- Consider the daily \(\log\) returns of the GE stock of Exercise 7.1. Obtain estimates \(\hat{\theta}_{b}^{(1)}\) and \(\hat{\theta}_{r}^{(3)}\) of the extremal index of (a) the positive return series
- Consider the monthly log returns of GM stock in m-gmsp5008.txt. Build an adequate TGARCH model for the series. Write down the fitted model and test for the significance of the leverage effect. Obtain
- Consider the monthly stock returns of S\&P composite index from January 1975 to December 2008 in Exercise 1.2. Answer the following questions:(a) What is the average annual log return over the
- Consider the daily log returns of American Express stock from January 1999 to December 2008 as in Exercise 1.1. Use the 5\% significance level to perform the following tests:(a) Test the null
- Now consider similar questions of the previous exercise for the IBM stock returns.(a) Is there any weekday effect on the daily simple returns of IBM stock? Estimate your model and test the hypothesis
- Consider the growth rates, in percentages, of the quarterly real GDP of United Kingdom, Canada, and the United States used in the chapter. Fit a VAR(4) model to the series, simplify the model by
- Consider a bivariate time series \(\boldsymbol{z}_{t}\), where \(z_{1 t}\) is the change in monthly U.S. treasury bills with maturity 3 months and \(z_{2 t}\) is the inflation rate, in percentage, of
- Consider the U.S. quarterly gross private saving (GPSAVE) and gross private domestic investment (GPDI) from first quarter of 1947 to the third quarter of 2012. The data are from the Federal Reserve
- Consider two components of U.S. monthly industrial production index from December 1963 to December 2012. The two components are(a) nondurable consumer goods and(b) materials. The data are in columns
- Consider two components of U.S. monthly industrial production index from December 1963 to December 2012. The two components are(a) business equipments and(b) materials. The data are in columns 5 and
- Consider the bivariate VMA(1) model\[ \boldsymbol{z}_{t}=\boldsymbol{a}_{t}-\left[\begin{array}{rr} -0.3 & 0.2 \\1.1 & 0.6 \end{array}\right] \boldsymbol{a}_{t-1} \]where \(a_{t}\) is a Gaussian
- Write down the structure of a three-dimensional VARMA model if the vector time series has the following three components: \(\operatorname{SCM}(0,0), \operatorname{SCM}(0,1)\), and
- Consider the three SCMs of Question 3. If the maximum elements, in absolute value, of the three rows of the transformation matrix \(T\) are \((1,1),(2,3)\), and \((3,2)\), respectively. Write down
- Consider the realized volatilities of the Alcoa stock from January 2, 2003, to May 7, 2004, for 340 observations. The realized volatilities are the sum of squares of intraday \(m\)-minute log
- Simulation is helpful in learning vector time series. Define the matricesUse the commandto generate 300 observations from the VAR(1) model\[z_{t}=C z_{t-1}+a_{t}\]where \(a_{t}\) are iid bivariate
- Use the matrices of Problem 1 and the following commandto generate 200 observations from the VMA(1) model, \(\boldsymbol{z}_{t}=\boldsymbol{a}_{t}-\boldsymbol{C} \boldsymbol{a}_{t-1}\), where
- 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
- For a VARMA time series \(\boldsymbol{z}_{t}\), derive the result of Equation (1.20). e-1 T and Te = ve ive-i l>1. i=1 (1.20)
- The file m-pgspabt.txt consists of monthly simple returns of Procter & Gamble stock, S&P composite index, and Abbott Laboratories from January 1962 to December 2011. The data are from CRSP. Transform
- Prove Lemma 2.2.Data from Lemma 2.2. Lemma 2.2 For a VAR(p) model in Equation (2.21) with a, being a serially uncorrelated innovation process with mean zero and positive-definite covariance a,
- Consider, again, the quarterly growth series \(z_{t}\) of Problem 4. Obtain Bayesian estimation of a VAR(4) model. Write down the fitted model.
