please help with this problem, very difficult! Thanks!
Real GDP: Deviations from HP Trend .04 02 0 Deviation from Trend -.02 -.04 .06 1950 1960 1970 1980 1990 2000 2010 2020 Source: FRED (GDPC1) Guide for Problem 1 1. On the FRED website, you can access the time series of interest by using the search box. So simply type GDPC1 for GDP data and so on. Make sure these variables are quarterly. You can check and modify this by clicking the "edit graph". You can download these data series by clicking "Download". 2. Once you have the time series in Excel it's time to apply the HP filter. Below is a simple way to do it with the tools available in Excel. First, we construct the objective function. As a reminder, if we let { yr},_, be the original series, the HP trend {x*},_, is the (x,}!_, which solves the following problem: (1.1) min(x 1=1 where a is the smoothing parameter. (a) In a blank Excel sheet, put the dates in column A and the data in column B. (b) Construct the log of the series in column C. This corresponds to { yr},, in equation (1.1). (c) Construct the HP trend for the series, which corresponds to the {x,},_, which solves (1.1). Follow these steps: i. Make an initial guess for {x },_1. Specifically, use x, = yr for t = 1,..., T. Put this in column D. ii. Create the series { (y. - x,) }, and put this in column E. 21 HP filter For this question you are asked to compute the HP filter decomposition of GDP. You are asked to solve the minimization problem directly with using built-in functions in Excel. Refer to the guide at the end of this problem set for a step-by-step guide. Some additional notes: 1. Use quarterly data from 2000 to 2018 included. 2. Use the variable: Real Gross Domestic Product [GDPC1] as your GDP data. You can find this variable in FRED http://research.stlouisfed.org/fred2/. 3. Include two graphs: (1) one for the trend together with the original data; (2) the second one reserve it for the cycle like below. Real GDP and HP Trend Ln Real GDP HP Trend Log Scale 8.5 N 1950 1960 1970 1980 1990 2000 2010 2020 Source: FRED (GDPC1)iii. Create the series {[(x,+1 x,) (3|:r x,_1)]2}:21 and put this in column F. iv. Set 11 = 1600 (This is a standard value when using quarterly data). Put this in column G, row 1. v. In column H, compute the value of the objective function in equation (1.1) given our initial guess and the previous steps. vi. Now apply the Solver Excel-tool to nd the HP trend {35:};1' You should minimize the value of the objective function in part V by changing the values of {36,}?=1 in col- umn D. You now have the HP ltered data! To get the cyclical component calculate e, = y, x: for each
