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Journal articles on the topic 'Vector autoregressive process'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Tovstik, T. M. "Vector autoregression process. Stationarity and simulation." Journal of Physics: Conference Series 2099, no. 1 (November 1, 2021): 012068. http://dx.doi.org/10.1088/1742-6596/2099/1/012068.

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Abstract For vector discrete-parameter random autoregressive processes and for a mixed autoregression/moving-average model, we obtain conditions which should be satisfied by the correlation functions or the model coefficients in order that the process be weakly stationary. Fairly simple tests are used. Algorithms for modeling such vector stationary processes are given. Examples are presented clarifying testing criteria for stationarity of models defned in terms of the coefficients or the correlation functions of the process.

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2

Cheng, Tsung-Chi, Ping-Hung Hsieh, and Su-Fen Yang. "Process Control for the Vector Autoregressive Model." Quality and Reliability Engineering International 30, no. 1 (December 17, 2012): 57–81. http://dx.doi.org/10.1002/qre.1477.

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3

Grynkiv, Galyna, and Lars Stentoft. "Stationary Threshold Vector Autoregressive Models." Journal of Risk and Financial Management 11, no. 3 (August 5, 2018): 45. http://dx.doi.org/10.3390/jrfm11030045.

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This paper examines the steady state properties of the Threshold Vector Autoregressive model. Assuming that the trigger variable is exogenous and the regime process follows a Bernoulli distribution, necessary and sufficient conditions for the existence of stationary distribution are derived. A situation related to so-called “locally explosive models”, where the stationary distribution exists though the model is explosive in one regime, is analysed. Simulations show that locally explosive models can generate some of the key properties of financial and economic data. They also show that assessing the stationarity of threshold models based on simulations might well lead to wrong conclusions.

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4

Brockwell, Peter J., Richard A. Davis, and A. Alexandre Trindade. "Asymptotic properties of some subset vector autoregressive process estimators." Journal of Multivariate Analysis 90, no. 2 (August 2004): 327–47. http://dx.doi.org/10.1016/j.jmva.2003.10.001.

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5

Bodnar, T., and T. Zabolotskyy. "Estimation and inference of the vector autoregressive process under heteroscedasticity." Theory of Probability and Mathematical Statistics 83 (2011): 27–45. http://dx.doi.org/10.1090/s0094-9000-2012-00839-9.

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6

Gourieroux, Christian, and Joann Jasiak. "Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation." Journal of Econometrics 200, no. 1 (September 2017): 118–34. http://dx.doi.org/10.1016/j.jeconom.2017.01.011.

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7

Dufour, Jean-Marie. "Unbiasedness of Predictions from Etimated Vector Autoregressions." Econometric Theory 1, no. 3 (December 1985): 387–402. http://dx.doi.org/10.1017/s0266466600011270.

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Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds: specifically, if a vector autoregression of arbitrary finite order is fitted to a sample from any process in this class, the fitted model will produce unbiased forecasts, in the sense that the prediction errors have distributions symmetric about zero. Different numbers of lags may be used for each variable in each autoregression and variables may even be missing, without unbiasedness being affected. This property is exact in finite samples. Similarly, the residuals from the same autoregressions have distributions symmetric about zero.

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8

la Cour, Lisbeth. "A PARAMETRIC CHARACTERIZATION OF INTEGRATED VECTOR AUTOREGRESSIVE (VAR) PROCESSES." Econometric Theory 14, no. 2 (April 1998): 187–99. http://dx.doi.org/10.1017/s0266466698142020.

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This paper provides a polynomial factorization theorem that is then used to extend the characterization parts of the parametric representation theorems of Johansen (1992, Econometric Theory 8, 188–202) for vector autoregressive processes integrated of up to order 2. A characterization theorem is provided in the general case of an I(d) process. For the discussion of the complicated polynomial cointegration properties of such processes, the case of an I(3) process is considered as an example.

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9

Gallego, Jose L. "The exact likelihood function of a vector autoregressive moving average process." Statistics & Probability Letters 79, no. 6 (March 2009): 711–14. http://dx.doi.org/10.1016/j.spl.2008.10.030.

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10

Yang, Minxian. "SOME PROPERTIES OF VECTOR AUTOREGRESSIVE PROCESSES WITH MARKOV-SWITCHING COEFFICIENTS." Econometric Theory 16, no. 1 (February 2000): 23–43. http://dx.doi.org/10.1017/s026646660016102x.

