Prasad Bidarkota January 10, 2005
Topics in
Econometrics (ECO 7429)
Ref. No. 18974
Department of
Economics,
Spring Semester 2005
Further References:
Walter Enders (2004),
Applied Econometric Time Series, John Wiley & Sons, Inc.
Chapter 1: Difference Equations, p. 1-47.
Further References:
Walter Enders (2004),
Applied Econometric Time Series, John Wiley & Sons, Inc.
Chapter 2: Stationary Time Series Models, p. 48-107.
Further References:
Andrew C. Harvey (1991),
An Econometric Analysis of Time Series, 2nd Edition,
Chapter 3: The Method of Maximum Likelihood, p. 84-121.
Further References:
Andrew C. Harvey (1991),
An Econometric Analysis of Time Series, 2nd Edition,
Chapter 4: Numerical Optimization, p. 122-145.
See the accompanying list of readings.
List of
I. AUTOREGRESSIVE
CONDITIONAL HETEROSKEDASTICITY
ARCH AND GARCH
CLASS OF MODELS
Enders, W., Applied Econometric Time Series, John Wiley & Sons,
Inc. (1995). (Chapter 3)
Hamilton, James D., Time Series Analysis,
Engle, R.F. (1982),
‘Autoregressive conditional heteroskedasticity with estimates of the variance
of
1. Generalized Autoregressive Conditional
Heteroskedasticity (GARCH) Model
Bollerslev, T. (1986), ‘Generalized autoregressive conditional heteroskedasticity,’ Journal of Econometrics, 31, 307-327.
Lumsdaine, R.L. (1996), ‘Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1,1) and covariance stationary GARCH(1,1) models,” Econometrica, Vol.64, No.3, 575-96.
Lumsdaine, R.L. (1995),
‘Finite-sample properties of the maximum likelihood estimator in GARCH(1,1) and
IGARCH(1,1) models: a
Nelson, D.B. (1990), ‘Stationarity and persistence in the GARCH(1,1) model,’ Econometric Theory, 6, 318-334.
2. Exponential Generalized Autoregressive Conditional
Heteroskedasticity (EGARCH) Model
Nelson, D.B. (1990), ‘Conditional heteroskedasticity in asset returns: a new approach,’ Econometrica, Vol.59, No.2, 347-370.
3. Multivariate GARCH Models
Bollerslev, T. and R.F. Engle (1993), ‘Common persistence in conditional variances,’ Econometrica, Vol.61, No.1, 167-186.
Bollerslev, T. (1987), ‘A conditionally heteroskedastic time series model for speculative prices and rates of return,’ The Review of Economics and Statistics, 542-547.
Cosimano, T.F. and D.W. Jansen
(1988), ‘Estimates of the variance of
Engle, R.F. (1983), ‘Estimates of
the variance of
French, K.R., G.W. Schwert, and R.F. Stambaugh (1987), ‘Expected stock returns and volatility, Journal of Financial Economics, 19, 3-29.
Pagan, A. and G.W. Schwert (1990), ‘Alternative models for conditional stock volatility,’ Journal of Econometrics, 45, 267-290.
Bollerslev, T., R.Y. Chou, and K.F. Kroner (1992), ‘ARCH modeling in finance: A review of the theory and empirical evidence,’ Journal of Econometrics, 52, 5-59.
Hansen, B.E. (1995), ‘Regression with nonstationary volatility,’ Econometrica, Vol.63, No.5, 1113-1132.
Look under State Space Models – State Space Models and ARCH
Lamoureux, C.G. and W.D. Lastrapes (1990), ‘Persistence in variance, structural change, and the GARCH model, Journal of Business and Economic Statistics, Vol.8, No.2, 225-234.
Simonato, J-G (1992), Estimation of GARCH process in the presence of structural change, Economics Letters, 40, 155-158.
Look under Markov Switching Models – ARCH and Regime Switching Models
Danielsson, J.
(1994), ‘Stochastic volatility in asset prices: estimation with simulated
maximum likelihood,’ Journal of Econometrics, 64, 375-400.
