## Documentation |

[1] Ait-Sahalia, Y. "Testing Continuous-Time
Models of the Spot Interest Rate." *The Review of
Financial Studies*. Spring 1996, Vol. 9, No. 2, pp. 385–426.

[2] Ait-Sahalia, Y. "Transition Densities
for Interest Rate and Other Nonlinear Diffusions." *The
Journal of Finance. *Vol. 54, No. 4, August 1999.

[3] Amano, R. A., and S. van Norden. "Unit Root Tests and the Burden of Proof." Bank of Canada. Working paper 92–7, 1992.

[4] Andrews, D. W. K. "Heteroskedasticity and Autocorrelation
Consistent Covariance Matrix Estimation." *Econometrica*.
v. 59, 1991, pp. 817-858.

[5] Andrews, D. W. K., and J. C. Monohan. "An Improved
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimator." *Econometrica*. v. 60, 1992,
pp. 953-966.

[6] Baillie, R. T., and T. Bollerslev. "Prediction
in Dynamic Models with Time-Dependent Conditional Variances." *Journal
of Econometrics*. Vol. 52, 1992, pp. 91–113.

[7] Belsley, D. A., E. Kuh, and R. E. Welsh. *Regression
Diagnostics*. New York, NY: John Wiley & Sons, Inc.,
1980.

[8] Bera, A. K., and H. L. Higgins. "A
Survey of ARCH Models: Properties, Estimation and Testing." *Journal
of Economic Surveys*. Vol. 7, No. 4, 1993.

[9] Bollerslev, T. "A Conditionally Heteroskedastic
Time Series Model for Speculative Prices and Rates of Return." *Review
of Economics and Statistics*. Vol. 69, 1987, pp. 542–547.

[10] Bollerslev, T. "Generalized Autoregressive
Conditional Heteroskedasticity." *Journal of Econometrics*.
Vol. 31, 1986, pp. 307–327.

[11] Bollerslev, T., R. Y. Chou, and K. F. Kroner.
"ARCH Modeling in Finance: A Review of the Theory and Empirical
Evidence." *Journal of Econometrics*.
Vol. 52, 1992, pp. 5–59.

[12] Bollerslev, T., R. F. Engle, and D. B. Nelson.
"ARCH Models." *Handbook of Econometrics*.
Vol. 4, Chapter 49, Amsterdam: Elsevier Science B.V., 1994, pp. 2959–3038.

[13] Bollerslev, T., and E. Ghysels. "Periodic
Autoregressive Conditional Heteroscedasticity." *Journal
of Business and Economic Statistics*. Vol. 14, 1996, pp.
139–151.

[14] Box, G. E. P. and D. Pierce. "Distribution of Residual
Autocorrelations in Autoregressive-Integrated Moving Average Time
Series Models." *Journal of the American Statistical Association*.
Vol. 65, 1970, pp. 1509–1526.

[15] Box, G. E. P., G. M. Jenkins, and G. C.
Reinsel. *Time Series Analysis: Forecasting and Control*.
3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.

[16] Breusch, T.S., and Pagan, A.R. "Simple test for heteroscedasticity
and random coefficient variation". *Econometrica*.
v. 47, 1979, pp. 1287–1294.

[17] Brockwell, P. J. and R. A. Davis. *Introduction
to Time Series and Forecasting*. 2nd ed. New York, NY:
Springer, 2002.

[18] Brooks, C., S. P. Burke, and G. Persand.
"Benchmarks and the Accuracy of GARCH Model Estimation." *International
Journal of Forecasting*. Vol. 17, 2001, pp. 45–56.

[19] Brown, M. B. and Forsythe, A. B. "Robust Tests for Equality
of Variances." *Journal of the American Statistical Association*.
69, 1974, pp. 364–367.

[20] Burke, S. P. "Confirmatory Data Analysis: The Joint Application of Stationarity and Unit Root Tests." University of Reading, UK. Discussion paper 20, 1994.

[21] Campbell, J. Y., A. W. Lo, and A. C. MacKinlay.
Chapter 12. "The Econometrics of Financial Markets." *Nonlinearities
in Financial Data*. Princeton, NJ: Princeton University
Press, 1997.

[22] Caner, M., and L. Kilian. "Size Distortions
of Tests of the Null Hypothesis of Stationarity: Evidence and Implications
for the PPP Debate." *Journal of International Money
and Finance*. Vol. 20, 2001, pp. 639–657.

[23] Cecchetti, S. G., and P. S. Lam. "Variance-Ratio
Tests: Small-Sample Properties with an Application to International
Output Data." *Journal of Business and Economic Statistics*.
Vol. 12, 1994, pp. 177–186.