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Some statistical properties of a vector autoregressive process with Markov-switching coefficients are considered. Sufficient conditions for this nonlinear process to be covariance stationary are given. The second moments of the process are derived under the conditions. The autocovariance matrix decays at exponential rate, permitting the application of the law of large numbers. Under the stationarity conditions, although sharing the “mean-reverting” property with conventional linear stationary processes, the process offers richer short-run dynamics such as conditional heteroskedasticity, asymmetric responses, and occasional nonstationary behavior.

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11

Lütkepohl, Helmut. "COMPARISON OF CRITERIA FOR ESTIMATING THE ORDER OF A VECTOR AUTOREGRESSIVE PROCESS." Journal of Time Series Analysis 6, no. 1 (January 1985): 35–52. http://dx.doi.org/10.1111/j.1467-9892.1985.tb00396.x.

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12

Komasi, Mehdi, and Soroush Sharghi. "Hybrid wavelet-support vector machine approach for modelling rainfall–runoff process." Water Science and Technology 73, no. 8 (January 25, 2016): 1937–53. http://dx.doi.org/10.2166/wst.2016.048.

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Because of the importance of water resources management, the need for accurate modeling of the rainfall–runoff process has rapidly grown in the past decades. Recently, the support vector machine (SVM) approach has been used by hydrologists for rainfall–runoff modeling and the other fields of hydrology. Similar to the other artificial intelligence models, such as artificial neural network (ANN) and adaptive neural fuzzy inference system, the SVM model is based on the autoregressive properties. In this paper, the wavelet analysis was linked to the SVM model concept for modeling the rainfall–runoff process of Aghchai and Eel River watersheds. In this way, the main time series of two variables, rainfall and runoff, were decomposed to multiple frequent time series by wavelet theory; then, these time series were imposed as input data on the SVM model in order to predict the runoff discharge one day ahead. The obtained results show that the wavelet SVM model can predict both short- and long-term runoff discharges by considering the seasonality effects. Also, the proposed hybrid model is relatively more appropriate than classical autoregressive ones such as ANN and SVM because it uses the multi-scale time series of rainfall and runoff data in the modeling process.

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13

Lütkepohl, Helmut, and D. S. POSKITT. "Testing for Causation Using Infinite Order Vector Autoregressive Processes." Econometric Theory 12, no. 1 (March 1996): 61–87. http://dx.doi.org/10.1017/s0266466600006447.

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Tests for Granger-causality have been performed in numerous empirical studies. These tests are usually based on finite order vector autoregressive (VAR) processes, and the assumption is made that the model fitted to the available data corresponds to the true data generating mechanism. In the present study, the more general assumption is made that a finite order VAR model is fitted to a potentially infinite order process. The order is assumed to increase with the sample size. Asymptotic properties of tests for Granger-causality as well as other types of causality concepts are derived. Some limited small sample results are obtained using simulation methods.

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Gutiérrez-Gutiérrez, Jesús, Marta Zárraga-Rodríguez, Pedro Crespo, and Xabier Insausti. "Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes." Entropy 20, no. 9 (September 19, 2018): 719. http://dx.doi.org/10.3390/e20090719.

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In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.

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15

Johansen, SØren. "A REPRESENTATION THEORY FOR A CLASS OF VECTOR AUTOREGRESSIVE MODELS FOR FRACTIONAL PROCESSES." Econometric Theory 24, no. 3 (January 22, 2008): 651–76. http://dx.doi.org/10.1017/s0266466608080274.

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Based on an idea of Granger (1986, Oxford Bulletin of Economics and Statistics 48, 213–228), we analyze a new vector autoregressive model defined from the fractional lag operator 1 − (1 − L)d. We first derive conditions in terms of the coefficients for the model to generate processes that are fractional of order zero. We then show that if there is a unit root, the model generates a fractional process Xt of order d, d > 0, for which there are vectors β so that β‼Xt is fractional of order d − b, 0 < b ≤ d. We find a representation of the solution that demonstrates the fractional properties. Finally we suggest a model that allows for a polynomial fractional vector, that is, the process Xt is fractional of order d, β‼Xt is fractional of order d − b, and a linear combination of β‼Xt and ΔbXt is fractional of order d − 2b. The representations and conditions are analogous to the well-known conditions for I(0), I(1), and I(2) variables.

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16

Jakšić, Saša. "Modelling CESEE Countries Export Dynamics: Global Vector Autoregressive Approach." Zagreb International Review of Economics and Business 25, no. 2 (November 1, 2022): 39–63. http://dx.doi.org/10.2478/zireb-2022-0014.