- Consider four components of U.S. monthly industrial production index from January 1947 to December 2012 for 792 data points. The four components are durable consumer goods (IPDCONGD), nondurable
- Consider, again, the \(z_{t}\) series of Problem 6. The time plots show the existence of possible aberrant observations, especially at the beginning of the series. Repeat the analyses of Problem 6,
- Consider the quarterly U.S. federal government debt from the first quarter of 1970 to the third quarter of 2012. The first series is the federal debt held by foreign and international investors and
- Consider the quarterly growth rates (percentage change a year ago) of real gross domestic products of Brazil, South Korea, and Israel from 1997.I to 2012.II for 62 observations. The data are from the
- Consider the monthly unemployment rates of the States of Illinois, Michigan, and Ohio of the United States from January 1976 to November 2009. The data were seasonally adjusted and are available from
- Suppose that \(z_{t}\) is a \(k\)-dimensional weakly stationary, zero-mean time series following the \(\operatorname{VARMA}(2, q)\) modelwhere \(\left\{\boldsymbol{a}_{t}\right\}\) is a white noise
- Consider the monthly log returns of CRSP decile portfolios 1, 2 , and 5 from January 1961 to September 2011.(a) Specify a VMA model for the three-dimensional log returns.(b) Estimate the specified
- Consider the quarterly U.S. Federal government debt held by(a) foreign and international investors and(b) by the Federal Reserve Banks, in billions of dollars, from 1970.I to 2012.III. Let \(z_{t}\)
- Write down the structure of a three-dimensional VARMA model if the Kronecker indices of the vector time series are \(\{1,2,1\}\). How many parameters does the model employ if it includes the constant
- Write down the structure of a three-dimensional VARMA model if the Kronecker indices of the vector time series are \(\{1,0,1\}\).
- Consider the monthly unemployment rates of Illinois, Michigan, and Ohio from January 1976 to November 2009. The data are seasonally adjusted and can be obtained from the Federal Reserve Bank of St.
- Consider, again, the monthly unemployment rates of the states of Illinois, Michigan, and Ohio in the prior question. Specify three SCMs for the data. No estimation is needed.
- Derive the error-correction form in Equation (5.68) for a \(\operatorname{VAR}(p)\) model. P-1 Azt = zt-p+Azti + c(t) + (B)at, i=1 (5.68)
- Consider the quarterly real GDP of United Kingdom, Canada, and the United States from the first quarter of 1980 to the second quarter of 2011. The data are available from the Federal Reserve Bank of
- Consider the daily closing prices of the stocks of Billiton Ltd. of Australia and Vale S.A. of Brazil with tick symbols BHP and VALE, respectively. The data are obtained from Yahoo Finance and the
- Consider the U.S. monthly personal consumption expenditures (PCE) and disposable personal income (DSPI) from January 1959 to March 2012. The data are from FRED of the Federal Reserve Bank of St.
- Consider the U.S. populations of men and women from January 1948 to December 2012. The data are available from FRED of the Federal Reserve Bank of St. Louis and are in thousands. See also the files
- Consider the annual real gross domestic products per capita of four OECD countries. The countries are (a) United States, (b) Germany, (c) United Kingdom, and (d) France. The real GDP are in 2011 U.S.
- Consider, again, the annual real gross domestic products per capita for United States. and United Kingdom of Problem 6. Use multivariate exponential smoothing to produce one-step ahead forecasts of
- Housing markets in the United States have been under pressure since the 2007 subprime financial crisis. In this problem, we consider the housing starts for the West and South regions of U.S. Census.
- Consider the monthly unemployment rate and the industrial production index of United States from January 1967 to December 2012 for 552 observations. The data are seasonally adjusted and obtained from
- Consider the monthly data from the Institute of Supply Management from 1988 to 2012 for exactly 300 observations. The variables used are (a) production index of manufacturing, (b) inventories index,
- Consider monthly simple returns of 40 stocks from NASDAQ and NYSE for years 2002 and 2003. The data are in the file m-apca40stocks.txt. The file has 40 columns. The first row of the file contains the
- Consider the annual real GDP of 14 countries from 1960 to 2011 for 52 observations. The data are obtained from FRED of the Federal Reserve Bank of St. Louis, in 2005 millions of U.S. dollars, and in
- Again, consider the 14 annual real GDP growth rates, in percentages, of the prior problem.(a) Perform a model-based clustering analysis with AR order \(p=2\) and 2 clusters.(b) Standardize the 14
- Consider the monthly log returns of Fama bond portfolio (6 months), S&P composite index, and Procter & Gamble stock from January 1962 to December 2011 for 600 observations. The simple returns are
- Again, consider the three-dimensional monthly \(\log\) returns of Problem 1. Fit a DCC model of Tse and Tsui (2002) with Student- \(t\) innovations to the data and obtain the time-varying
- Consider the daily log returns of EXXON-Mobil, S\&P composite index, and Apple stock used in Example 7.6. Fit a dynamically orthogonal component (DOC) model to the series. Write down the fitted
- The file m-pgspabt-6211.txt contains the monthly simple returns of Procter & Gamble stock, S&P composite index, and Abbot Laboratories stock from January 1962, to December 2011. Compute the
- Again, consider the three-dimensional log returns of Problem 1. Fit a \(t\)-copula model with marginal Student \(-t\) innovations to the data. White down the fitted model and compute the resulting
- Focus on the daily log returns, in percentages, of EXXON-Mobil stock and the S\&P composite index used in Example 7.6. Fit a BEKK \((1,1)\) model to the innovations of log returns. Write down the
- Again, consider the three-dimensional log return series of Problem 1. Fit a multivariate volatility model based on the Cholesky decomposition of the data. Is the model adequate? Why?Data from Problem
- Consider the monthly simple excess returns of 10 U.S. stocks from January 1990 to December 2003 for 168 observations. The 3-month Treasury bill rate on the secondary market is used to compute the
- Consider the daily returns of GE stock from January 2, 1998, to December 31, 2008. The data can be obtained from CRSP or the file d-ge9808 . txt. Convert the simple returns into log returns. Suppose
- The file d-csco9808. txt contains the daily simple returns of Cisco Systems stock from 1998 to 2008 with 2767 observations. Transform the simple returns to \(\log\) returns. Suppose that you hold a
- Use Hill's estimator and the data d-csco9808.txt to estimate the tail index for daily \(\log\) returns of Cisco stock.
