Matlab
Assignment1_e406_w2021_modified.dvi Economics 406 Winter 2021 Assignment 1 This assignment is due on Friday January 29 Monday February 1 at midnight, EST. This assignment is worth 10% of your total grade. Carefully, read the instructions before starting. • This short assignment uses Matlab and a large Canadian macro data set that can be downloaded from https://www.stevanovic.uqam.ca/DS_LCMD.html. Use the De- cember 2020 vintage of the data. • In this assignment, you will learn how to load, read, plot data in Matlab, and perform an H-P filter on monthly data. • When you submit the data, you will need to submit, your codes and a written summary of your results (where applicable). You do not need to submit the data. • Please use the publish command in Matlab to publish your results and comments. When you upload your assignment on Learn, you will have to upload your script file (your .m file) and your output from the publish command (in word or PDF). Alternatively, you can save and submit your file (codes and comments) using a live script file (.mlx file) which can easily be run in Matlab (see the example I provided on Learn). • Marks will be allocated if you can successfully execute all parts of the assignment. Make sure your codes are running and you are getting the desired results before submitting the assignment. Marks will be deducted if there are errors in your code or if your code does not run or not executing what was asked in the assignment • Use the instructions to name the new variables • You should use the command % in Matlab to indicate the beginning of a new section • Start your data in January 1981 1. Add GPI new (GDP goods, variable 3) and SPI new (GDP services, variable 4) to create a new variable, call it GDP GS (for GDP goods and services) [2 mark] 2. Take the log of the 4 variable (GDP new, GDP GS, BSI new, RT new ) and denote the log of each variable as lGDP new for GDP new, lGDP GS for GDP GS, etc... [4 marks] 1 Wing Sheung Chu Wing Sheung Chu 3. Using the subplot command, plot the log of each time-series (using the subplot com- mand, you should have a 4 × 4 figure with each time series plotted on its own) [11 marks] 4. Using the level of the values (not the log) of the four time series, take the annualized growth rate which is defined as gm = [ ( Xm Xm−1 ) 12 − 1 ] ×100 (where gm is the annualized percent change and Xm is the variable in month m). You can denote your new variable with a g in front. For example the annualized growth rate of GDP new is denoted as gGDP new. (Your first data point will start in Jan 1982) [8 marks] 5. Using the level of the values (not the log) of the four time series, take the year over year growth rate which is defined as gy = [( Xm Xm−12 ) − 1 ] ×100 (where gy is the year over year percent change and Xm is the variable in month m). You can denote your new variable with a gy in front. For example the year over year growth rate of GDP new is denoted as gyGDP new. (Your first data point will start in Jan 1982) [8 marks] 6. Which one should we use to denote annual percent change, annualized growth rate or year over year growth rate and why? [10 marks] 7. Using the subplot command, plot the annualized growth rate and the year-over-year growth rate of each real variables. You should plot the annualized and year over year growth rate of the same variable on one plot. For example, gGDP new and gyGDP new should be on the same graph [10 marks] 8. Using the log-level of the four time series in real term, and using an H-P filter (see example file posted or use the Help Matlab menu to know more about the hpfilter command), detrend each time series. You should set λ = 129, 600. Denote your trend variable with a t and your cycles with a c. For example, denote the trend of lGDP new as tlGDP new and the cycle as clGDP new. [14 marks] 9. Create another variable and call it YGAP. Let Y GAP = clGDP new × 100 [1 mark] 10. Plot gGDP new, gyGDP new and YGAP on the same graph. Comment on the differ- ences between the three times series (in particular comment on how different it would be if you were using any of these measures as a measure of recession) [12 marks] 11. Using the log-level of RT new (that is lRRT new) and using an H-P filter (set λ = 129, 600) graph the cyclical component of this time series after multiplying it by 100. Compared to its trend, was the fall in retail trade GDP after March 2020 significant? [10 marks] 2