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Abstract One of the main aspects of the transition process in Central, Eastern and Southeastern European (CESEE) countries was the trade liberalisation. As their financial systems are still underdeveloped and the trade channel is the dominant shock transmitter, this paper focuses on export dynamics for a selected set of CESEE countries. The employed methodology, Global Vector Autoregressive (GVAR) approach, allows modelling interactions and spillovers among countries. Furthermore, it enables joint modelling of exports and imports. This is of particular importance as the opening of new markets enabled astonishing export growth, but also opened the CESEE markets to foreign products. The empirical analysis reveals that a shock in German imports has a larger impact on CESEE countries’ exports than a shock in German output. Moreover, the results indicate that the role of the real exchange rate is less pronounced in comparison to previous similar research.

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17

Atmaja, Dinul Darma, Widowati Widowati, and Budi Warsito. "FORECASTING STOCK PRICES ON THE LQ45 INDEX USING THE VARIMAX METHOD." MEDIA STATISTIKA 14, no. 1 (March 8, 2021): 98–107. http://dx.doi.org/10.14710/medstat.14.1.98-107.

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Forecasting using the Autoregressive Integrated Moving Average (ARIMA) method is not appropriate to predict more than one stock price because this method is only able to model one dependent variable. Therefore, to expect more than one stock prices, the ARIMA method expansion can be used, namely the Vector Autoregressive Integrated Moving Average (VARIMA) method. Furthermore, this research will discuss forecasting stock prices on the LQ45 index using the Vector Autoregressive Integrated Moving Average with Exogenous Variable (VARIMAX) method. Then, after the initial model formation process, the best model is the VARIMAX (0,1,2) model. Finally, the results of this study using the VARIMAX (0,1,2) model obtained the predictive value of the prices and the error values of stocks on the LQ45 index.

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18

Nielsen, Bent. "ANALYSIS OF COEXPLOSIVE PROCESSES." Econometric Theory 26, no. 3 (October 7, 2009): 882–915. http://dx.doi.org/10.1017/s0266466609990144.

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A vector autoregressive model allowing for unit roots as well as an explosive characteristic root is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Cointegrating and coexplosive vectors can be found that eliminate these common factors. The likelihood ratio test for a simple hypothesis on the coexplosive vectors is analyzed. The method is illustrated using data from the extreme Yugoslavian hyperinflation of the 1990s.

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19

Iwok, Iberedem A. "Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts." International Journal of Statistics and Probability 6, no. 2 (February 13, 2017): 1. http://dx.doi.org/10.5539/ijsp.v6n2p1.

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In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a process is equivalent to obtaining the properties of an infinite process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

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20

Mercy, Chepngetich. "Application of Vector Autoregressive (VAR) Process in Modelling Reshaped Seasonal Univariate Time Series." Science Journal of Applied Mathematics and Statistics 3, no. 3 (2015): 124. http://dx.doi.org/10.11648/j.sjams.20150303.15.

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21

Lütkepohl, Helmut. "Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process." Econometric Theory 4, no. 1 (April 1988): 77–85. http://dx.doi.org/10.1017/s0266466600011865.

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The coefficients of the moving average (MA) representation of a vector autoregressive (VAR) process are the dynamic multipliers of the system. These quantities are often used to analyze the relationships between the variables involved. Assuming that the actual data generation process is stationary and has a VAR representation of unknown and possibly infinite order, the asymptotic distribution of the MA coefficients is derived. A computationally simple formula for the asymptotic co variance matrix is obtained.

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22

Anderson, T. W. "A Note on a Vector-Variate Normal Distribution and a Stationary Autoregressive Process." Journal of Multivariate Analysis 72, no. 1 (January 2000): 149–50. http://dx.doi.org/10.1006/jmva.1999.1837.

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23

McAleer, Michael, Felix Chan, Suhejla Hoti, and Offer Lieberman. "GENERALIZED AUTOREGRESSIVE CONDITIONAL CORRELATION." Econometric Theory 24, no. 6 (July 9, 2008): 1554–83. http://dx.doi.org/10.1017/s0266466608080614.

