238 2.0903226 3.36 1.865 1.8616129 3.68 1.818809524 1.7510714 3.33 1.933333333 1.72 3.59 2006904762 1.5566667 3.45 1.755714286 1.5958065 3.44 1793809524 1.5686667 13.65 1.817142857 1.6367742 394 1.823809524 1.9416129 4.51 1.791428571 2069 5.41 1.949761905 2.3296774 5.17 2.005952381 2.2846667 6.01 2.122619048 2.2054839 6.425 2.123095238 23141935 7.15 2109047619 2.4557143 6.77 2.449047619 2.5206452 7.42 2.607857143 26353333 7.51 2.402380952 2.6006452 6.34 2291904762 27036667 7.01 2.31666666729183871 7.58 2005547619 28506452 5.83 2.036190476 2774 6.55 2.055238095 26877419 6.26 2.313333333 2.847 6.57 2.346666667 2.253871 6.54 2.387380952 21712903 6.77 2.433333333 2.1751724 6.66 2.527619048 2.2648387 6.54 2.46 2.1856667 6.08 2.253809524 2.096129 7.08 1.95952381 2.067 8822 2092857143 2.5112903 8.18 2.241190476 2.5848387 7.68 2.250238095 2.3773333 7.84 2.130714286 24358065 7.83 20060238095 2.3926667 7.25 2.091904762 2.2964516 7.78 2.256190476 2.3058065 7.55 2.269285714 2.3828571 7.43 2.212857143 2.5541935 7.1 2.190952381 2.519 7.32 2.250238095 2.6893548 7.47 2.280238095 2536 5.99 249214285724770968 5.85 2.537380952 2.366129 4.415 2.530714286 2272 4.1825 2.393809524 1.9748387 4.2225 2.234761905 12.238 42 2.32452381 2.2845161 4.37 2.252857143 2.2245161 4.555 2.40047619 2.535 4.95 24 3.2519355 5.14 2.430238095 2.6176667 4.6875 2.432857143 2.343871 4.3425 2.518809524 2.12 3.57 2.466428571 2.14 3.59 2.298571429 2.2609677 26775 2219285714 1.749 32175 2.00952381 1.6887097 3.4825 1.80452381 2.507 3.74 1.411666667 1.9816129 3.58 1.124285714 1.4058065 3.815 1.204285714 1.3946429 3.7625 1.138571429 1.4806452 3.6725 1.296428571 1.582 3.515 1411190476 1.5983871 4.15 1.424285714 1.5403333 3.66 1.211904762 1.5554839 3.6325 1.020714286 1.4587097 3.6975 1.082857143 1.528 38225 1.10047619 1.5645161 3.7525 1.01047619 1.505 3.6175 10.88547619 1.4280645 3.72 0.754285714 1.346129 3.525 0.721904762 1.3882759 3.465 0.894047619 1.3841935 3.8325 0.970238095 1.5306667 3.9275 1.112142857 1.5803226 3.4675 1.160952381 1.6346667 3225 1.063095238 1.4987097 2.785 1.064761905 1.4093548 29875 1.075714286 1.557 3.1475 1.185238095 1.633871 3.2675 1.087142857 1.6326667 3.37 1.237380952 1.7377419 3.3975 1.25 1.4896774 3.4675 1.273095238 1.5071429 3.4925 1.17452381 1.5209677 3.48 1.215714286 1.5826667 3.62 1.154285714 1.4796774 3.505 1.075714286 1.5246667 3.4375 1.110238095 1.5216129 3.2725 1.143809524 1.5354839 3.1525 1.186190476 1.5553333 3.0875 1.228095238 1.4209677 3.2975 1.348571429 1.3886667 3.3575 1.378095238 1.2445161 3.415 1516666667 1.3090323 3.615 1.4881666667 1.4289286 3.7275 1.493571429 1.46322588 3.8675 1.577380952 3.79 1.666190476 3.5025 1.615952381 3.6725 1.69 3.36 162047619 3.1425 1.672142857 3.5125 1.68452381 3.705 1.356190476 13.75 1.179047619 3.6875 1.223333333 4.31 1.308333333 3.555 1.38452381 3.6025 1.52047619 4.22 1.448333333 4.65 1.301428571 4.1275 1.36547619 3.69 1.305 3.73 1.355952381 3.85 1.284761905 3.6775 1.357857143 3.9275 1.425714286 3.895 1.36952381 38 1.203333333 3.4125 0.69547619 3.085 0.394047619 3.26 0.68 3.39 10.912142857 4.625 0.969285714 3.2025 