Hernández, Juan R.
(2016):
*Unit Root Testing in ARMA Models: A Likelihood Ratio Approach.*

Preview |
PDF
MPRA_paper_100857.pdf Download (862kB) | Preview |

## Abstract

Abstract: In this paper I propose a Likelihood Ratio test for a unit root (LR) with a local-to-unity Autoregressive parameter embedded in ARMA(1,1) models. By dealing explicitly with dependence in a time series through the Moving Average, as opposed to the long Autorregresive lag approximation, the test shows gains in power and has good small-sample properties. The asymptotic distribution of the test is shown to be independent of the short-run parameters. The Monte Carlo experiments show that the LR test has higher power than the Augmented Dickey Fuller test for several sample sizes and true values of the Moving Average parameter. The exception is the case when this parameter is very close to -1 with a considerably small sample size.

Item Type: | MPRA Paper |
---|---|

Original Title: | Unit Root Testing in ARMA Models: A Likelihood Ratio Approach |

Language: | English |

Keywords: | Likelihood ratio test; ARMA model; Unit root test. |

Subjects: | C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes |

Item ID: | 100857 |

Depositing User: | Juan R. Hernandez |

Date Deposited: | 05 Jun 2020 10:25 |

Last Modified: | 05 Jun 2020 10:25 |

References: | ANG, A. AND M. PIAZZESI (2003): “A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables,” Journal of Monetary Economics, 50, 745 – 787. BERGSTROM, A. R. (1984): “Continuous time stochastic models and issues of aggregation over time,” Elsevier, vol. 2 of Handbook of Econometrics, 1145 – 1212. CHAMBERS, M. J. (2009): “Discrete Time Representations of Cointegrated Continuous Time Models with Mixed Sample Data,” Econometric Theory, 25, pp. 1030–1049. CHAMBERS, M. J. AND J. R. HERNANDEZ (2015): “Likelihood-Based Tests for a Unit Root in a Near-Integrated ARMA Model,” Mimeo. CHAMBERS, M. J. AND J. R. MCCRORIE (2007): “Frequency domain estimation of temporally aggregated Gaussian cointegrated systems,” Journal of Econometrics, 136, 1 – 29. DAVIDSON, J. (1994): Stochastic Limit Theory: An Introduction for Econometricians, Oxford University Press. DAVIDSON, J. (2000): Econometric Theory, Blackwell Publishing. DICKEY, D. A. AND W. A. FULLER (1979): “Distribution of the Estimators for Autoregressive Time Series With a Unit Root,” Journal of the American Statistical Association,74, pp. 427–431. ELLIOTT, G., T. J. ROTHENBERG, AND J. H. STOCK (1996): “Efficient Tests for an Autoregressive Unit Root,” Econometrica, 64, pp. 813–836. HALDRUP, N. AND M. JANSSON (2007): “Improving Size and Power in Unit Root Testing,” in Handbook of Econometrics, ed. by T. C. Mills and K. Patterson, Palgrave Macmillan, vol. 1 of Handbook of Econometrics, 865 – 934. HANNAN, E. J. (1973): “The Asymptotic Theory of Linear Time-Series Models,” Journal of Applied Probability, 10, pp. 130–145. JANSSON, M. AND M. O. NIELSEN (2012): “Nearly efficient likelihood ratio tests of the unit root hypothesis,” Econometrica, 80, 2321–2332. JOHANSEN, S. (1988): “Statistical analysis of cointegration vectors,” Journal of Economic Dynamics and Control, 12, 231 – 254. JOHANSEN, S. (1995): Likelihood Based Inference in Cointegrated Vector Autoregresive Models, Advanced Texts in Econometrics, Oxford University Press. KIM, D. H. (2009): “Challenges in macro-finance modeling,” Federal Reserve Bank of St. Louis Review, 519–544. LARSSON, R. (1998): “Bartlett Corrections for Unit Root Test Statistics,” Journal of Time Series Analysis, 19, 425–438. NG, S. AND P. PERRON (2001): “Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power,” Econometrica, 69, pp. 1519–1554. PHILLIPS, P. C. B. (1987a): “Time Series Regression with a Unit Root,” Econometrica, 55, pp. 277–301. PHILLIPS, P. C. B. (1987b): “Towards a Unified Asymptotic Theory for Autoregression,” Biometrika, 74, pp. 535–547. PHILLIPS, P. C. B. (1991): “Optimal Inference in cointegrated Systems,” Econometrica, 59, pp. 283– 306. PHILLIPS, P. C. B. AND P. PERRON (1988): “Testing for a Unit Root in Time Series Regression,” Biometrika, 75, pp. 335–346. ROSSANA, R. J. AND J. J. SEATER (1995): “Temporal Aggregation and Economic Time Series,” Journal of Business & Economic Statistics, 13, pp. 441–451. ROTHENBERG, T. J. AND J. H. STOCK (1997): “Inference in a nearly integrated autoregressive model with nonnormal innovations,” Journal of Econometrics, 80, 269 – 286. SAID, S. E. AND D. A. DICKEY (1984): “Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order,” Biometrika, 71, pp. 599–607. SAID, S. E. AND D. A. DICKEY (1985): “Hypothesis Testing in ARIMA(p, 1, q) Models,” Journal of the American Statistical Association, 80, pp. 369–374. SAIKKONEN, P. (1995): “Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems,” Econometric Theory, 11, pp. 888– 911. SAIKKONEN, P. (2001): “Statistical Inference in cointegrated Vector Autoregressive Models with Nonlinear Time Trends in Cointegrating Relations,” Econometric Theory, 17, pp. 327–356. SAIKKONEN, P. AND H. LUTKEPOHL (1999): “Local Power of Likelihood Ratio Tests for the Cointegrating Rank of a VAR Process,” Econometric Theory, 15, pp. 50–78. STOCK, J. H. (1994): “Unit roots, structural breaks and trends,” in Handbook of Econometrics, ed. by R. F. Engle and D. L. McFadden, Elsevier, vol. 4, 2739 – 2841. WHITE, H. (2001): Asymptotic Theory for Econometricians. Revised Edition, Emerald. YAO, Q. AND P. J. BROCKWELL (2006): “Gaussian Maximum Likelihood Estimation for ARMA Models. I. Time Series,” Journal of Time Series Analysis, 857–875. ZYGMUND, A. (1959): Trigonometric Series, no. v. 1 in Cambridge Mathematical Library, Cambridge University Press. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/100857 |