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This paper develops a generalized autoregressive conditional correlation (GARCC) model when the standardized residuals follow a random coefficient vector autoregressive process. As a multivariate generalization of the Tsay (1987, Journal of the American Statistical Association 82, 590–604) random coefficient autoregressive (RCA) model, the GARCC model provides a motivation for the conditional correlations to be time varying. GARCC is also more general than the Engle (2002, Journal of Business & Economic Statistics 20, 339–350) dynamic conditional correlation (DCC) and the Tse and Tsui (2002, Journal of Business & Economic Statistics 20, 351–362) varying conditional correlation (VCC) models and does not impose unduly restrictive conditions on the parameters of the DCC model. The structural properties of the GARCC model, specifically, the analytical forms of the regularity conditions, are derived, and the asymptotic theory is established. The Baba, Engle, Kraft, and Kroner (BEKK) model of Engle and Kroner (1995, Econometric Theory 11, 122–150) is demonstrated to be a special case of a multivariate RCA process. A likelihood ratio test is proposed for several special cases of GARCC. The empirical usefulness of GARCC and the practicality of the likelihood ratio test are demonstrated for the daily returns of the Standard and Poor's 500, Nikkei, and Hang Seng indexes.

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Li, Yuanyuan, and Dietmar Bauer. "Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size." Econometrics 8, no. 3 (September 17, 2020): 38. http://dx.doi.org/10.3390/econometrics8030038.

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In this paper the theory on the estimation of vector autoregressive (VAR) models for I(2) processes is extended to the case of long VAR approximation of more general processes. Hereby the order of the autoregression is allowed to tend to infinity at a certain rate depending on the sample size. We deal with unrestricted OLS estimators (in the model formulated in levels as well as in vector error correction form) as well as with two stage estimation (2SI2) in the vector error correction model (VECM) formulation. Our main results are analogous to the I(1) case: We show that the long VAR approximation leads to consistent estimates of the long and short run dynamics. Furthermore, tests on the autoregressive coefficients follow standard asymptotics. The pseudo likelihood ratio tests on the cointegrating ranks (using the Gaussian likelihood) used in the 2SI2 algorithm show under the null hypothesis the same distributions as in the case of data generating processes following finite order VARs. The same holds true for the asymptotic distribution of the long run dynamics both in the unrestricted VECM estimation and the reduced rank regression in the 2SI2 algorithm. Building on these results we show that if the data is generated by an invertible VARMA process, the VAR approximation can be used in order to derive a consistent initial estimator for subsequent pseudo likelihood optimization in the VARMA model.

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Al-Dhaifallah, Mujahed, Kottakkaran Nisar, Praveen Agarwal, and Alaa Elsayyad. "Modeling and identification of heat exchanger process using least squares support vector machines." Thermal Science 21, no. 6 Part B (2017): 2859–69. http://dx.doi.org/10.2298/tsci151026204a.

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In this paper, Hammerstein model and non-linear autoregressive with eXogeneous inputs (NARX) model are used to represent tubular heat exchanger. Both models have been identified using least squares support vector machines based algorithms. Both algorithms were able to model the heat exchanger system with-out requiring any a priori assumptions regarding its structure. The results indicate that the blackbox NARX model outperforms the NARX Hammerstein model in terms of accuracy and precision.

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Li, Xiaozhong, and Feng Huang. "Empirical Study on the Relationship between Agricultural Economic Structure Growth and Environmental Pollution Based on Time-Varying Parameter Vector Autoregressive Model." Journal of Environmental and Public Health 2022 (August 10, 2022): 1–11. http://dx.doi.org/10.1155/2022/5684178.

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In order to better demonstrate the relationship between agricultural economic structure growth and environmental pollution, an autoregressive model based on time-varying parameter vector was proposed. In the process of developing the research, this paper introduces the LDMI method, based on the time-varying parameter vector autoregression model, with the help of sampling formula calculation and other methods. Efforts were made to obtain credible conclusions. The experiment result shows that in this study, a total of 10,000 samples were taken. According to this value, 10000/116.15 = 86, which means that at least 86 unrelated samples can be obtained. Therefore, we can determine that each indicator mentioned in this paper has valid samples when it is introduced into the time-varying parameter vector autoregression (TVP-VAR) model for parameter estimation. After sampling detection image analysis and data calculation, the effect of energy structure, energy intensity industrial structure, and scale effect on the emission scale of environmental pollutants was obtained. It is proved that through the research of this paper, two main conclusions are finally obtained, and the influence of the five factors mentioned above is summarized.

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27

Hsiao, Cheng. "IDENTIFICATION AND DICHOTOMIZATION OF LONG- AND SHORT-RUN RELATIONS OF COINTEGRATED VECTOR AUTOREGRESSIVE MODELS." Econometric Theory 17, no. 5 (September 25, 2001): 889–912. http://dx.doi.org/10.1017/s026646660117502x.