1.008095238 3.485 0943571429 3 9 0 1 2 3 4 7 3 a 1 2 3 4 5 7 3 9 0 1 2 3 4 3 a 1 2 3 4 5 3 9 0 1 2 3 4 7 3 0 1 2 3 4 5 7 3 9 0 1 3 3 4 7 3 a 1 2 3 4 5 3 9 0 1 2 3 4 3 a 1 2 3 4 In the price_data dataset, you will see three series of historical monthly price data: corn price (US$/bushel), crude oil price (US$/gallon), and ethanol price (US$/gallon). Please refer to the metadata sheet for descriptions about these prices. The corn and oil prices cover the period from January 2003 to September 2020, and the ethanol price covers from November 2005 to March 2018. First, transform the price data to logarithmic level (to ease the empirical analysis). You can use the LOG() function in Excel. So, we create the following new price variables by taking the logarithm of the prices and multiplying by 100. (Data transformation worth 5 points.) .com = log(P)*100 poi = log(P)*100 potreino! = log(Pethenol)*100 All the empirical analysis below will use these new (log) price variables. In the questions below, please clearly describe your process (for example, the steps you followed to perform the analysis, the functions used in R and/or Excel), so that I can replicate your work/results if needed. Part I: risk assessment. (20 points in total, 5 pints each) a) Visualize your price variables (i.e., draw a time series chart for pcorn, poil, pethanol). Describe any particular patterns/trends that are apparent in prices. b) Calculate the constant volatility, CV for each market (i.e., for pcorn, poil, pethanol), and compare the risk levels between these markets. c) Divide the sample into three subsamples: before Jan 2007, from Jan 2007 to Dec 2013, and from Jan 2014 to the end. Do the same assessment as the question (b) for each subsample. Compare (e.g., different periods within a market and same period across markets) and comment on your results. d) Calculate the moving average volatility and CV for each market (i.e., for pcorn, poil, pethanol). Choose two different windows (for example, n=24 and 36) for your calculation. Make one or more graphs to visualize your results. Compare and comment on your results. You may use the TTR package (runSDO, run Mean() and other functions) in R You can comment/discuss in the following areas: overall market volatility, any trend, characteristics of specific periods, comparison between markets, and so on. 2 Part II: Market interdependence. (15 points in total, 5 pints each) e) Draw a scatter plot and calculate correlation coefficients for each pair of price data (i.e., three correlation coefficients in total). Comment on your results (for example, which two markets are most connected and which two markets are the least connected). f) Calculate the dynamic correlation coefficient for each pair of price data. You can either do it using the moving average approach or you can do it by dividing your data into subsamples as we did in question (c). Make one or more graphs to visualize your results. Compare and comment on your results. g) Run the following four simple linear regressions. Interpret and discuss your results. (hint: B measures the