[24] Cochrane, J. "How Big is the Random
Walk in GNP?" *Journal of Political Economy*.
Vol. 96, 1988, pp. 893–920.

[25] Cribari-Neto, F. "Asymptotic Inference Under Heteroskedasticity
of Unknown Form." *Computational Statistics & Data Analysis*.
v. 45, 2004, pp. 215-233.

[26] Dagum, E. B. *The X-11-ARIMA Seasonal Adjustment
Method*. Number 12–564E. Statistics Canada, Ottawa,
1980.

[27] Davidson, R., and J. G. MacKinnon. *Econometric
Theory and Methods*. Oxford, UK: Oxford University Press,
2004.

[28] den Haan, W. J., and A. Levin. "A Practitioner's Guide
to Robust Covariance Matrix Estimation." In *Handbook of
Statistics*. Edited by G. S. Maddala and C. R. Rao. Amsterdam:
Elsevier, 1997.

[29] Dickey, D. A., and W. A. Fuller.
"Distribution of the Estimators for Autoregressive Time Series
with a Unit Root." *Journal of the American Statistical
Association*. Vol. 74, 1979, pp. 427–431.

[30] Dickey, D. A., and W. A. Fuller.
"Likelihood Ratio Statistics for Autoregressive Time Series
with a Unit Root." *Econometrica*. Vol.
49, 1981, pp. 1057–1072.

[31] Elder, J., and P. E. Kennedy.
"Testing for Unit Roots: What Should Students Be Taught?" *Journal
of Economic Education*. Vol. 32, 2001, pp. 137–146.

[32] Enders, W. *Applied Econometric
Time Series*. Hoboken, NJ: John Wiley & Sons, Inc.,
1995.

[33] Engle, Robert F. "Autoregressive Conditional
Heteroskedasticity with Estimates of the Variance of United Kingdom
Inflation." *Econometrica*. Vol. 50, 1982,
pp. 987–1007.

[34] Engle, R. F. and C. W. J. Granger. "Co-Integration and Error-Correction: Representation, Estimation, and Testing." Econometrica. v. 55, 1987, pp. 251–276.

[35] Engle, Robert F., D. M. Lilien, and R. P.
Robins. "Estimating Time Varying Risk Premia in the Term Structure:
The ARCH-M Model." *Econometrica*. Vol.
59, 1987, pp. 391–407.

[36] Faust, J. "When Are Variance Ratio
Tests for Serial Dependence Optimal?" *Econometrica*.
Vol. 60, 1992, pp. 1215–1226.

[37] Findley, D. F., B. C. Monsell, W. R. Bell, M. C. Otto,
and B.-C. Chen. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment
Program." *Journal of Business & Economic Statistics*.
Vol. 16, Number 2, 1998, pp. 127–152 .

[38] Gallant, A. R. *Nonlinear Statistical Models*.
Hoboken, NJ: John Wiley & Sons, Inc., 1987.

[39] Glasserman, P. *Monte Carlo
Methods in Financial Engineering*. New York: Springer-Verlag,
2004.

[40] Glosten, L. R., R. Jagannathan, and D. E.
Runkle. "On the Relation between the Expected Value and the
Volatility of the Nominal Excess Return on Stocks." *The
Journal of Finance*. Vol. 48, No. 5, 1993, pp. 1779–1801.

[41] Godfrey, L. G. *Misspecification Tests in Econometrics*.
Cambridge, UK: Cambridge University Press, 1997.

[42] Gourieroux, C. *ARCH Models and
Financial Applications*. New York: Springer-Verlag, 1997.

[43] Granger, C. W. J., and P. Newbold. "Spurious
Regressions in Econometrics." *Journal of Econometrics*.
Vol 2, 1974, pp. 111–120.

[44] Greene, W. H. *Econometric Analysis*.
6th ed. Upper Saddle River, NJ: Prentice Hall, 2008.

[45] Goldfeld, S. M., and Quandt, R. E. "Some Tests for Homoscedasticity". *Journal
of the American Statistical Association*. v. 60, 1965,
pp. 539–547.

[46] Hagerud, G. E. "Modeling Nordic Stock
Returns with Asymmetric GARCH." *Working Paper Series
in Economics and Finance*. No. 164, Stockholm:
Department of Finance, Stockholm School of Economics, 1997.

[47] Hagerud, G. E. "Specification Tests
for Asymmetric GARCH." *Working Paper Series in
Economics and Finance*. No. 163, Stockholm: Department
of Finance, Stockholm School of Economics, 1997.

[48] Hamilton, J. D. *Time Series Analysis*.
Princeton, NJ: Princeton University Press, 1994.