- The file d-hpq3dx9808. txt contains dates and the daily simple returns of Hewlett-Packard, the CRSP value-weighted index, equal-weighted index, and the S\&P 500 index from 1998 to 2008. The returns
- Consider the daily returns of Alcoa (AA) stock and the S&P 500 composite index (SPX) from 1998 to 2008. The simple returns and dates are in the file d-aaspx9808.txt. Transform the simple returns to
- Consider, again, the daily log returns of Alcoa (AA) stock in Exercise 7.5. Focus now on the daily positive log returns. Answer the same questions as in Exercise 7.5. However, use threshold 3% in
- Consider the daily returns of SPX in d-aaspx9808.txt. Transform the returns into \(\log\) returns and focus on the daily negative log returns.(a) Fit the generalized extreme value distribution to the
- Consider the monthly log stock returns, in percentages and including dividends, of Merck & Company, Johnson & Johnson, General Electric, General Motors, Ford Motor Company, and value-weighted index
- The Federal Reserve Bank of St. Louis publishes selected interest rates and U.S. financial data on its website: http://research.stlouisfed.org/fred2/.Consider the monthly 1 -year and 10 -year
- Again consider the monthly 1 -year and 10 -year Treasury constant maturity rates from April 1953 to October 2009. Consider the log series of the data and build a VARMA model for the series. Discuss
- Again consider the monthly 1 -year and 10 -year Treasury constant maturity rates from April 1953 to October 2009. Are the two interest rate series threshold cointegrated? Use the interest spread
- The bivariate AR(4) model \(\boldsymbol{x}_{t}-\boldsymbol{\Phi}_{4} \boldsymbol{x}_{t-4}=\boldsymbol{\phi}_{0}+\boldsymbol{a}_{t}\) is a special seasonal model with periodicity 4 , where
- The bivariate MA(4) model \(\boldsymbol{x}_{t}=\boldsymbol{a}_{t}-\boldsymbol{\Theta}_{4} \boldsymbol{a}_{t-4}\) is another seasonal model with periodicity 4 , where
- Consider the monthly U.S. 1-year and 3-year Treasury constant maturity rates from April 1953 to March 2004. The data can be obtained from the Federal Reserve Bank of St. Louis or from the file
- Consider the monthly simple excess returns, in percentages and including dividends, of 13 stocks and the S&P 500 composite index from January 1990 to December 2008. The monthly 3-month Treasury bill
- Consider the monthly log stock returns, in percentages and including dividends, of Merck & Company, Johnson & Johnson, General Electric, General Motors, Ford Motor Company, and value-weighted
- The file m-excess-c10sp-9003.txt contains the monthly simple excess returns of 10 stocks and the S&P 500 index. The 3-month Treasury bill rate on the secondary market is used to compute the excess
- Again, consider the 10 stock returns in m-excess-c10sp-9003.txt. The stocks are from companies in 3 industrial sectors. ABT, LLY, MRK, and PFE are major drug companies, \(\mathrm{F}\) and GM are
- Again, consider the 10 excess stock returns in the file m-excess-c10sp9003.txt. Perform a principal component analysis on the returns and obtainthe scree plot. How many common factors are there? Why?
- Again, consider the 10 excess stock returns in the file m-excess-c10sp9003.txt. Perform a statistical factor analysis. How many common factors are there if the 5% significance level is used? Plot the
- The file m-fedip.txt contains year, month, effective federal funds rate, and the industrial production index from July 1954 to December 2003. The industrial production index is seasonally adjusted.
