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State-dependent Autoregressive Models with p Lags: Properties, Estimation and Forecasting

Fabio Gobbi Sabrina Mulinacci
Central European Journal of Economic Modelling and Econometrics | 2022 | No 1 | 81-108 | DOI: 10.24425/cejeme.2022.140513
Keywords convolution-based autoregressive models level-increment dependence nonlinear time series maximum likelihood forecasting accuracy
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Abstract

In this paper we consider a class of nonlinear autoregressive models in which a specific type of dependence structure between the error term and the lagged values of the state variable is assumed. We show that there exists an equivalent representation given by a p-th order state-dependent autoregressive (SDAR(p)) model where the error term is independent of the last p lagged values of the state variable (y_{t-1},…,y_{t-p}) and the autoregressive coefficients are specific functions of them. We discuss a quasi-maximum likelihood estimator of the model parameters and we prove its consistency and asymptotic normality. To test the forecasting ability of the SDAR(p) model, we propose an empirical application to the quarterly Japan GDP growth rate which is a time series characterized by a level-increment dependence. A comparative analyses is conducted taking into consideration some alternative and competitive models for nonlinear time series such as SETAR and AR-GARCH models.
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Authors and Affiliations

Fabio Gobbi
1
Sabrina Mulinacci
2
  1. Department of Economics and Statistics, University of Siena, Italy
  2. Department of Statistical Sciences, University of Bologna, Italy

Applying autoregressive models in analysis of GRACE-Mascon time-series

Ozge Gunes Cuneyt Aydin
Advances in Geodesy and Geoinformation | 2022 | vol. 71 | No 2 | e25 | DOI: 10.24425/agg.2022.141299
Keywords GRACE Mascon equivalent water thickness temporal correlation colored noise autoregressive models
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Abstract

This study discusses how to model the noise in a Gravity Recovery and Climate Experiment (GRACE)-Mascon derived Equivalent Water Thicknesses (EWT) time-series. GRACE has provided unique information for monitoring variations in EWT of continents in regional or basin scale since 2002. To analyze a GRACE EWT time-series, a standard harmonic regression model is used, but usually assuming white noise-only stochastic model. However, like almost all kinds of geodetic time-series, it has been shown that the GRACE EWT time-series contains temporal correlations causing colored noise in the data. As well known in geodetic modelling studies, neglecting these correlations leads to underestimating the uncertainties, and so misinterpreting the significancy of the parameter estimates such as trend rate, amplitudes of signals etc. In this study, autoregressive noise modeling, which has some advantageous compared to the approaches and methods frequently applied in geodetic studies, is considered for GRACE EWT time series. For this aim, three important basins, namely theYangtze, Murray–Darling and Amazon basins have been examined. Among some applied autoregressive models, the ARMA(1,1) model is obtained as the best-fitting noise model for analyzing the EWT changes in each basin. The obtained results are discussed in terms of forecasting, significancy and consistency with GRACE-FO mission.
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Authors and Affiliations

Ozge Gunes
1
ORCID: ORCID
Cuneyt Aydin
1
ORCID: ORCID
  1. Yildiz Technical University, Istanbul, Turkey

City Backbone Network Traffic Forecasting

Tansaule Serikov Аinur Zhetpisbayeva Ainur Аkhmediyarova Sharafat Mirzakulova Aigerim Kismanova Aray Tolegenova Waldemar Wójcik
International Journal of Electronics and Telecommunications | 2021 | vol. 67 | No 3 | 319-324 | DOI: 10.24425/ijet.2021.135983
Keywords time series packet intensity Dickie Fuller test Kwiatkowski-Phillips Perron-Shin-Schmitt test were forecasting Integrated Moving Average Autoregression Model
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Abstract

The work considers a one-dimensional time series protocol packet intensity, measured on the city backbone network. The intensity of the series is uneven. Scattering diagrams are constructed. The Dickie Fuller test and Kwiatkowski-Phillips Perron-Shin-Schmitt test were applied to determine the initial series to the class of stationary or nonstationary series. Both tests confirmed the involvement of the original series in the class of differential stationary. Based on the Dickie Fuller test and Private autocorrelation function graphs, the Integrated Moving Average Autoregression Model model is created. The results of forecasting network traffic showed the adequacy of the selected model.
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Bibliography

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[9] I Rizkya, K Syahputri, R. M.Sari, I. Siregar and J. Utaminingrum, “Autoregressive Integrated Moving Average (ARIMA) Model of Forecast Demand in Distribution Centre,” Department of Industrial Engineering, Faculty of Engineering, Universitas Sumatera Utara in IOP Conf. Series: Materials Science and Engineering 598, 2019, 012071.
[10] N.Albanbay, B.Medetov, M. A. Zaks, “Statistics of Lifetimes for Transient Bursting States in Coupled Noisy Excitable Systems,” Journal of Computational and Nonlinear Dynamics. vol. 15, no. 12, 2020, https://doi.org/10.1115/1.4047867
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Authors and Affiliations

Tansaule Serikov
1
Аinur Zhetpisbayeva
1
Ainur Аkhmediyarova
2
Sharafat Mirzakulova
3
Aigerim Kismanova
1
Aray Tolegenova
1
Waldemar Wójcik
4
  1. S.Seifullin Kazakh AgroTechnical University, Nur-Sultan, Kazakhstan
  2. Institute of Information and Computational Technologies, Almaty, Kazakhstan
  3. Turan University, Almaty, Kazakhstan
  4. Lublin University of Technology, Poland

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