[49] Haug, A. "Testing Linear Restrictions on Cointegrating
Vectors: Sizes and Powers of Wald Tests in Finite Samples." *Econometric
Theory*. v. 18, 2002, pp. 505–524.

[50] Helwege, J., and P. Kleiman. "Understanding
Aggregate Default Rates of High Yield Bonds." Federal Reserve
Bank of New York * Current Issues in Economics and Finance*.
Vol.2, No. 6, 1996, pp. 1-6.

[51] Hentschel, L. "All in the Family:
Nesting Symmetric and Asymmetric GARCH Models." *Journal
of Financial Economics*. Vol. 39, 1995, pp. 71–104.

[52] Hull, J. C. *Options, Futures,
and Other Derivatives*. 5th ed. Englewood Cliffs, NJ: Prentice
Hall, 2002.

[53] Hodrick, Robert J, and Edward C. Prescott.
"Postwar U.S. Business Cycles: An Empirical Investigation." *Journal
of Money, Credit, and Banking*. Vol. 29, No. 1, February
1997, pp. 1–16.

[54] Kutner, M. H., C. J. Nachtsheim, J. Neter,
and W. Li. *Applied Linear Statistical Models*.
5th Ed. New York: McGraw-Hill/Irwin, 2005.

[55] Kwiatkowski, D., P. C. B. Phillips, P. Schmidt
and Y. Shin. "Testing the Null Hypothesis of Stationarity against
the Alternative of a Unit Root." *Journal of Econometrics*.
Vol. 54, 1992, pp. 159–178.

[56] Johansen, S. *Likelihood-Based
Inference in Cointegrated Vector Autoregressive Models*.
Oxford: Oxford University Press, 1995.

[57] Johnson, N. L., S. Kotz, and N. Balakrishnan. *Continuous
Univariate Distributions*. Vol. 2, 2nd ed. New York: John
Wiley & Sons, 1995.

[58] Judge, G. G., W. E. Griffiths, R. C. Hill, H. Lϋtkepohl,
and T. C. Lee. *The Theory and Practice of Econometrics*.
New York, NY: John Wiley & Sons, Inc., 1985.

[59] Juselius, K. *The Cointegrated VAR Model*.
Oxford: Oxford University Press, 2006.

[60] Leybourne, S. J. and B. P. M. McCabe. "A
Consistent Test for a Unit Root." *Journal of Business
and Economic Statistics*. Vol. 12, 1994, pp. 157–166.

[61] Leybourne, S. J. and B. P. M. McCabe.
"Modified Stationarity Tests with Data-Dependent Model-Selection
Rules." *Journal of Business and Economic Statistics*.
Vol. 17, 1999, pp. 264–270.

[62] Ljung, G. and G. E. P. Box. "On a Measure of Lack of
Fit in Time Series Models." *Biometrika*. Vol.
66, 1978, pp. 67–72.

[63] Lo, A. W., and A. C. MacKinlay. "Stock
Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification
Test." *Review of Financial Studies*.
Vol. 1, 1988, pp. 41–66.

[64] Lo, A. W., and A. C. MacKinlay. "The
Size and Power of the Variance Ratio Test." *Journal
of Econometrics*. Vol. 40, 1989, pp. 203–238.

[65] Lo, A. W., and A. C. MacKinlay. *A
Non-Random Walk Down Wall St.* Princeton, NJ: Princeton
University Press, 2001.

[66] Loeffler, G., and P. N. Posch. *Credit
Risk Modeling Using Excel and VBA*. West Sussex, England:
Wiley Finance, 2007.

[67] Long, J. S., and L. H. Ervin. "Using Heteroscedasticity-Consistent
Standard Errors in the Linear Regression Model." *The American
Statistician*. v. 54, 2000, pp. 217-224.

[68] Longstaff, F. A., and E. S. Schwartz.
"Valuing American Options by Simulation: A Simple Least-Squares
Approach." *The Review of Financial Studies*.
Spring 2001, Vol. 14, No. 1, pp. 113–147.

[69] Lütkepohl, H. *New Introduction
to Multiple Time Series Analysis*. Berlin: Springer, 2005.

[70] MacKinnon, J. G. "Numerical Distribution Functions for Unit Root and Cointegration Tests." Journal of Applied Econometrics. v. 11, 1996, pp. 601–618.

[71] MacKinnon, J. G., and H. White. "Some Heteroskedasticity-Consistent
Covariance Matrix Estimators with Improved Finite Sample Properties." *Journal
of Econometrics*. v. 29, 1985, pp. 305-325.