Sandmann, G. and S.J. Koopman (1998), ‘Estimation of stochastic
volatility models via
3. Miscellaneous Volatility Models
Brenner, R.J., R.H. Harjes, and K.F. Kroner (1996), Another look at
models of the short-term interest rate,” Journal of Financial and
Quantitative Analysis, Vol.31, No.1, 85-107.
Brunner, A.D. and G.D. Hess (1993), ‘Are higher levels of inflation less predictable? A state-dependent conditional heteroskedasticity approach,’ Journal of Business and Economic Statistics, Vol.11, No.2, 187-197.
Ding, Z., C.W.J. Granger, and R.F. Engle (1993), ‘A long memory property of stock market returns and a new model,’ Journal of Empirical Finance, 1, 83-106.
Engle, R.F. and G. Gonzalez-Rivera (1991), “Semiparametric ARCH models,” Journal of Business & Economic Statistics, Vol.9, No.4, 345-359.
Bera, A.K. and M.L. Higgins (1992), “A test for conditional heteroskedasticity in time series models,” Journal of Time Series Analysis, Vol.13, No.6, 501-519.
Demos, A. and E. Sentana (1998), ‘Testing for GARCH effects: a one-sided approach,’ Journal of Econometrics, 86, 97-127.
McLeod, A.I. and W.K. Li (1983), ‘Diagnostic checking ARMA time series models using squared-residual autocorrelations,’ Journal of Time Series Analysis, Vol.4, No.4, 269-273.
Diebold, F.X. and J.A. Lopez (1995), ‘Modeling volatility
dynamics,’ in K. Hoover (ed.), Macroeconometrics: Developments, Tensions and
Prospects,
Weiss, A.A. (1984), ‘ARMA models with ARCH errors,’ Journal of Time Series Analysis, Vol.5, No.2, 129-143.
P.F. Christofferson and F.X. Diebold (1997), ‘How relevant is
volatility forecasting for financial risk management?’ Working Paper,
Department of Economics,
Engle, R.F. and A.J. Patton
(2001), ‘What good is a volatility model?’ Working Paper, Department of
Economics,
Andersen, T.G., T. Bollerslev,
F.X. Diebold, and P. Labys (2000), ‘The distribution of realized exchange rate
volatility,’ Working Paper, Department of Economics, University of
Andersen, T.G., T. Bollerslev,
F.X. Diebold, and P. Labys (2001), ‘Modeling and forecasting realized
volatility,’ Working Paper, Department of Economics, University of
Brooks, C., S.P. Burke, and G. Persand (2001), ‘Benchmarks and the accuracy of GARCH model estimation,’ International Journal of Forecasting 17, 45-56.
Simulations of ARCH processes
Tong, Howell, Non-Linear Time Series: A Dynamical System
Approach,
Tong, H., and K.S. Lim, “Threshold autoregression, limit cycles and cyclical data,” Journal of the Royal Statistical Society, Series B (1980), 245-292.
Chan, K.S. and H. Tong, “On estimating thresholds in autoregressive models,” Journal of Time Series Analysis, Vol.7, No.3 (1986), 179-190.
Tsay, R.S., “Detecting and modeling nonlinearity in univariate time series analysis,” Statistica Sinica, 1(1991), 431-451.
Granger, C.W.J. and T.
Terasvirta, Modeling Nonlinear Economic Relationships,
Tsay, R.S., “Non-linear time series analysis of blowfly population,” Journal of Time Series Analysis, Vol.9, No.3 (1988), 247-63.
Potter, S.M., “A non-linear approach to U.S. GNP,” Journal of Applied Econometrics, Vol.10 (1995), 109-25.
Beaudry, P. and G. Koop, “Do recessions permanently change output?” Journal of Monetary Economics, 31 (1993), 149-63.
Elwood, S.K., “Is the persistence of shocks to output asymmetric,” Journal of Monetary Economics 41 (1998), 411-426.
Hess, G.D. and
Blanchard, O.J. and M.W. Watson,
“Are business cycles all alike?” The American Business Cycle: Continuity and
Change, R.J. Gordon (ed.), University of
DeLong, J.B. and L.H. Summers,
“Are business cycles symmetrical?” The American Business Cycle: Continuity and
Change, R.J. Gordon (ed.), University of
Scheinkman, J.A. and B.LeBaron, “Non-linear dynamics and GNP data,” Economic Complexity: Chaos, Sunspots, Bubbles, and Non-linearity, W.A. Barnett et al. (eds.), Cambridge University Press (1989), 213-27.
