The file \(q\)-fdebt.txt contains the U.S. quarterly federal debts held by

(a) foreign and international investors,

(b) federal reserve banks, and

(c) the public. The data are from the Federal Reserve Bank of St. Louis, from 1970 to 2012 for 171 observations, and not seasonally adjusted. The debts are in billions of dollars. Take the log transformation and the first difference for each time series. Let \(\boldsymbol{z}_{t}\) be the differenced \(\log\) series.

- Plot the time series \(z_{t}\).

- Obtain the first five lags of sample CCMs of \(z_{t}\).

- Test \(H_{0}: \boldsymbol{ho}_{1}=\cdots=\boldsymbol{ho}_{10}=\mathbf{0}\) versus \(H_{a}: \boldsymbol{ho}_{i} eq \mathbf{0}\) for some \(i\), where \(i \in\{1, \ldots, 10\}\). Draw the conclusion using the \(5 \%\) significance level.

You may use the following commands of MTS to process the data:

Transcribed Image Text:

da=read.table("q-fdebt.txt", header=T) debt log (da [, 3:5]); tdx=da [,1] +da [,2]/12 MTSplot (debt, tdx); zt=diffM (debt); MTSplot (zt, tdx [-1])