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bin width for these data sets and sample size. Describe what wou you were to use bin widths of 0.01 or 1.00. Switch to another E either or both of the series, if you think that this would be more the actual distribution of the data. 1 d. Compare the coefficients of skewness and kurtosis with the val would expect in a Normal distribution: 0 and 3 respectively. Com match of your estimates with the values expected from the Norma haron't yot studied this distribution or loernod how to do a fo TO

bin width for these data sets and sample size. Describe what wou you were to use bin widths of 0.01 or 1.00. Switch to another E either or both of the series, if you think that this would be more the actual distribution of the data. 1 d. Compare the coefficients of skewness and kurtosis with the val would expect in a Normal distribution: 0 and 3 respectively. Com match of your estimates with the values expected from the Norma haron't yot studied this distribution or loernod how to do a fo TO

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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bin width for these data sets and sample size. Describe what would happen if you were to use bin widths of 0.01 or 1.00. Switch to another bin width for either or both of the series, if you think that this would be more revealing of the actual distribution of the data. 1 d. Compare the coefficients of skewness and kurtosis with the values that you would expect in a Normal distribution: 0 and 3 respectively. Comment on the match of your estimates with the values expected from the Normal. Of course, we haven't yet studied this distribution or learned how to do a formal test, so this is just an introductory example, illustrating one way in which skewness and kurtosis measures will be used later. 1 e. Finally, consider the original series, before transformation. Because these series have upward trends, it does not make sense to talk of the mean or other measures calculated above as being approximately constant, as we might be willing to do for the transformed series. It is nonetheless possible to compute sample measures, even though they are not estimating anything well defined. This illustrates the importance of doing some theoretical study of probability and distributions so that we can understand what is going on. Meanwhile, compute the sample mean on the first half and the latter half of your data points for P: you will notice the you get substantially different numbers. Now, Pt-Pt-1, where t compute the percentage change in the series as = 1, 2,... N is the index set for this time series. Notice that when you compute the propor- tionate change you will again lose one observation, because you can't do it for the first observation (you would need observation zero, which by definition you don't have). For this transformation, again compute the sample mean on the first half and the latter half of your sample. The numbers should now be closer to each other and if you plot the result, it should look like Ap. You will discuss this in the tutorial after the assignment is handed in; for now just compute some numbers as a basis for the discussion. Pt-1
Transcribed Image Text:bin width for these data sets and sample size. Describe what would happen if you were to use bin widths of 0.01 or 1.00. Switch to another bin width for either or both of the series, if you think that this would be more revealing of the actual distribution of the data. 1 d. Compare the coefficients of skewness and kurtosis with the values that you would expect in a Normal distribution: 0 and 3 respectively. Comment on the match of your estimates with the values expected from the Normal. Of course, we haven't yet studied this distribution or learned how to do a formal test, so this is just an introductory example, illustrating one way in which skewness and kurtosis measures will be used later. 1 e. Finally, consider the original series, before transformation. Because these series have upward trends, it does not make sense to talk of the mean or other measures calculated above as being approximately constant, as we might be willing to do for the transformed series. It is nonetheless possible to compute sample measures, even though they are not estimating anything well defined. This illustrates the importance of doing some theoretical study of probability and distributions so that we can understand what is going on. Meanwhile, compute the sample mean on the first half and the latter half of your data points for P: you will notice the you get substantially different numbers. Now, Pt-Pt-1, where t compute the percentage change in the series as = 1, 2,... N is the index set for this time series. Notice that when you compute the propor- tionate change you will again lose one observation, because you can't do it for the first observation (you would need observation zero, which by definition you don't have). For this transformation, again compute the sample mean on the first half and the latter half of your sample. The numbers should now be closer to each other and if you plot the result, it should look like Ap. You will discuss this in the tutorial after the assignment is handed in; for now just compute some numbers as a basis for the discussion. Pt-1
1. Obtain data on the consumer price index (CPI) and US gross domestic product (GDP) from the FRED (Federal Reserve Economic Data) data section of the web site of the Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org. Click on 'research and databases' and then FRED economic data. Scroll down to 'at a glance' and you'll see CPI for all urban consumers. Then click on 'popular series' to get gross domestic product. Note that this is not the same as the real GDP series that you see in 'at a glance'. You can then download the data by clicking on the download button on the right side of your screen. This will transfer a file to your computer in the format you choose. While I normally prefer to keep copies of small data sets such as these in a human-readable ASCII text format, you might prefer to download them simply as .xls files as inputs to Excel, Matlab, Python, R, etc. We can label these two data series as P and Y. If you download the files in human-readable (ASCII) text format, you will have to edit the files to eliminate explanatory information and dates before processing with your data analysis program. You can use a plain-text editor (e.g. Notepad, OxEdit, etc) to do this. In your assignment, indicate the day on which you downloaded the data, since the data sets may be updated. 1 a. Plot graphs of the two data series. Then, take the (natural, base-e) logarithm of each series and plot those (we'll call them p and y, lower case). Then, starting from the second observation in each series, take the changes in the log series (eg log(Pt) – log(Pt-1) = Pt — Pt-1) and plot those. We'll call these Ap and Ay. 1 b. Compute the sample values of the mean, variance, standard error, coeffi- cients of skewness and kurtosis of Ap and Ay. 1 b. Compute the medians of Ap and Ay, noting that the series may have an even or odd number of observations depending when you download. 1 c. Produce histograms of the data on Ap and Ay, with a bin width of 0.1, to start with. Comment on the apparent appropriateness, or otherwise, of this 1
Transcribed Image Text:1. Obtain data on the consumer price index (CPI) and US gross domestic product (GDP) from the FRED (Federal Reserve Economic Data) data section of the web site of the Federal Reserve Bank of St. Louis: https://fred.stlouisfed.org. Click on 'research and databases' and then FRED economic data. Scroll down to 'at a glance' and you'll see CPI for all urban consumers. Then click on 'popular series' to get gross domestic product. Note that this is not the same as the real GDP series that you see in 'at a glance'. You can then download the data by clicking on the download button on the right side of your screen. This will transfer a file to your computer in the format you choose. While I normally prefer to keep copies of small data sets such as these in a human-readable ASCII text format, you might prefer to download them simply as .xls files as inputs to Excel, Matlab, Python, R, etc. We can label these two data series as P and Y. If you download the files in human-readable (ASCII) text format, you will have to edit the files to eliminate explanatory information and dates before processing with your data analysis program. You can use a plain-text editor (e.g. Notepad, OxEdit, etc) to do this. In your assignment, indicate the day on which you downloaded the data, since the data sets may be updated. 1 a. Plot graphs of the two data series. Then, take the (natural, base-e) logarithm of each series and plot those (we'll call them p and y, lower case). Then, starting from the second observation in each series, take the changes in the log series (eg log(Pt) – log(Pt-1) = Pt — Pt-1) and plot those. We'll call these Ap and Ay. 1 b. Compute the sample values of the mean, variance, standard error, coeffi- cients of skewness and kurtosis of Ap and Ay. 1 b. Compute the medians of Ap and Ay, noting that the series may have an even or odd number of observations depending when you download. 1 c. Produce histograms of the data on Ap and Ay, with a bin width of 0.1, to start with. Comment on the apparent appropriateness, or otherwise, of this 1
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