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We show that the usual rank condition is necessary and sufficient to identify a vector autoregressive process whether the variables are I(0) or I(d) for d = 1,2,.... We then use this rank condition to demonstrate the interdependence between the identification of short-run and long-run relations of cointegrated process. We find that both the short-run and long-run relations can be identified without the existence of prior information to identify either relation. But if there exists a set of prior restrictions to identify the short-run relation, then this same set of restrictions is sufficient to identify the corresponding long-run relation. On the other hand, it is in general not possible to identify the long-run relations without information on the complete structure. The relationship between the identification of a vector autoregressive process and a Cowles Commission dynamic simultaneous equations model is also clarified.

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Zarepour, M., and S. M. Roknossadati. "MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS." Econometric Theory 24, no. 3 (January 22, 2008): 677–95. http://dx.doi.org/10.1017/s0266466608080286.

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We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases.

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Saikkonen, Pentti, and Helmut Lutkepohl. "Trend Adjustment Prior to Testing for the Cointegrating Rank of a Vector Autoregressive Process." Journal of Time Series Analysis 21, no. 4 (July 2000): 435–56. http://dx.doi.org/10.1111/1467-9892.00192.

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Koivisto, Matti, Janne Seppänen, Ilkka Mellin, Jussi Ekström, John Millar, Ivan Mammarella, Mika Komppula, and Matti Lehtonen. "Wind speed modeling using a vector autoregressive process with a time-dependent intercept term." International Journal of Electrical Power & Energy Systems 77 (May 2016): 91–99. http://dx.doi.org/10.1016/j.ijepes.2015.11.027.

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31

Yasin, Hasbi, Budi Warsito, Rukun Santoso, and Suparti. "Soft Computation Vector Autoregressive Neural Network (VAR-NN) GUI-Based." E3S Web of Conferences 73 (2018): 13008. http://dx.doi.org/10.1051/e3sconf/20187313008.

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Vector autoregressive model proposed for multivariate time series data. Neural Network, including Feed Forward Neural Network (FFNN), is the powerful tool for the nonlinear model. In autoregressive model, the input layer is the past values of the same series up to certain lag and the output layers is the current value. So, VAR-NN is proposed to predict the multivariate time series data using nonlinear approach. The optimal lag time in VAR are used as aid of selecting the input in VAR-NN. In this study we develop the soft computation tools of VAR-NN based on Graphical User Interface. In each number of neurons in hidden layer, the looping process is performed several times in order to get the best result. The best one is chosen by the least of Mean Absolute Percentage Error (MAPE) criteria. In this study, the model is applied in the two series of stock price data from Indonesia Stock Exchange. Evaluation of VAR-NN performance was based on train-validation and test-validation sample approach. Based on the empirical stock price data it can be concluded that VAR-NN yields perfect performance both in in-sample and in out-sample for non-linear function approximation. This is indicated by the MAPE value that is less than 1% .

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Vu, Viet-Hung, Zhaoheng Liu, Marc Thomas, and Bruce Hazel. "Modal analysis of a light-weight robot with a rotating tool installed at the end effector." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 9 (December 2, 2015): 1664–76. http://dx.doi.org/10.1177/0954406215619451.

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This paper investigates vibration of a moving flexible robot through modal analysis and by constructing vibration spectra of operational signals. A vector autoregressive model combined with a sliding window technique is used for signal processing in order to take into account system nonstationarity. Modal decomposition is conducted on the state matrix constructed from the appropriate vector autoregressive model parameters. A complete modal decomposition and spectrum construction algorithm able of highlighting the structural modes and harmonic excitations is presented. Through accurate identification from the vector autoregressive model, the method presented is able to discriminate, display and monitor the harmonics and structural modes during the processes investigated. This method is validated first by numerical simulation and then experimentally with a flexible robot performing three processes: moving a manipulator through the workspace, steady rotation of a grinder on the end effector and moving the manipulator combined with rotating the grinder. It is found on the operating robot that participation of the first structural mode is negligible when rotating the grinder but must be taken into account when moving the manipulator. The analysis presented and results obtained provide a sound basis for further investigation of vibroimpact behaviour in a robotic grinding process.

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Jakšić, Saša. "Modelling Determinants of Inflation in CESEE Countries: Global Vector Autoregressive Approach." Review of Economic Perspectives 22, no. 1 (June 1, 2022): 137–69. http://dx.doi.org/10.2478/revecp-2022-0007.