Brunner, A.D., “On the dynamic properties of asymmetric models of real GNP,” The Review of Economics and Statistics, 79 (1997), 321-326.
Brunner, A.D., “Conditional asymmetries in real GNP: A seminonparametric approach,” Journal of Business and Economic Statistics, Vol.10, No.1 (1992), 65-72.
Brannas, K. and J.G. De Gooijer, “Autoregressive-asymmetric moving average models for business cycle data,” Journal of Forecasting, Vol.13 (1994), 529-544.
Brannas, K. and H. Ohlsson, “Asymmetric time series and temporal aggregation,” The Review of Economics and Statistics, 81 (1999), 341-344.
Neftci, S.N., “Are economic time series asymmetric over the business cycle?” Journal of Political Economy, Vol.92, No.2 (1984), 307-28.
Falk, B., “Further evidence on the asymmetric behavior of economic time series over the business cycle,” Journal of Political Economy, Vol.94, No.5 (1986), 1096-1109.
Sichel, D.E., “Are business cycles asymmetric? A correction,” Journal of Political Economy, Vol.97, No.5 (1989), 1255-60.
Rothman, P., “Further evidence on the asymmetric behavior of unemployment rates over the business cycle,” Journal of Macroeconomics, Vol.13, No.2 (1991), 291-298.
Pesaran, M.H. and S.M. Potter, “A
floor and ceiling model of
Ramsey, J.B. and P. Rothman, “Time irreversibility and business cycle asymmetry,” Journal of Money, Credit, and Banking, 28 (1996), 1-21.
III. MARKOV
SWITCHING MODELS
Hamilton, J.D., ‘A new approach to the economic analysis of nonstationary
time series and the business cycle,’ Econometrica, Vol.57, No.2 (1989),
357-84.
Phillips, K.L., ‘A two-country model of stochastic output with changes in regime,’ Journal of International Economics, 31 (1991), 121-142.
Lam, P-s., ‘The Hamilton model with a general autoregressive component: Estimation and comparison with other models of economic time series,’ Journal of Monetary Economics, 26 (1990), 409-32.
Durland, J.M. and T.H. McCurdy, ‘Duration-dependent transitions in a
Markov model of US GNP growth,’ Journal of Business and Economic Statistics,
Vol.12, No.3 (1994), 279-288.
Cecchetti, S.G., P-s. Lam, and N.C. Mark, 1990, Mean reversion in
equilibrium asset prices, The American Economic Review 80, 398-418.
Cecchetti, S.G., P-s. Lam, and N.C. Mark, 1993, The equity premium and
the risk-free rate, Journal of Monetary Economics 31, 21-45.
Engel, C. and J.D. Hamilton (1990), ‘Long swings in the dollar: Are they in the data and do markets know it?’ The American Economic Review 80, No.4, 689-713.
Evans, M. and K. Lewis, ‘Do expected shifts in inflation affect estimates
of the long-run Fisher relation?’ Journal of Finance, Vol.L, No.1
(1995), 225-253.
Garcia, R. and P. Perron, ‘An analysis of the real interest rate under
regime shifts,’ The Review of Economics and Statistics (1996), 111-123.
Hamilton, J.D., ‘Rational expectations econometric analysis of changes in
regime: An investigation of the term structure of interest rates,’ Journal
of Economic Dynamics and Control, 12 (1988), 385-423.
Raymond, J.E. and R.W. Rich (1997), “Oil and the macroeconomy: a Markov
state-switching approach,” Journal of Money, Credit, and Banking,
Vol.29, No.2, 193-213.
Cai, J., ‘A Markov model of switching-regime ARCH,’ Journal of
Business and Economic Statistics, Vol.12, No.3 (1994), 309-316.
Gray, Stephen F. (1996), “Modeling the conditional distribution of interest rates as a regime-switching process,” Journal of Financial Economics, 42, 27-62.
Hamilton, J.D. and R. Susmel, ‘Autoregressive conditional
heteroskedasticity and changes in regime,’ Journal of Econometrics, 64
(1994), 307-333.