[72] McCullough, B. D., and C. G. Renfro. "Benchmarks
and Software Standards: A Case Study of GARCH Procedures." *Journal
of Economic and Social Measurement*. Vol. 25, 1998, pp.
59–71.

[73] McLeod, A.I. and W.K. Li. "Diagnostic Checking
ARMA Time Series Models Using Squared-Residual Autocorrelations."*Journal
of Time Series Analysis*. Vol. 4, 1983, pp. 269–273.

[74] Morin, N. "Likelihood Ratio Tests on Cointegrating Vectors,
Disequilibrium Adjustment Vectors, and their Orthogonal Complements."* European
Journal of Pure and Applied Mathematics*. v. 3, 2010, pp.
541–571.

[75] Nelson, D. B. "Conditional Heteroskedasticity
in Asset Returns: A New Approach." *Econometrica*.
Vol. 59, 1991, pp. 347–370.

[76] Nelson, C., and C. Plosser. "Trends
and Random Walks in Macroeconomic Time Series: Some Evidence and Implications." *Journal
of Monetary Economics*. Vol. 10, 1982, pp. 130–162.

[77] Newey, W. K., and K. D. West. "A
Simple Positive Semidefinite, Heteroskedasticity and Autocorrelation
Consistent Covariance Matrix." *Econometrica*.
Vol. 55, 1987, pp. 703–708.

[78] Newey, W. K, and K. D. West. "Automatic
Lag Selection in Covariance Matrix Estimation." *The
Review of Economic Studies*. v. 61 No. 4, 1994, pp. 631–653.

[79] Pankratz, A. *Forecasting with Dynamic Regression
Models.* John Wiley & Sons, 1991˙.

[80] Ng, S., and P. Perron. "Unit
Root Tests in ARMA Models with Data-Dependent Methods for the Selection
of the Truncation Lag." *Journal of the American
Statistical Association*. Vol. 90, 1995, pp. 268–281.

[81] Park, R. E. "Estimation with Heteroscedastic Error Terms". *Econometrica*.
34, 1966 p. 888.

[82] Perron, P. "Trends and Random Walks
in Macroeconomic Time Series: Further Evidence from a New Approach." *Journal
of Economic Dynamics and Control*. Vol. 12, 1988, pp. 297–332.

[83] Peters, J. P. "Estimating and Forecasting Volatility of Stock Indices Using Asymmetric GARCH Models and Skewed Student-t Densities." Working Paper. Belgium: École d'Administration des Affaires, University of Liège, March 20, 2001.

[84] Phillips, P. "Time Series Regression
with a Unit Root." *Econometrica*. Vol.
55, 1987, pp. 277–301.

[85] Phillips, P., and P. Perron. "Testing
for a Unit Root in Time Series Regression." *Biometrika*.
Vol. 75, 1988, pp. 335–346.

[86] Schwert, W. "Effects of Model Specification
on Tests for Unit Roots in Macroeconomic Data." *Journal
of Monetary Economics*. Vol. 20, 1987, pp. 73–103.

[87] Schwert, W. "Tests
for Unit Roots: A Monte Carlo Investigation." *Journal
of Business and Economic Statistics*. Vol. 7, 1989, pp.
147–159.

[88] Shreve, S. E. *Stochastic Calculus
for Finance II: Continuous-Time Models*. New York: Springer-Verlag,
2004.

[89] Sims, C., Stock, J., and Watson, M. "Inference
in Linear Time Series Models with Some Unit Roots." *Econometrica*.
Vol. 58, 1990, pp. 113–144.

[90] Tsay,R.S. *Analysis of Financial Time Series*.
Hoboken, NJ: John Wiley & Sons, Inc., 2005.

[91] Turner, P. M. "Testing for Cointegration Using the Johansen
Approach: Are We Using the Correct Critical Values?" *Journal
of Applied Econometrics*. v. 24, 2009, pp. 825–831.

[92] U.S. Federal Reserve Economic Data (FRED), Federal Reserve
Bank of St. Louis, `http://research.stlouisfed.org/fred`.

[93] White, H. "A Heteroskedasticity-Consistent Covariance
Matrix and a Direct Test for Heteroskedasticity." *Econometrica*.
v. 48, 1980, pp. 817-838.

[94] White, H. *Asymptotic Theory for Econometricians*.
New York: Academic Press, 1984.

[95] White, H., and I. Domowitz. "Nonlinear
Regression with Dependent Observations." *Econometrica*.
Vol. 52, 1984, pp. 143–162.

[96] Wold, H. *A Study in the Analysis of Stationary
Time Series*. Uppsala, Sweden: Almqvist & Wiksell,
1938.

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