Testing For Stationarity On Selected Linear And Non-Linear Time Series Models Of Different Orders
DOI:
https://doi.org/10.33003/fjorae.2024.0101.08Keywords:
Stationarity,, Autoregressive Models,, Different Orders,, Linear and Non-Linear ModelsAbstract
In this research, Understanding the assumptions of time series models is crucial. In this study, we aim to analyse and modify Autoregressive models on selected linear and nonlinear time series models to determine their stationarity and non-stationarity at different orders, it would be useful to conduct tests on the null hypothesis of a unit root. The study examines the power and type I error rates of different statistical tests, such as Kwiatkowski, Phillips, Schmidt and Shin (KPSS), Augmented Dickey-Fuller (ADF), and Phillips Perron (PP). These tests are used to determine whether a given dataset is stationary or non-stationary. The study also considers different orders of Autoregressive (AR) and Trigonometric Smooth Transition Autoregressive (TSTAR) models, as well as various sample sizes. A Python software was utilised to conduct an investigation simulating the performance of stationarity and unit root tests. The experiments were carried out using sample sizes; 20, 50, 70, 100, 120, 150, 180, 200, 230 and 250 for various orders of Autoregressive (AR) and Trigonometric Smooth Transition Autoregressive (TSTAR) models. The tests were compared based on their respective power percentages to determine their relative performance. The study determined that Phillips Perron (PP) is the optimal choice across all the conditions examined, including the models, sample sizes, and ordering.
References
Abdel Zaher, M., Elbarbary, S., Sultan, S.A., El-Qady, G., Ismail, A., & Takla, E.M. (2018a). Crustal thermal structure of the Farafra oasis, Egypt, based on airborne potential field data. Geothermics 75, pages 220–234. https://doi.org/10.1016/j.geothermics.2018.05.006
Amelot, L. M. M., SubadarAgathee, U., & Sunecher, Y. (2021). Time series modelling, NARX neural network and hybrid KPCA–SVR approach to forecast the foreign exchange market in Mauritius. African Journal of Economic and Management Studies, 12(1), 18-54.
Barnett, D.F. Hendry, S. Hylleberg, T. Ter¨asvirta, D. Tjøstheim and A.H. W¨urtz (eds.), Nonlinear Econometric Modeling, Cambridge: Cambridge University Press.
Barrientos, A. F., &Canale, A. (2021). A Bayesian goodness-of-fit test for regression. Computational Statistics & Data Analysis, 155, 107104.
Boero, G. and Marrocu, E. (2018). The performance of SETAR models: a regime conditional evaluation of point, interval and density forecasts, Working Paper.
Boero, G. and Marrocu, E. (2022). The performance of non-linear exchange rate models:a forecasting comparison, Journal of Forecasting, Vol. 21(7), 513-542.
Bollerslev, T. (2023). Reprint of: Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time Series Analysis, Forecasting and Control, 2nd ed. New York: Prentice-Hall.
Cheng, C., Guan, Y., Chen, G., &Gan, M. (2020,). Parameters Estimation of RBF-AR Model Based on EM and Variable Projection Algorithm. In 2020 Chinese Control And Decision Conference (CCDC) (pp. 1678-1683). IEEE.
CHIADMI, M. (2020). ISLAMIC STOCK MARKET: Modeling Volatility and Comparative Study. International Journal of Economics and Financial Issues, 1(1-2), 11-
Choi I (2006). Nonstationary Panels." In TC Mills, K Patterson (eds.), Econometric Theory, volume 1 of Palgrave Handbook of Econometrics, chapter 13, pp. 511{539. Palgrave MacMillan, New York
Clements, M. and Smith, J. (2001). Evaluating forecasts from SETAR models of exchange rates, Journal of International Money and Finance, Vol. 20(1),133-148.
Clements, M., and Smith, J. (2018): A Monte Carlo Study of the Forecasting Performance of Empirical SETAR Models. Journal of Applied Econometrics 14: 123–41.
Corbet, S., Hou, Y. G., Hu, Y., & Oxley, L. (2021). An analysis of investor behavior and information flows surrounding the negative WTI oil price futures event. Energy Economics, 104, 105589.