Kim, C-j., ‘Unobserved-component time series models with Markov switching
heteroskedasticity: Changes in regime and the link between inflation rates and
inflation uncertainty,’ Journal of Business & Economic Statistics,
Vol.11, No.3 (1993), 341-349.
Look under Non-Gaussian Errors – State Space Models and Regime Switching
Garcia, R. (1998), ‘Asymptotic null distribution of the likelihood ratio test in Markov switching models,’ International Economic Review 39, No.3, 763-788.
Ghysels, E., R.E. McCulloch, and R.S. Tsay (1998), ‘Bayesian inference for periodic regime-switching models,’ Journal of Applied Econometrics 13, 129-143.
Hansen, B.E. (1992), ‘The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP,’ Journal of Applied Econometrics, Vol.7 (supplement), S61-S82.
Hansen, B.E. (1996), ‘Inference when a nuisance parameter is not identified under the null hypothesis,’ Econometrica 64, No.2, 413-430.
IV. STATE SPACE
MODELS
Hamilton, James D., Time Series Analysis,
Clark, P. K. (1987), “The cyclical component of
Gregory, A.W., A.C. Head, and J. Raynauld (1997), “Measuring world business cycles,” International Economic Review, Vol.38, No.3, 677-701.
Harvey, A. C. (1985), “Trends and cycles in macroeconomic time series,” Journal of Business and Economic Statistics,” Vol.3, No.3, 216-27.
Harvey, A. C. and A. Jaeger (1993), “Detrending, stylized facts and the business cycle,” Journal of Applied Econometrics,” 231-247.
Nelson, C.R. (1988), “Spurious trend and cycle in the state space decomposition of a time series with a unit root,” Journal of Economic Dynamics and Control, 12, 475-488.
Watson, M. (1986), “Univariate detrending methods with stochastic trends,” Journal of Monetary Economics, 18, 49-75.
Antonic, M. (1986), “High and volatile real interest rates: Where does the Fed fit in?” Journal of Money, Credit, and Banking, Vol.18, No.1, 18-27.
Burmeister, E. and K.D. Wall (1982), “Kalman filtering estimation of
unobserved rational expectations with an application to the German
hyperinflation,” Journal of Econometrics, 20, 255-284.
Burmeister, E., K.D. Wall and J.D. Hamilton (1986), ‘Estimation of
unobserved monthly inflation using Kalman filtering,’ Journal of Business
and Economic Statistics, Vol.4, No.2, 147-160.
Garbade, K. and P. Wachtel (1978), “Time variation in the relationship
between inflation and interest rates,” Journal of Monetary Economics, 4,
755-765.
Hamilton, J.D. (1985), ‘Uncovering financial market expectations of inflation,’ Journal of Political Economy, Vol.93, No.6, 1224-1241.
Elwood, S.R. (1998), “Testing for excess sensitivity in consumption: a state-space / unobserved components approach,” Journal of Money, Credit, and Banking, Vol.30, No.1, 64-82.
Wolff, C.C.P. (1987), “Forward foreign exchange rates, expected spot rates, and premia: a signal-extraction approach,” The Journal of Finance, Vol.XLII, No.2, 395-406.
Doran, H.E. (1992), “Constraining
Kalman filter and smoothing estimates to satisfy time-varying restrictions,” The Review of Economics and Statistics (1992), 568-572.
Look under Non-Gaussian Errors – State Space Models and Regime Switching
Harvey, A., E. Ruiz, and E. Sentana (1992), ‘Unobserved component time series models with ARCH disturbances,’ Journal of Econometrics, 52, 129-157.
V. LONG MEMORY
MODELS
FRACTIONALLY
INTEGRATED CLASS OF MODELS
Baillie, R. T. (1996), “Long memory processes and fractional integration
in econometrics,” Journal of Econometrics (Annals), Vol.73, No.1, 5-59.
Granger, C. W. J. and R. Joyeux (1980), “An introduction to long memory
time series models and fractional differencing,” Journal of Time Series
Analysis, Vol.1, No.1, 15-29.
Hosking, J. R. M. (1981), “Fractional Differencing,” Biometrika,
68, 1, 165-76.
