Unit root test combination via random forests. (English) Zbl 07910575
Valenzuela, Olga (ed.) et al., Theory and applications of time series analysis and forecasting. Selected contributions from the 7th international conference on time series and forecasting, ITISE 2021, Gran Canaria, Spain, July 19–21, 2021. Cham: Springer. Contrib. Stat., 31-46 (2023).
Summary: There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.
For the entire collection see [Zbl 1515.62014].
For the entire collection see [Zbl 1515.62014].
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
| 62P20 | Applications of statistics to economics |
| 91-06 | Proceedings, conferences, collections, etc. pertaining to game theory, economics, and finance |
| 91B84 | Economic time series analysis |
Keywords:
ARIMA time series; conditional inference trees; Monte Carlo simulation; sequential testing; supervised machine learningReferences:
| [1] | Ayat, L., Burridge, P.: Unit root tests in the presence of uncertainty about the non-stochastic trend. J. Econometrics 95, 71-96 (2000) · Zbl 1125.62330 |
| [2] | Beaulieu, J.J., Miron, J.A.: Seasonal unit roots in aggregate U.S. data. J. Econometrics 55, 305-328 (1993) · Zbl 0756.62041 |
| [3] | Biau, G., Devroye, L., Lugosi, G.: Consistency of random forests and other averaging classifiers. J. Mach. Learn. Res. 9, 2015-2033 (2008) · Zbl 1225.62081 |
| [4] | Breiman, L.: Random forests. Mach. Learn. 45, 5-32 (2001) · Zbl 1007.68152 |
| [5] | Cario, M.C., Nelson, B.L.: Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois, 1-19 (1997) |
| [6] | Clements, M.P., Hendry, D.F.: Forecasting with difference-stationary and trend-stationary models. Economet. J. 4, S1-S19 (2001) · Zbl 1004.62074 |
| [7] | Cochrane, J.H.: A critique of the application of unit root tests. J. Econ. Dyn. Control 15, 275-284 (1991) · Zbl 0722.62060 |
| [8] | DeJong, D.N., Nankervis, J.C., Savin, N.E., Whiteman, C.H.: Integration versus trend stationarity in time series. Econometrica 60, 423-433 (1992) · Zbl 0744.62151 |
| [9] | DeJong, D.N., Nankervis, J.C., Savin, N.E., Whiteman, C.H.: The power problems in time series with autoregressive errors. J. Econometrics 53, 323-343 (1992) |
| [10] | Dickey, D.A., Fuller, W.A.: Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74, 427-431 (1979) · Zbl 0413.62075 |
| [11] | Dickey, D.A., Fuller, W.A.: Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057-1072 (1981) · Zbl 0471.62090 |
| [12] | Dickey, D.A., Hasza, D.P., Fuller, W.A.: Testing for unit roots in seasonal time series. J. Am. Stat. Assoc. 79, 355-367 (1984) · Zbl 0559.62074 |
| [13] | Diebold, F.X., Rudebusch, G.D.: On the Dickey-Fuller tests against fractional alternatives. Econ. Lett. 35, 155-160 (1991) |
| [14] | Elliott, G., Müller, U.K.: Minimizing the impact of the initial condition on testing for unit roots. J. Econometrics 135, 285-310 (2006) · Zbl 1418.62318 |
| [15] | Elliott, G., Rothenberg, T.J., Stock, J.H.: Efficient tests for an autoregressive unit root. Econometrica 64, 813-836 (1996) · Zbl 0888.62088 |
| [16] | Ernst, P.A., Shepp, L.A., Wyner, A.J.: Yule’s “nonsense correlation” solved!. Ann. Stat. 45, 1789-1809 (2017) · Zbl 1412.60117 |
| [17] | Franses, P.H.: Seasonality, non-stationarity and the forecasting of monthly time series. Int. J. Forecasting 7, 199-208 (1991) |
| [18] | Fuller, W.A.: Introduction to Statistical Time Series. Wiley, New York (1976) · Zbl 0353.62050 |
| [19] | Gómez, V., Maravall, A.: Automatic Modeling Methods for Univariate Series. In: Peña, D., Tiao, G.C., Tsay, R.S. (eds.) A Course in Time Series Analysis, pp. 171-201. Wiley, New York (2001) |
| [20] | Granger, C.W.J., Newbold, P.: Spurious regressions in econometrics. J. Econometrics 2, 111-120 (1974) · Zbl 0319.62072 |
| [21] | Hansen, B.E., Racine, J.S.: Bootstrap model averaging unit root inference. McMaster University, Department of Economics Working Paper No. 2018-09 (2018) |
| [22] | Harvey, D.I., Leybourne, S.J., Taylor, A.M.R.: Unit root testing in practice: dealing with uncertainty over the trend and initial condition. Economet. Theor. 25, 587-636 (2009) · Zbl 1253.62060 |
