On the distribution of the residual cross-correlations of infinite order vector autoregressive series and applications

2006 ◽  
Vol 76 (1) ◽  
pp. 58-68 ◽  
Author(s):  
Chafik Bouhaddioui ◽  
Roch Roy
Keyword(s):  
Infinite Order ◽  
Vector Autoregressive ◽  
Cross Correlations ◽  
Autoregressive Series

scholarly journals Adjustment models for multivariate geodetic time series with vector-autoregressive errors

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boris Kargoll ◽  
Alexander Dorndorf ◽  
Mohammad Omidalizarandi ◽  
Jens-André Paffenholz ◽  
Hamza Alkhatib
Keyword(s):  
Least Squares Method ◽  
Functional Model ◽  
Expectation Maximization Algorithm ◽  
Two Dimensions ◽  
Vector Autoregressive ◽  
Wide Range ◽  
Engineering Geodesy ◽  
Cross Correlations ◽  
T Distribution ◽  
Multivariate T

Abstract In this contribution, a vector-autoregressive (VAR) process with multivariate t-distributed random deviations is incorporated into the Gauss-Helmert model (GHM), resulting in an innovative adjustment model. This model is versatile since it allows for a wide range of functional models, unknown forms of auto- and cross-correlations, and outlier patterns. Subsequently, a computationally convenient iteratively reweighted least squares method based on an expectation maximization algorithm is derived in order to estimate the parameters of the functional model, the unknown coefficients of the VAR process, the cofactor matrix, and the degree of freedom of the t-distribution. The proposed method is validated in terms of its estimation bias and convergence behavior by means of a Monte Carlo simulation based on a GHM of a circle in two dimensions. The methodology is applied in two different fields of application within engineering geodesy: In the first scenario, the offset and linear drift of a noisy accelerometer are estimated based on a Gauss-Markov model with VAR and multivariate t-distributed errors, as a special case of the proposed GHM. In the second scenario real laser tracker measurements with outliers are adjusted to estimate the parameters of a sphere employing the proposed GHM with VAR and multivariate t-distributed errors. For both scenarios the estimated parameters of the fitted VAR model and multivariate t-distribution are analyzed for evidence of auto- or cross-correlations and deviation from a normal distribution regarding the measurement noise.

OPTIMAL MULTISTEP VAR FORECAST AVERAGING

2020 ◽  
Vol 36 (6) ◽  
pp. 1099-1126
Author(s):  
Jen-Che Liao ◽  
Wen-Jen Tsay
Keyword(s):  
Infinite Order ◽  
Asymptotic Optimality ◽  
Model Misspecification ◽  
Model Averaging ◽  
Finite Sample ◽  
Forecast Horizon ◽  
Simulation Experiments ◽  
Vector Autoregressive ◽  
One Step ◽  
Mallows Model

This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave-h-out cross-validation averaging (MCVAh) criteria (with h denoting the forecast horizon), which are valid for iterative and direct multistep forecast averaging, respectively. Under the framework of stationary VAR processes of infinite order, we provide theoretical justifications by establishing asymptotic unbiasedness and asymptotic optimality of the proposed forecast averaging approaches. Specifically, MMMA exhibits asymptotic optimality for one-step-ahead forecast averaging, whereas for direct multistep forecast averaging, the asymptotically optimal combination weights are determined separately for each forecast horizon based on the MCVAh procedure. To present our methodology, we investigate the finite-sample behavior of the proposed averaging procedures under model misspecification via simulation experiments.

Infinite-Order Cointegrated Vector Autoregressive Processes

1996 ◽  
Vol 12 (5) ◽  
pp. 814-844 ◽  
Author(s):  
Pentti Saikkonen ◽  
HELMUT Lütkepohl
Keyword(s):  
Sample Size ◽  
Error Correction ◽  
Infinite Order ◽  
Asymptotic Properties ◽  
Error Correction Model ◽  
Autoregressive Processes ◽  
Correction Model ◽  
Vector Autoregressive ◽  
Vector Autoregressive Processes ◽  
Linear Restrictions

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.

Testing for Causation Using Infinite Order Vector Autoregressive Processes

1996 ◽  
Vol 12 (1) ◽  
pp. 61-87 ◽  
Author(s):  
Helmut Lütkepohl ◽  
D.S. POSKITT
Keyword(s):  
Granger Causality ◽  
Finite Order ◽  
Infinite Order ◽  
Empirical Studies ◽  
Asymptotic Properties ◽  
General Assumption ◽  
Small Sample ◽  
Order Process ◽  
Vector Autoregressive ◽  
Vector Autoregressive Processes

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.

Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process

1988 ◽  
Vol 4 (1) ◽  
pp. 77-85 ◽  
Author(s):  
Helmut Lütkepohl
Keyword(s):  
Asymptotic Distribution ◽  
Simple Formula ◽  
Infinite Order ◽  
Moving Average ◽  
Autoregressive Process ◽  
Generation Process ◽  
Data Generation ◽  
Vector Autoregressive ◽  
Variance Matrix ◽  
Vector Autoregressive Process

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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