1. Fractionally Integrated Generalized Autoregressive
Conditional Heteroskedasticity (FIGARCH) Model
1. Stock Returns Data
Crato, N.,1994, “Some international evidence regarding the stochastic
memory of stock returns,” Applied Financial Economics 4, 33-9.
Lo, A., 1991, “Long-term memory in stock market prices,” Econometrica
59, 1279-313.
Diebold, F. X. and G. D. Rudebusch (1989), “Long memory and persistence
in aggregate output,” Journal of Monetary Economics, 24, 189-209.
Sowell, F., “Modeling long-run behavior with the fractional ARIMA model,”
Journal of Monetary Economics, 29 (1992a), 277-302.
Baillie, R.T., C-f. Chung, and M.A. Tieslau (1996), ‘Analysing inflation
by the fractionally integrated ARFIMA-GARCH model,’ Journal of Applied
Econometrics, 11, 23-40.
Cheung, Y-W. (1993), “Long memory in foreign-exchange rates,” Journal
of Business & Economic Statistics, Vol.11, No.1, 93-101.
Crato, N. and P. Rothman (1994), “Fractional integration analysis of
long-run behavior of
Hassler, U. and J. Wolters (1995), Long memory in inflation rates: international evidence,” Journal of Business & Economic Statistics, Vol.13, No.1, 37-45.
Diebold, F. X. and G. D. Rudebusch (1991), “Is consumption too smooth? Long memory and the Deaton paradox,” The Review of Economics and Statistics 73, 1-9.
Hosking, J.R.M., “Modeling persistence in hydrological time series using fractional differencing,” Water Resources Research, Vol.20, No.12 (1984), 1898-1908.
Chambers, M.J. (1998), “Long memory and aggregation in macroeconomic time
series,” International Economic Review, Vol.39, No.4, 1053-1072.
Cheung, Y-W. (1993), “Tests for fractional integration: a Monte Carlo investigation,” Journal of Time Series Analysis, Vol.14, No.4, 331-345.
Agiakloglou, C., P. Newbold and M. Wohar (1993), “Bias in an estimator of the fractional difference parameter,” Journal of Time Series Analysis, Vol.14, No.3, 235-46.
Cheung, Y-w. and F. X. Diebold (1994), “On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean,” Journal of Econometrics, 62, 301-16.
Chung, C. F. (1994), “A note on calculating the autocovariances of the fractionally integrated ARMA models,” Economics Letters, 45, 293-97.
Geweke, J. and S. Porter-Hudak (1983), “The estimation and application of long memory time series models,” Journal of Time Series Analysis, Vol.4, No.4, 221-238.
Gonzalo, J. and C.W. Granger, “Estimation of common long-memory components in cointegrated systems,” Journal of Business and Economic Statistics, Vol.13, No.1, 27-35.
Li, W.K. and A.I. McLeod, “Fractional time series modeling,” Biometrika, 73, 1 (1986), 217-21.
Sowell, F., “Maximum likelihood estimation of stationary univariate fractionally integrated time series models,” Journal of Econometrics, 53 (1992b) 165-88.
VI. NON-GAUSSIAN
ERRORS
1. Basic Non-Gaussian Time Series Models
Akgiray, V. and G.G. Booth, 1988, “The stable-law model of stock
returns,” Journal of Business and Economic Statistics, Vol.6, No.1, 51-57.
So, Jacky C., 1987, “The sub-Gaussian distribution of currency futures: stable Paretian or nonstationary?” The Review of Economics and Statistics 69, 100-107.
de Vries, C.G., 1991, “On the relation between GARCH and stable
processes,” Journal of Econometrics 48, 313-24.
Ghose, D. and K.F. Kroner, 1995, “The relationship between GARCH and
symmetric stable processes: Finding the source of fat tails in financial data,”
Journal of Empirical Finance 2, 225-51.
Liu, S.M. and B.W. Brorsen (1995), ‘Maximum likelihood estimation of a
GARCH-stable model,’ Journal of Applied Econometrics, 10, 273-285.
McCulloch, J. H. (1985), ‘Interest-risk sensitive deposit insurance
premia: stable ACH estimates,’ Journal of Banking and Finance, 9,
137-56.
