R programming for economics

Estimate an ARMA Model Write a code to perform the following steps. The goal is to construct an ARMA model to t total factor productivity time series of the USA. 1. Consider the yearly GDP per capita series given in the excel le from the sheet marked \Data".1 Extract the GDP per capita series for the USA from 1960 to 2022 and take log of it. Call this series fytg and plot it. Label the gure (x axis and y axis) clearly. 2. Filter the series using Hodrick-Prescott lter (HP lter) and nd the residual. Use 6.25 as the smoothing parameter since this is yearly data.2 Let us denote the resulting residual series by ftg. 3. Plot the time series of ftg. Label the gure (x axis and y axis) clearly. 4. Plot empirical autocorrelation function (ACF) and partial autocorrelation function (PACF) of ftg. Label the gure (x axis and y axis) clearly. 5. Estimate ARMA(p,q) models on ftg for dierent combinations of p and q where p = 0; 1; : : : ; 9 and q = 0; 1; : : : ; 9. Estimate them using two for loops, one on p and another on q. Compute Akaike information criteria (AIC) for each estimation. Construct a 1010 matrix (note that both p and q can take 10 values ranging from 0 to 9) and ll up the matrix where the p; q-th element of the matrix would be the AIC for the estimated ARMA(p,q).3 6. Which model would you pick based on the information criteria?