Dickey, D.A. and W.A. Fuller (2009). Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association 74, 427-431.
Dickey,D. and W.fuller (1981).Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root” Econometrica, 49,1057-1072.
Dickey,D. and W.fuller.(1979).Distribution of the Estimations for Autoregressive Time Series with a Unit Root” Journal of the American Statistical Association, 74,427-431.
Diebold, F. X. and J. A. Nason, (1990). Nonparametric exchange rate prediction, Journal of
Ding, S., Shi, X., & Wu, Y. (2020). Beta approximation and its applications. Journal of Statistical Computation and Simulation, 90(7), 1251-1266.
Enders, W.(2009). Applied Econometric Time Series: John Wiley & Sons.
Franses , P.H. and van Dijk, D. (2020). Nonlinear error-correction models for interest rates in the Netherlands.
Fuller,W.(1996).Introduction to Statistical Time Series ,Second Edition .john willey, New York
Gairola, G., &Dey, K. (2022). Price discovery and risk management in asset class: a bibliometric analysis and research agenda. Applied Economics Letters, 1-12.
Granger, C., and Teräsvirta, T. (2018). Modeling Nonlinear Economic Relationships. Oxford University Press, New York.
Hamilton J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, NJ.
Hargreaves, C. P. (2019). Nonstationary time series analysis and cointegration: Oxford
Hargreaves, Colin P. (1994). Nonstationary time series analysis and cointegration: OxfordUniversity Press.
Harvill, J. L. and Ray, B.K (1999). A note on tests for nonlinearity in a vector time series, Biometrika, 86(3), 728–734.
Hipel, K.W. and McLeod, A.I. (1994). Time series Modeling of Water Resources and Environmental Systems. Amsterdam: Elsevier.
Maulana, A., &Slamet, I. (2020,). Prediction of Indonesian financial crisis using Markov regime switching autoregressive conditional heteroscedasticity models based on bank deposits and lending/deposit interest rate indicators. In Journal of Physics: Conference Series (Vol. 1563, No. 1, p. 012017). IOP Publishing.
Mcleod, A.I. and Li, W.K. (2019) Diagnostic checking ARMA time series models using squared-residual autocorrelation. Journal of Time Series Analysis 4, 269-273.
Okorie, D. I., & Lin, B. (2021). Stock markets and the COVID-19 fractal contagion effects. Finance Research Letters, 38, 101640.
Oulhiq, R., Benjelloun, K., Kali, Y., &Saad, M. (2022). A data mining based approach for process identification using historical data. International Journal of Modelling and Simulation, 42(2), 335-349.
Salcedo-Sanz, S., Casillas-Pérez, D., Del Ser, J., Casanova-Mateo, C., Cuadra, L., Piles, M., & Camps-Valls, G. (2022). Persistence in complex systems. Physics Reports, 957, 1-73.
Sankar, T. J., &Pushpa, P. (2022). Implementation of Time Series Stochastic Modeling for Zea mays Production in India. Mathematical Statistician and Engineering Applications, 71(4), 611-621.
Terasvirta, T., (2020). The Performance of Ramsey test and white test of Terasvirta Test in detecting Nonlinearity.
Terasvirta, T., Tstheim, D., & Granger, C. W. (2022). Modelling nonlinear economic time series. University Press.
Wątorek, M., Drożdż, S., Kwapień, J., Minati, L., Oświęcimka, P., &Stanuszek, M. (2021). Multiscale characteristics of the emerging global cryptocurrency market. Physics Reports, 901, 1-82.
Yang, Y., Ling, S., & Wang, Q. (2022). Consistency of global LSE for MA (1) models. Statistics & Probability Letters, 182, 109292.
Zellner A, Palm FC (1974). Time Series Analysis and Simultaneous Equation Econometric Models." Journal of Econometrics, 2(1), 17- 54
Zhang, J. T., Guo, J., & Zhou, B. (2022). Testing equality of several distributions in separable metric spaces: A maximum mean discrepancy-based approach. Journal of Econometrics.
Zhang, J., Li, B., Liu, X., & Wan, X. (2023). Asymptotic behavior of the portmanteau tests in an integer-valued AR model. Journal of Nonparametric Statistics, 1-25.