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Abstract After a prolonged period of relatively stable price levels, the beginning of the third decade of the 21st century has brought inflation once again into the spotlight. This paper focuses on the inflation dynamics in a set of post-communist countries that eventually became members of the European Union. Due to EU accession augmented by the globalization process and involvement in global value chains (GVC), the international impacts are becoming progressively important for the domestic inflation dynamics and domestic variables are not sufficient to fully describe the domestic inflation dynamics. The employed methodology, Global Vector Autoregressive (GVAR) approach, allows modelling interactions and spillovers among countries, making the most of its advantages over the usual VAR models that model each economy separately and panel models, where countries are often treated as independent units. The results of the empirical analysis confirm that the globalisation process has led to increasing the importance of international impacts on the domestic inflation dynamics. On the other hand, the results also indicate that accounting for a larger set of countries decreases the severity of the commodity price shocks and makes them less persistent. Furthermore, monetary policy acts as a buffer against adverse shocks, especially in the countries that are still not members of the euro-zone. The findings of the paper show that the analysed countries are pronouncedly heterogeneous. Hence, each of the analysed economies has its own set of country-specific factors which, from country to country, play a more important or a less significant role in explaining national inflation dynamics. Thus, the paper should contribute to a more comprehensive understanding of the inflation dynamics in the policy-making context.

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Yamaguchi, Nobuhiko. "Visualizing States of Time-Series Data by Autoregressive Gaussian Process Dynamical Models." Journal of Advanced Computational Intelligence and Intelligent Informatics 21, no. 5 (September 20, 2017): 825–31. http://dx.doi.org/10.20965/jaciii.2017.p0825.

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Gaussian process dynamical models (GPDMs) are used for nonlinear dimensionality reduction in time series by means of Gaussian process priors. An extension of GPDMs is proposed for visualizing the states of time series. The conventional GPDM approach associates a state with an observation value. Therefore, observations changing over time cannot be represented by a single state. Consequently, the resulting visualization of state transition is difficult to understand, as states change when the observation values change. To overcome this issue, autoregressive GPDMs, called ARGPDMs, are proposed. They associate a state with a vector autoregressive (VAR) model. Therefore, observations changing over time can be represented by a single state. The resulting visualization is easier to understand, as states change only when the VAR model changes. We demonstrate experimentally that the ARGPDM approach provides better visualization compared with conventional GPDMs.

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Boczoń, Marta, and Jean-François Richard. "Balanced Growth Approach to Tracking Recessions." Econometrics 8, no. 2 (April 23, 2020): 14. http://dx.doi.org/10.3390/econometrics8020014.

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In this paper, we propose a hybrid version of Dynamic Stochastic General Equilibrium models with an emphasis on parameter invariance and tracking performance at times of rapid changes (recessions). We interpret hypothetical balanced growth ratios as moving targets for economic agents that rely upon an Error Correction Mechanism to adjust to changes in target ratios driven by an underlying state Vector AutoRegressive process. Our proposal is illustrated by an application to a pilot Real Business Cycle model for the US economy from 1948 to 2019. An extensive recursive validation exercise over the last 35 years, covering 3 recessions, is used to highlight its parameters invariance, tracking and 1- to 3-step ahead forecasting performance, outperforming those of an unconstrained benchmark Vector AutoRegressive model.

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Larsson, Rolf. "APPROXIMATION OF THE ASYMPTOTIC DISTRIBUTION OF THE LOG LIKELIHOOD RATIO TEST FOR COINTEGRATION." Econometric Theory 15, no. 6 (December 1999): 789–813. http://dx.doi.org/10.1017/s0266466699156019.

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Tail approximation of the asymptotic distribution of the log likelihood ratio test for cointegration in a vector autoregressive process is studied. In dimension 2, an approximation of weighted χ2 type is derived by applying multivariate saddlepoint approximation techniques to a Fourier inversion integral.

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Moon, Todd K., and Jacob H. Gunther. "Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates." Entropy 22, no. 5 (May 19, 2020): 572. http://dx.doi.org/10.3390/e22050572.

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Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.

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38

Gutiérrez-Gutiérrez, Jesús, Xabier Insausti, and Marta Zárraga-Rodríguez. "Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing." Mathematics 8, no. 4 (April 14, 2020): 582. http://dx.doi.org/10.3390/math8040582.