response of y variable to x variable. For example, in Equation (1) below, the B measures the percentage change in corn prices relative to the 1% change in oil prices.) (1) porn = a + b* poi + E (2) porn = a + * p* etiana (3) pethanol = a + b* poil + E = a + * pethanol + E + (4) pol 0 1 2 3 4 3 5 7 3 0 1 2 3 4 3 06/30/2003 07/31/2003 08/31/2003 09/30/2003 10/31/2003 11/30/2003 12/31/2003 01/31/2004 02/29/2004 03/31/2004 [04/30/2004 05/31/2004 06/30/2004 07/31/2004 08/312004 09/30/2004 10/31/2004 11/30/2004 12/31/2004 01/31/2005 [02/28/2005 03/31/2005 04/30/2005 05/31/2005 106/30/2005 07/31/2005 08/31/2005 09/30/2005 10/31/2005 11/30/2005 12/31/2005 01/31/2006 02/28/2006 03/31/2006 04/30/2006 [05/31/2006 06/30/2006 07/31/2006 08/31/2006 09/30/2006 10/31/2006 11/30/2006 12/31/2006 01/31/2007 02/28/2007 03/31/2007 04/30/2007 05/31/2007 06/30/2007 07/31/2007 08/31/2007 09/30/2007 10/31/2007 11/30/2007 12/31/2007 01/31/2008 02/29/2008 03/31/2008 04/30/2008 05/31/2008 06/30/2008 07/31/2008 08/31/2008 09/30/2008 10/31/2008 11/30/2008 12/31/2008 01/31/2009 02/28/2009 03/31/2009 [04/30/2009 05/31/2009 06/30/2009 07/31/2009 08/312009 09/30/2009 10/31/2009 11/30/2009 12/31/2009 01/31/2010 [02/28/2010 03/31/2010 04/30/2010 05/31/2010 06/30/2010 07/31/2010 08/31/2010 09/30/2010 10/31/2010 11/30/2010 12/31/2010 01/31/2011 02/28/2011 03/31/2011 04/30/2011 05/31/2011 06/30/2011 07/31/2011 08/31/2011 09/30/2011 10/31/2011 11/30/2011 12/31/2011 01/31/2012 02/29/2012 03/31/2012 04/30/2012 05/31/2012 06/30/2012 07/31/2012 3/31/2012 09/30/2012 10/31/2012 11/30/2012 12/31/2012 01/31/2013 02/28/2013 03/31/2013 04/30/2013 [05/31/2013 106/30/2013 07/31/2013 08/31/2013 09/30/2013 10/31/2013 11/30/2013 12/31/2013 01/31/2014 02/28/2014 03/31/2014 04/30/2014 05/31/2014 06/30/2014 07/31/2014 08/31/2014 09/30/2014 10/31/2014 11/30/2014 12/31/2014 01/31/2015 02/28/2015 03/31/2015 04/30/2015 05/31/2015 06/30/2015 07/31/2015 08/31/2015 09/30/2015 10/31/2015 11/30/2015 12/31/2015 01/31/2016 02/29/2016 03/31/2016 04/30/2016 05/31/2016 06/30/2016 07/31/2016 08/31/2016 09/30/2016 10/31/2016 11/30/2016 12/31/2016 01/31/2017 02/28/2017 [03/31/2017 04/30/2017 05/31/2017 06/30/2017 07/31/2017 08/31/2017 09/30/2017 10/31/2017 11/30/2017 12/31/2017 01/31/2018 02/28/2018 03/31/2018 04/30/2018 05/31/2018 106/30/2018 07/31/2018 08/31/2018 09/30/2018 10/31/2018 11/30/2018 12/31/2018 01/31/2019 02/28/2019 03/31/2019 04/30/2019 05/31/2019 06/30/2019 07/31/2019 08/31/2019 09/30/2019 10/31/2019 11/30/2019 12/31/2019 01/31/2020 [02/29/2020 03/31/2020 04/30/2020 [05/31/2020 06/30/2020 07/31/2020 08/31/2020 09/30/2020 2.31 0.73 206 10.732380952 2.32 0.751666667 21 0674047619 242 0.722380952 2.49 0740714286 246 0765 26 0.816904762 2.8 0.825952381 3.09 0.874761905 3.06 0875 2.89 0.959047619 2.43 0.90547619 202 0970952381 218 1.069047619 1.76 1.093809524 1.76 1.268571429 1.74 1.154047619 1.8 1.027380952 1.77 1.115238095 1.98 1.146428571 1.91 1.290238095 19 1.261428571 2.02 1.186428571 1.94 1.341666667 212 1.404761905 1.77 1.547380952 1.74 1.561666667 1.61 1.482380952 1.62 1.388571429 1.9643333 1.91 