Kokoszka, P.S. and M.S. Taqqu, “Fractional ARIMA with stable innovations,” Stochastic Processes and their Applications, 60 (1995), 19-47.
Kokoszka, P.S. and M.S. Taqqu (1996), “Infinite variance stable moving averages with long memory,” Journal of Econometrics, 73, 79-99.
Baillie, R.T., C-f. Chung and M.A. Tieslau (1996), ‘Analysing inflation
by the fractionally integrated ARFIMA-GARCH model,’ Journal of Applied
Econometrics, 11, 23-40.
Bidarkota, P.V., Asymmetries in the Conditional Mean Dynamics of Real GNP: Robust Evidence, The Review of Economics and Statistics, Vol.82, Issue 1 (2000), 153-157.
Bidarkota, P.V., Sectoral Investigation of Asymmetries in the Conditional Mean Dynamics of the Real U.S. GDP, Studies in Non-Linear Dynamics and Econometrics, Vol.3, No.4 (1999), 191-200.
Harvey, Andrew C., Forecasting, Structural Time Series Models and the
Kalman Filter, Cambridge University Press (1989), New York. (Section
3.7)
Kitagawa, G. (1987), ‘Non-Gaussian state space modeling of nonstationary time series,’ Journal of the American Statistical Association, Vol.82, No.400,1032-63.
Hodges, P.E. and D.F. Hale (1993), ‘A computational method for estimating densities of non-Gaussian nonstationary univariate time series,’ Journal of Time Series Analysis, Vol.14, No.2, 163-178.
Kitagawa, G. (1996), ‘
Kitagawa, G. and W. Gersch
(1996), ‘Smoothness priors analysis of time series,’ Lecture Notes in
Statistics 116, Springer-Verlag,
Le Breton, A. and M. Musiela (1993), ‘A generalization of the Kalman filter to models with infinite variance,’ Stochastic Processes and their Applications, 47, 75-94.
Rutkowski, M. (1994), ‘Optimal linear filtering and smoothing for a discrete-time stable linear model,’ Journal of Multivariate Analysis, 50, 68-92.
Sorenson, H.W. and D.L. Alspach (1971), ‘Recursive Bayesian estimation using Gaussian sums,’ Automatica, 7, 465-479.
Stuck, B.W. (1978), ‘Minimum error dispersion linear filtering of scalar symmetric stable processes,’ IEEE Transactions on Automatic Control AC-23, 507-509.
Bidarkota, P.V., Alternative Regime Switching Models for Forecasting Inflation, Journal of Forecasting (forthcoming).
Bidarkota, P.V. and J. H. McCulloch, “Optimal Univariate Inflation Forecasting with Symmetric Stable Shocks, Journal of Applied Econometrics, Vol.13, No.6 (1998), 659-670.
Chauvet, M. (1998), ‘An econometric characterization of business cycle dynamics with a factor structure and regime switching,’ International Economic Review, Vol.39, No.4, 969-996.
Kim, C-j., ‘Dynamic linear models with Markov-switching,’ Journal of
Econometrics, 60 (1994), 1-22.
Kim, C-J. and C.R. Nelson (1998), ‘Business cycle turning points, a new coincident index, and tests of duration dependence based on a dynamic factor model with regime switching,’ The Review of Economics and Statistics, 188-201.
Kim, M-J. and J-S. Yoo (1995), ‘New index of coincident indicators: A multivariate Markov switching factor model approach,’ Journal of Monetary Economics 36, 607-630.
Shephard, N. (1994), ‘Partial non-Gaussian state space,’ Biometrika 81, 1, 115-131.
Carter, C.K. and R. Kohn (1994), ‘On Gibbs sampling for state space models,’ Biometrika 81, 3, 541-553.
VII. FUTURE DIRECTIONS
Lo, Andrew W. (2000), “Finance: a selective survey,” Journal of the American Statistical Association, Vol.95, No.450, 629-635.
Solo, V. (2000), “The end of time series,” Journal of the American Statistical Association, Vol.95, No.452, 1346-1349.
Tsay, Ruey S. (2000), “Time Series and Forecasting: Brief History and Future Research,” Journal of the American Statistical Association, Vol.95, No.450, 638-643.