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In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

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Demetrescu, Matei, Helmut Lütkepohl, and Pentti Saikkonen. "Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term." Econometrics Journal 12, no. 3 (November 1, 2009): 414–35. http://dx.doi.org/10.1111/j.1368-423x.2009.00297.x.

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Shea, B. L. "A NOTE ON THE GENERATION OF INDEPENDENT REALIZATIONS OF A VECTOR AUTOREGRESSIVE MOVING-AVERAGE PROCESS." Journal of Time Series Analysis 9, no. 4 (July 1988): 403–10. http://dx.doi.org/10.1111/j.1467-9892.1988.tb00479.x.

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41

Choi, ByoungSeon. "On the covariance matrix estimators of the white noise process of a vector autoregressive model." Communications in Statistics - Theory and Methods 23, no. 1 (January 1994): 249–56. http://dx.doi.org/10.1080/03610929408831251.

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Wu, Hongmin, Yisheng Guan, and Juan Rojas. "Analysis of multimodal Bayesian nonparametric autoregressive hidden Markov models for process monitoring in robotic contact tasks." International Journal of Advanced Robotic Systems 16, no. 2 (March 1, 2019): 172988141983484. http://dx.doi.org/10.1177/1729881419834840.

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Robot introspection aids robots to understand what they do and how they do it. Previous robot introspection techniques have often used parametric hidden Markov models or supervised learning techniques, implying that the number of hidden states or classes is defined a priori and fixed through the entire modeling process. Fixed parameterizations limit the modeling power of a process to properly encode the data. Furthermore, first-order Markov models are limited in their ability to model complex data sequences that represent highly dynamic behaviors as they assume observations are conditionally independent given the state. In this work, we contribute a Bayesian nonparametric autoregressive Hidden Markov model for the monitoring of robot contact tasks, which are characterized by complex dynamical data that are hard to model. We used a nonparametric prior that endows our hidden Markov models with an unbounded number of hidden states for a given robot skill (or subtask). We use a hierarchical Dirichlet stochastic process prior to learn an hidden Markov model with a switching vector autoregressive observation model of wrench signatures and end-effector pose for the manipulation contact tasks. The proposed scheme monitors both nominal skill execution and anomalous behaviors. Two contact tasks are used to measure the effectiveness of our approach: (i) a traditional pick-and-place task composed of four skills and (ii) a cantilever snap assembly task (also composed of four skills). The modeling performance or our approach was compared with other methods, and classification accuracy measures were computed for skill and anomaly identification. The hierarchical Dirichlet stochastic process prior to learn an hidden Markov model with a switching vector autoregressive observation model was shown to have excellent process monitoring performance with higher identification rates and monitoring ability.

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Saikkonen, Pentti, and Helmut Lütkepohl. "TESTING FOR THE COINTEGRATING RANK OF A VAR PROCESS WITH AN INTERCEPT." Econometric Theory 16, no. 3 (June 2000): 373–406. http://dx.doi.org/10.1017/s0266466600163042.

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Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics, 52, 169–210) and others we also consider an alternative class of tests that is based on estimating the trend parameters of the deterministic term in a different way. The asymptotic local power of these tests is derived and compared to that of the corresponding LR tests. The small sample properties are investigated by simulations. The new tests are seen to be substantially more powerful than conventional LR tests.

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Hsiao, Cheng, and Siyan Wang. "Modified two-stage least-squares estimators for the estimation of a structural vector autoregressive integrated process." Journal of Econometrics 135, no. 1-2 (November 2006): 427–63. http://dx.doi.org/10.1016/j.jeconom.2005.07.019.

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Norrulashikin, Siti Mariam. "An Investigation Towards The Suitability Of Vector Autoregressive Approach On Modeling Meteorological Data." Modern Applied Science 9, no. 11 (September 30, 2015): 89. http://dx.doi.org/10.5539/mas.v9n11p89.

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In most meteorological problems, two or more variables evolve over time. These variables not only haverelationships with each other, but also depend on each other. Although in many situations the interest was onmodelling single variable as a vector time series without considering the impact other variables have on it. Thevector autoregression (VAR) approach to multiple time series analysis are potentially useful in many types ofsituations which involve the building of models for discrete multivariate time series. This approach has 4important stages of the process that are data pre-processing, model identification, parameter estimation, andmodel adequacy checking. In this research, VAR modeling strategy was applied in modeling three variables ofmeteorological variables, which include temperature, wind speed and rainfall data. All data are monthly data,taken from the Kuala Krai station from January 1985 to December 2009. Two models were suggested byinformation criterion procedures, however VAR (3) model is the most suitable model for the data sets based onthe model adequacy checking and accuracy testing.