- Consider the monthly simple returns, including dividends, of IBM stock, Hewlett-Packard (HPQ) stock, and the S&P composite index from January 1962 to December 2008 for 564 observations. The returns
- Focus on the monthly log returns of IBM and HPQ stocks from January 1962 to December 2008. Fit a \(\operatorname{DVEC}(1,1)\) model to the bivariate return series. Is the model adequate? Plot the
- Focus on the monthly log returns of the S&P composite index and HPQ stock. Build a BEKK model for the bivariate series. What is the fitted model? Plot the fitted volatility series and the
- Build a constant-correlation volatility model for the three monthly \(\log\) returns of IBM stock, HPQ stock, and S&P composite index. Write down the fitted model. Is the model adequate? Why?
- The file m-geibmsp2608. txt contains the monthly simple returns of General Electric stock, IBM stock, and the S&P composite index from January 1926 to December 2008. The returns include dividends.
- Again, consider the monthly log returns of GE, IBM, and S&P composite index from January 1926 to December 2008. Build a dynamic correlation model for the three-dimensional series. For simplicity,
- The file \(\mathrm{m}\)-spibmge.txt contains the monthly log returns in percentages of the S&P composite index, IBM stock, and GE stock from January 1926 to December 1999. Focus on GE stock and the
- Focus on the monthly log returns in percentages of GE stock and the S&P 500 index from January 1926 to December 1999. Build a time-varying correlation GARCH model for the bivariate series using the
- Consider the three-dimensional return series of the previous exercise jointly. Build a multivariate time-varying volatility model for the data, using the Cholesky decomposition. Discuss the
- An investor is interested in daily value at risk of his position on holding long \$0.5 million of Dell stock and \$1 million of Cisco Systems stock. Use \(5 \%\) critical values and the daily log
- Consider the ARMA(1,1) model \(y_{t}-0.8 y_{t-1}=a_{t}+0.4 a_{t-1} \quad\) with \(a_{t} \sim N(0,0.49)\). Convert the model into a state-space form using (a) Akaike's method, (b) Harvey's approach,
- The file aa-rv-20m txt contains the realized daily volatility series of Alcoa stock returns from January 2, 2003, to May 7, 2004; see the example in Section 11.1. The volatility series is constructed
- Consider the monthly simple excess returns of Pfizer stock and the S&P 500 composite index from January 1990 to December 2003. The excess returns are in m-pfesp-ex9003.txt with Pfizer stock
- Consider the AR(3) model\[ x_{t}=\phi_{1} x_{t-1}+\phi_{2} x_{t-2}+\phi_{3} x_{t-3}+a_{t}, \quad a_{t} \sim N\left(0, \sigma_{a}^{2}\right) \]and suppose that the observed data are\[
- The file m-ppiaco4709 txt contains year, month, day, and U.S. producer price index (PPI) from January 1947 to November 2009. The index is for all commodities and not seasonally adjusted. Let
- Suppose that \(x\) is normally distributed with mean \(\mu\) and variance 4 . Assume that the prior distribution of \(\mu\) is also normal with mean 0 and variance 25 . What is the posterior
- Consider the linear regression model with time series errors.Assume that \(z_{t}\) is an \(\operatorname{AR}(p)\) process (i.e., \(z_{t}=\phi_{1} z_{t-1}+\cdots+\phi_{p} z_{t-p}+a_{t}\) ). Let
- Consider the linear \(\operatorname{AR}(p)\) model. Suppose that \(x_{h}\) and \(x_{h+1}\) are two missing values with a joint prior distribution being multivariate normal with mean
- Consider the monthly log returns of Ford Motors stock from January 1965 to December 2008: (a) Build a GARCH model for the series, (b) build a stochastic volatility model for the series, and (c)
- Build a stochastic volatility model for the daily log return of Cisco Systems stock from January 2001 to December 2008. You may download the simple return of the stock from the CRSP database or the
- Build a bivariate stochastic volatility model for the monthly log returns of Ford Motors stock and the S&P composite index for the sample period from January 1965 to December 2008. Discuss the
- Consider the monthly log returns of Procter & Gamble stock and the valueweighted index from January 1965 to December 2008. The simple returns are given in the file m-pgvw6508.txt. Transform the data
- Consider the monthly data of 30-year mortgage rate and the 3-month Treasury Bill rate of the secondary market from April 1971 to September 2009.The data are in m-mort3mtb7109.txt. (a) Build a
- Derive multistep-ahead forecasts for a \(\operatorname{GARCH}(1,2)\) model at the forecast origin \(h\).
- Derive multistep-ahead forecasts for a \(\operatorname{GARCH}(2,1)\) model at the forecast origin \(h\).

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