| [23] | Hassler, U., Hosseinkouchack, M.: Understanding nonsense correlation between (independent) random walks in finite samples. Stat. Pap. 63, 181-195 (2022) · Zbl 1490.60107 |
| [24] | Hothorn, T., Hornik, K., Zeileis, A.: Unbiased recursive partitioning: a conditional inference framework. J. Comput. Graph. Stat. 15, 651-674 (2006) |
| [25] | Hylleberg, S., Engle, R.F., Granger, C.W.J., Yoo, B.S.: Seasonal integration and cointegration. J. Econometrics 44, 215-238 (1990) · Zbl 0709.62102 |
| [26] | Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root. J. Econometrics 54, 159-178 (1992) · Zbl 0871.62100 |
| [27] | Makridakis, S., Spiliotis, E., Assimakopoulos, V.: The M4 Competition: Results, findings, conclusion and way forward. Int. J. Forecasting 34, 802-808 (2018) |
| [28] | Makridakis, S., Spiliotis, E., Assimakopoulos, V.: The M4 Competition: 100,000 time series and 61 forecasting methods. Int. J. Forecasting 36, 54-74 (2020) |
| [29] | Müller, U.K., Elliott, G.: Tests for unit roots and the initial condition. Econometrica 71, 1269-1286 (2003) · Zbl 1152.62371 |
| [30] | Ng, S., Perron, P.: Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519-1554 (2001) · Zbl 1056.62529 |
| [31] | Ollech, D., Webel, K.: A random forest-based approach to combining and ranking seasonality tests. J. Economet. Method. forthcoming (2022) |
| [32] | Osborn, D.R., Chui, A.P.L., Smith, J.P., Birchenhall, C.R.: Seasonality and the order of intergration for consumption. Oxford B. Econ. Stat. 50, 361-377 (1988) |
| [33] | Palm, F.C., Smeekes, S., Urbain, J.-P.: Bootstrap unit-root tests: comparison and extensions. J. Time Ser. Anal. 29, 371-401 (2008) · Zbl 1164.62051 |
| [34] | Park, J.Y.: Bootstrap unit root tests. Econometrica 71, 1845-1895 (2003) · Zbl 1154.62366 |
| [35] | Perron, P.: Trends and random walks in macroeconomic time series - Further evidence from a new approach. J. Econ. Dyn. Control 12, 297-332 (1988) · Zbl 0659.62128 |
| [36] | Phillips, P.C.B.: Understanding spurious regressions in econometrics. J. Econometrics 33, 311-340 (1986) · Zbl 0602.62098 |
| [37] | Phillips, P.C.B.: Time series regression with a unit root. Econometrica 55, 277-301 (1987) · Zbl 0613.62109 |
| [38] | Phillips, P.C.B., Perron, P.: Testing for a unit root in time series regression. Biometrika 75, 335-346 (1988) · Zbl 0644.62094 |
| [39] | Psaradakis, Z.: Bootstrap tests for an autoregressive unit root in the presence of weakly dependent errors. J. Time Ser. Anal. 22, 577-594 (2001) · Zbl 0979.62068 |
| [40] | Rodrigues, P.M.M., Osborn, D.R.: Performance of seasonal unit root tests for monthly data. J. Appl. Stat. 26, 985-1004 (1999) · Zbl 0940.62080 |
| [41] | Said, S.E., Dickey, D.A.: Testing for unit roots in autoregressive moving average models of unknown order. Biometrika 71, 599-607 (1984) · Zbl 0564.62075 |
| [42] | Schwert, G.W.: Tests for unit roots: a Monte Carlo investigation. J. Bus. Econ. Stat. 7, 147-159 (1989) |
| [43] | Strobl, C., Boulesteix, A.-L., Kneib, T., Augustin, T., Zeileis, A.: Conditional variable importance for random forests. BMC Bioinformatics 9, Article 307 (2008) |
| [44] | Stone, C.J., Hansen, M.H., Kooperberg, C., Truong, Y.K.: Polynomial splines and their tensor products in extended linear modeling: 1994 Wald memorial lecture. Ann. Stat. 25, 1371-1470 (1997) · Zbl 0924.62036 |
| [45] | Swensen, A.R.: Bootstrapping unit root tests for integrated processes. J. Time Ser. Anal. 24, 99-126 (2003) · Zbl 1023.62090 |
| [46] | Webel, K., Ollech, D.: An overall seasonality test based on recursive feature elimination in conditional random forests. Proc. Int. Conf. Time Ser. Forecasting, 20-31 (2018) |
| [47] | West, K.D.: A note on the power of least squares tests for a unit root. Econ. Lett. 24, 249-252 (1987) · Zbl 1328.62547 |
| [48] | Wolters, J., Hassler, U.: Unit root testing. Allg. Stat. Arch. 90, 43-58 (2006) · Zbl 1103.62086 |
| [49] | Yule, G.U.: Why do we sometimes get nonsense correlations between time series? A study in sampling and the nature of time series. J. R. Stat. Soc. 89, 1-63 (1926) · JFM 52.0532.04 |
| [50] | Zivot, E., Andrews, D.W.K.: Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. J. Bus. Econ. Stat. 10, 251-270 (1992) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