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Gao, Ang. "Transmission Machine of International Financial Crisis Based on VAR Model." Frontiers in Business, Economics and Management 5, no. 1 (August 26, 2022): 48–52. http://dx.doi.org/10.54097/fbem.v5i1.1429.

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The financial crisis has always been accompanied by human economic activities, and its outbreak has a serious impact on people's normal life, and it has no warning, which is a problem of great concern to all countries in the current economic development. Based on the monthly data of long-term bond yields of eight countries (six European countries, the United States and Japan) from December 2009 to February 2012, through correlation test and Granger causality analysis, the results show that there is no Granger causality between the bond yields of various countries and the bond yields of Greece before the European debt crisis, but Granger causality exists between the bond yields of Germany, France and Italy and Greece after the crisis. Finally, it puts forward the process of China's complete opening of capital account and the problems that should be paid attention to after that. The latest development direction of vector autoregressive model is the identification of exogenous policy shocks and the estimation of panel vector autoregressive model. This paper studies and analyzes the transmission mechanism of international financial crisis. Vector autoregressive model is used to describe the transmission mechanism of international financial crisis. The enhancement of the ability to resist the contagion of financial crisis is an important factor to promote the sound development of China's economy. Starting with the related concepts of the transmission mechanism of international financial crisis, this paper probes into the specific transmission modes of international financial crisis and the suppression measures of the transmission mechanism of international financial crisis.

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Mei, Bin, Michael Clutter, and Thomas Harris. "Modeling and forecasting pine sawtimber stumpage prices in the US South by various time series models." Canadian Journal of Forest Research 40, no. 8 (August 2010): 1506–16. http://dx.doi.org/10.1139/x10-087.

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Among the three timberland return drivers (biological growth, timber price, and land price), timber price remains the most unpredictable. It affects not only periodic dividends from timber sales but also timber production strategies embedded in timberland management. Using various time series techniques, this study aimed to model and forecast real pine sawtimber stumpage prices in 12 southern timber regions in the United States. Under the discrete-time framework, the univariate autoregressive integrated moving average model was established as a benchmark, whereas other multivariate time series methods were applied in comparison. Under the continuous-time framework, both the geometric Brownian motion and the Ornstein–Uhlenbeck process were fitted. The results revealed that (i) the vector autoregressive model forecasted more accurately in the 1-year period by the mean absolute percentage error criterion, (ii) seven out of the 12 southern timber regions played dominant roles in the long-run equilibrium, and (iii) conditional variances and covariances from the bivariate generalized autoregressive conditional heteroscedasticity model well captured market risks.

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48

Mckenzie, Ed. "Some ARMA models for dependent sequences of poisson counts." Advances in Applied Probability 20, no. 4 (December 1988): 822–35. http://dx.doi.org/10.2307/1427362.

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A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

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Mckenzie, Ed. "Some ARMA models for dependent sequences of poisson counts." Advances in Applied Probability 20, no. 04 (December 1988): 822–35. http://dx.doi.org/10.1017/s0001867800018395.

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A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

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Ramajo, Julián, Miguel A. Márquez, and Geoffrey J. D. Hewings. "Spatiotemporal Analysis of Regional Systems." International Regional Science Review 40, no. 1 (July 27, 2016): 75–96. http://dx.doi.org/10.1177/0160017615571586.

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This article contributes to the recent literature in spatial econometrics that focuses on space–time data modeling implementing a multilocation time-series statistical framework to analyze a regional system. Drawing on the global vector autoregression approach introduced in Pesaran, Schuermann, and Weiner, a multiregional spatial vector autoregressive (MultiREG-SpVAR) model is formulated and then applied to study the spatiotemporal transmission of macroeconomic shocks across the regions in Spain. The empirical application analyzes the extent to which a region’s economic output growth is influenced by the growth of its neighbors ( push-in or inward growth effect), and also investigates the relevance of spillovers derived from temporary region specific output growth shocks ( push-out or outward growth effect). Our results identify some regions that perform as “growth generators” within the Spanish regional system since growth shocks from these regions spillover to a large number of regions of the country, playing a key role in the transmission of regional business cycles. The policy implications of our results suggest that national and/or regional governments should stimulate economic activity in these leading regions in order to enhance the economic recovery process of the whole Spanish economy.

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