1.41452381 2.0277419 1.99 1.559285714 2.3406452 2.08 1.467380952 2.41 2008 1.492619048 2.4312903 2.18 1.653333333 26336667 226 1.686666667 2.9925806 216 1.689285714 3.1733333 218 1.771666667 2.9741935 216 1.739047619 2.4890323 243 1.519047619 1.9056667 3.11 1.402142857 1.8332258 3.67 1.406666667 2.1936667 3.68 1.475238095 2.3445161 3.87 1.297857143 2.093871 4.14 1.411428571 2.0953571 3.55 1.439047619 2.3325806 3.44 1.523333333 2.1936667 3.75 1.510952381 2.2490323 3.3 1.606904762 2.083 3.26 1.764761905 20064516 32 1.722857143 1.8080645 3.5 1.902857143 1.5786667 3.56 2.042857143 1.6583871 3.75 2.256428571 1.9086667 4.41 2.183095238 2.1851613 4.89 2.213571429 2.2441935 5.36 2271190476 22844828 5.45 2.510714286 2.4732258 5.78 2.68047619 2.548 5.74 2.985714286 2.5193548 7.08 3.187619048 2764 5.63 3.17547619 26225806 5.58 2.777857143 2.3006452 4.63 2478809524 2.1893333 3.94 1.824047619 1.7903226 3.49 1.36452381 1.6836667 4 0.979047619 1.5435484 3.74 0.993095238 1.6041935 3.51 0930714286 1.5696429 4.01 1.141428571 1.5751613 3.4 1.182142857 1.6126667 421 1.40547619 1.7277419 3.33 1.658095238 1.7753333 3.21 1.527380952 17 3.16 1.691666667 1.6054839 3.19 1.652619048 1.697 3.43 1.802857143 1.8851613 3.73 1.856904762 21196667 39 1.773095238 2.0903226 3.36 1.865 1.8616129 3.68 1.818809524 1.7510714 3.33 1.933333333 1.72 3.59 2006904762 1.5566667 3.45 1.755714286 1.5958065 3.44 1793809524 1.5686667 13.65 1.817142857 1.6367742 394 1.823809524 1.9416129 4.51 1.791428571 2069 5.41 1.949761905 2.3296774 5.17 2.005952381 2.2846667 6.01 2.122619048 2.2054839 6.425 2.123095238 23141935 7.15 2109047619 2.4557143 6.77 2.449047619 2.5206452 7.42 2.607857143 26353333 7.51 2.402380952 2.6006452 6.34 2291904762 27036667 7.01 2.31666666729183871 7.58 2005547619 28506452 5.83 2.036190476 2774 6.55 2.055238095 26877419 6.26 2.313333333 2.847 6.57 2.346666667 2.253871 6.54 2.387380952 21712903 6.77 2.433333333 2.1751724 6.66 2.527619048 2.2648387 6.54 2.46 2.1856667 6.08 2.253809524 2.096129 7.08 1.95952381 2.067 8822 2092857143 2.5112903 8.18 2.241190476 2.5848387 7.68 2.250238095 2.3773333 7.84 2.130714286 24358065 7.83 20060238095 2.3926667 7.25 2.091904762 2.2964516 7.78 2.256190476 2.3058065 7.55 2.269285714 2.3828571 7.43 2.212857143 2.5541935 7.1 2.190952381 2.519 7.32 2.250238095 2.6893548 7.47 2.280238095 2536 5.99 249214285724770968 5.85 2.537380952 2.366129 4.415 2.530714286 2272 4.1825 2.393809524 1.9748387 4.2225 2.234761905 12.238 42 2.32452381 2.2845161 4.37 2.252857143 2.2245161 4.555 2.40047619 2.535 4.95 24 3.2519355 5.14 2.430238095 2.6176667 4.6875 2.432857143 2.343871 4.3425 2.518809524 2.12 3.57 2.466428571 2.14 3.59 2.298571429 2.2609677 26775 2219285714 1.749 32175 2.00952381 1.6887097 3.4825 1.80452381 2.507 3.74 1.411666667 1.9816129 3.58 1.124285714 1.4058065 3.815 1.204285714 1.3946429 3.7625 1.138571429 1.4806452 3.6725 1.296428571 1.582 3.515 1411190476 1.5983871 4.15 1.424285714 1.5403333 3.66 1.211904762 1.5554839 3.6325 1.020714286 1.4587097 3.6975 1.082857143 1.528 38225 1.10047619 1.5645161 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