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A test for strict stationarity in a random coefficient autoregressive model of order 1. (English) Zbl 1473.62075

Summary: We propose a test for the null of strict stationarity in a Random Coefficient AutoRegression (RCAR) of order 1. The test can also be used in the case of a standard AR(1) model, and it can be applied under minimal requirements on the existence of moments – in both cases without requiring any modifications or prior knowledge.

MSC:

62F05 Asymptotic properties of parametric tests
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Software:

FinTS; plfit
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Full Text: DOI

References:

[1] Akharif, A.; Hallin, M., Efficient detection of random coefficients in autoregressive models, Ann. Statist., 31, 2, 675-704 (2003) · Zbl 1039.62081
[2] Anděl, J., Autoregressive series with random parameters, Math. Oper.forsch. Stat., 7, 5, 735-741 (1976) · Zbl 0346.62066
[3] Aue, A.; Horváth, L., Quasi-likelihood estimation in stationary and nonstationary autoregressive models with random coefficients, Statist. Sinica, 973-999 (2011) · Zbl 1232.62116
[4] Aue, A.; Horváth, L.; Steinebach, J., Estimation in random coefficient autoregressive models, J. Time Series Anal., 27, 1, 61-76 (2006) · Zbl 1112.62084
[5] Banerjee, A. N.; Chevillon, G.; Kratz, M., Detecting and forecasting large deviations and bubbles in a near-explosive random coefficient model (2013)
[6] Berkes, I.; Horváth, L.; Ling, S., Estimation in nonstationary random coefficient autoregressive models, J. Time Series Anal., 30, 4, 395-416 (2009) · Zbl 1224.62046
[7] Clauset, A.; Shalizi, C. R.; Newman, M. E., Power-law distributions in empirical data, SIAM Rev., 51, 4, 661-703 (2009) · Zbl 1176.62001
[8] Distaso, W., Testing for unit root processes in random coefficient autoregressive models, J. Econometrics, 142, 1, 581-609 (2008) · Zbl 1418.62314
[9] Fryz, M., Conditional linear random process and random coefficient autoregressive model for EEG analysis, (2017 IEEE First Ukraine Conference on Electrical and Computer Engineering (UKRCON) (2017), IEEE), 305-309
[10] Giraitis, L.; Kapetanios, G.; Yates, T., Inference on stochastic time-varying coefficient models, J. Econometrics, 179, 1, 46-65 (2014) · Zbl 1293.62184
[11] Granger, C. W.; Swanson, N. R., An introduction to stochastic unit-root processes, J. Econometrics, 80, 1, 35-62 (1997) · Zbl 0885.62100
[12] Hill, J.; Li, D.; Peng, L., Uniform interval estimation for an AR(1) process with AR errors, Statist. Sinica, 26, 1, 119-136 (2016) · Zbl 1419.62232
[13] Hill, J.; Peng, L., Unified interval estimation for random coefficient autoregressive models, J. Time Series Anal., 35, 3, 282-297 (2014) · Zbl 1302.62187
[14] Horváth, L.; Trapani, L., Statistical inference in a random coefficient panel model, J. Econometrics, 193, 1, 54-75 (2016) · Zbl 1420.62386
[15] Horváth, L.; Trapani, L., Testing for randomness in a random coefficient autoregression, J. Econometrics, 209, 338-352 (2019) · Zbl 1452.62648
[16] Kapetanios, G.; Shin, Y.; Snell, A., Testing for a unit root in the nonlinear STAR framework, J. Econometrics, 112, 2, 359-379 (2003) · Zbl 1027.62065
[17] Koul, H. L.; Schick, A., Adaptive estimation in a random coefficient autoregressive model, Ann. Statist., 24, 3, 1025-1052 (1996) · Zbl 0906.62087
[18] Leybourne, S. J.; McCabe, B. P.; Tremayne, A. R., Can economic time series be differenced to stationarity?, J. Bus. Econom. Statist., 14, 4, 435-446 (1996)
[19] McCabe, B. P.; Tremayne, A. R., Testing a time series for difference stationarity, Ann. Statist., 1015-1028 (1995) · Zbl 0838.62082
[20] Nagakura, D., Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process, Statist. Probab. Lett., 79, 24, 2476-2483 (2009) · Zbl 1176.62087
[21] Nicholls, D. F.; Quinn, B. G., Random Coefficient Autoregressive Models: An Introduction: An Introduction, Vol. 11 (2012), Springer Science & Business Media
[22] Phillips, P. C.B., Time series regression with a unit root and infinite-variance errors, Econometric Theory, 6, 01, 44-62 (1990)
[23] Regis, M.; Serra, P.; Heuvel, E. R., Random autoregressive models: A structured overview, Econometric Rev. (2021), forthcoming
[24] Ślęzak, J.; Burnecki, K.; Metzler, R., Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems, New J. Phys., 21, 7, Article 073056 pp. (2019)
[25] Stenseth, N. C.; Falck, W.; Chan, K.-S.; Bjørnstad, O. N.; O?Donoghue, M.; Tong, H.; Boonstra, R.; Boutin, S.; Krebs, C. J.; Yoccoz, N. G., From patterns to processes: phase and density dependencies in the Canadian lynx cycle, Proc. Natl. Acad. Sci., 95, 26, 15430-15435 (1998)
[26] Trapani, L., Testing for strict stationarity in a random coefficient autoregressive model, Econometric Rev., 40, 3, 220-256 (2021) · Zbl 1480.62182
[27] Tsay, R. S., Conditional heteroscedastic time series models, J. Amer. Statist. Assoc., 82, 398, 590-604 (1987) · Zbl 0636.62092
[28] Tsay, R. S., Unit Root Tests with Threshold Innovations (1997), University of Chicago
[29] Tsay, R. S., Analysis of Financial Time Series, Vol. 543 (2005), John wiley & sons
[30] Zhao, Z.-W.; Wang, D.-H., Statistical inference for generalized random coefficient autoregressive model, Math. Comput. Modelling, 56, 7, 152-166 (2012) · Zbl 1255.62289
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