Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates.

New estimation methods for autoregressive process in the presence of white observation noise

P46 Assessing the effects of treatment in observational studies: Adjusting for disease severity

In this paper, we consider the Europe oil prices, Brent, West Texas Intermediate, WTI, American stock market index based on the market capitalizations of 500 large companies having common stock listed on the NYSE or NASDAQ, S & P 500 , and the real gross domestic product, GDP. Based on the rolling test of Granger causality, the Europe oil prices data does Granger-cause the real gross domestic product data and S & P 500 data. So, the vector autoregressive model can be suggested. The one-step prediction method selects the vector autoregressive model as the optimal model for GDP data and S & P 500 data. The main purpose of this paper is to select the optimal model (and variable) based on Vuong’s model selection test. So, we consider the estimation and model selection of the vector autoregressive time series model with Normal innovation. The maximum likelihood method is proposed for the estimation of unknown parameters. We provide Vuong’s test for order and model selection, i.e. for selecting the order and a suitable subset of regressors, in a vector autoregressive model. Our results show that Vuong’s test confirms the causality test for GDP and S & P 500 data. Also, the results of Vuong’s test confirms the results of the predictive method.

A vector autoregressive (VAR) model is a widely used parametric method that captures linear interdependencies between multivariate time series data. However, conventional VAR models are frequently constrained by some assumptions of linearity and stationarity, limiting their ability to capture complex and nonlinearity dynamic observed in real life data. This research aims to develop Multivariate Random Forest Technique for VAR model. Augmented Dickey Fuller (ADF) was applied to test the stationarity of the time series data. Simulated stationary time series data and real time series dataset were applied for modeling VAR model in order to compare their forecast performance. The forecast performance for the proposed technique and existing technique for VAR models were based on Mean Absolute Error and Root Mean Square Error. The proposed multivariate Random Forest technique for VAR model has been developed. The results for unit root test for real life data indicate that all the variables are stationary at level. The result for simulated data in term of forecast performance indicated that the proposed multivariate Random Forest techniques for VAR model outperform existing technique (conventional VAR model) in long term forecasting, while the conventional VAR model outperform proposed multivariate Random Forest technique in short term forecast based on MAE and RMSE. The results for real dataset indicated that the proposed multivariate Random Forest technique for VAR model is superior in terms of forecast performance than that of conventional VAR model in short-term and long-term forecast based on MAE and RMS since the proposed technique has the least value of MAE and RMSE in short and long-term forecasting than the conventional VAR model.

In this paper, our purpose is to estimate time-varying Rayleigh fading channels in Orthogonal Frequency Division Multiplexing (OFDM) mobile systems. When the fading channel is approximated by an AutoRegressive (AR) process, the direct estimation of the model parameters from the noisy observations available at the receiver may yield biased values. To avoid this drawback, the joint estimation of both the channel and its AR parameters must be addressed. Existing solutions to this dual estimation issue require Kalman filtering. This kind of filtering is optimal in the H2 sense provided that the underlying state-space model is accurate. Moreover, the initial state, the driving process and the measurement noise must be independent, white and Gaussian. However, in real cases, these assumptions may no longer be satisfied. To relax them, we propose to consider a structure based on two cross-coupled H2 filters. This method makes it possible to provide robust estimation of the fading channel and its AR parameters.

Maximum likelihood autoregressive model parameter estimation with noise corrupted independent snapshots

The best accuracy for estimated spectra is obtained with parsimonious time series models, which have the smallest number of parameters to guarantee unbiased models. Durbin 's method for the estimation of moving average (MA) parameters uses the estimated parameters of a long autoregressive (AR) model to calculate MA parameters. Probably all pejorative remarks on the quality of Durbin's method in the literature are based on suboptimal or wrong choices for the method of AR estimation or for the order of the intermediate AR model. That AR order should be considerably higher than the order of the best predicting AR model and it should grow with the sample size. Furthermore, the Burg estimates for the AR parameters give the best results because they have the smallest variance of all AR methods with a small bias. The triangular autocorrelation bias of the popular Yule-Walker method of AR estimation can cause large bias errors in finite samples, which makes it unsuited. Durbin's method applied to the proper number of AR parameters estimated with Burg's method outperforms all other known MA estimation methods, asymptotically as well as in finite samples. The accuracy is generally close to the Cramer-Rao bound.

This paper addresses the critical problem of estimating time-evolving effective brain connectivity. Current approaches based on sliding window analysis or time-varying coefficient models do not simultaneously capture both slow and abrupt changes in causal interactions between different brain regions. To overcome these limitations, we develop a unified framework based on a switching vector autoregressive (SVAR) model. Here, the dynamic connectivity regimes are uniquely characterized by distinct vector autoregressive (VAR) processes and allowed to switch between quasi-stationary brain states. The state evolution and the associated directed dependencies are defined by a Markov process and the SVAR parameters. We develop a three-stage estimation algorithm for the SVAR model: 1) feature extraction using time-varying VAR (TV-VAR) coefficients, 2) preliminary regime identification via clustering of the TV-VAR coefficients, 3) refined regime segmentation by Kalman smoothing and parameter estimation via expectation-maximization algorithm under a state-space formulation, using initial estimates from the previous two stages. The proposed framework is adaptive to state-related changes and gives reliable estimates of effective connectivity. Simulation results show that our method provides accurate regime change-point detection and connectivity estimates. In real applications to brain signals, the approach was able to capture directed connectivity state changes in functional magnetic resonance imaging data linked with changes in stimulus conditions, and in epileptic electroencephalograms, differentiating ictal from nonictal periods. The proposed framework accurately identifies state-dependent changes in brain network and provides estimates of connectivity strength and directionality. The proposed approach is useful in neuroscience studies that investigate the dynamics of underlying brain states.

One of the efforts to suppress the increasing number of COVID-19 cases is the government's provision of a COVID-19 vaccine. This study examines the effect of the number of people who have been vaccinated, the first dose of vaccine, on the addition of new cases and cured cases. The three variables were analysed simultaneously using the help of the Vector Autoregressive (VAR) model. The data is on the number of new, recovered cases and people vaccinated per day from January 13 to December 30, 2021, in West Kalimantan Province. The main steps in this study are order identification, parameter estimation, and interpretation of the results. In this study, the order selection of the VAR model is limited to a maximum of the fourth order. Parameter estimation uses the Ordinary Least Square (OLS) method from several possible orders. Furthermore, the model selection is based on the smallest AIC and BIC values. The result is that the second-order VAR model has the smallest AIC and BIC values, so this model is said to be the best model. The interpretation of the equation obtained is that 74.1% of the factors adding new cases, the number of people being vaccinated, and the addition of cured cases at one and two last times affect the addition of new cases on that day. Meanwhile, the addition of new cases today was only influenced by 42.2% by new cases, the number of people being vaccinated, and the addition of recovered cases in the previous one and two days.

This paper is based on the vector autoregressive (VAR) model, and the model optimization is completed by determining the lag order to eliminate the autocorrelation in the error term through model comparison. The variables in the tax-related risk of the betting agreement are formed into a vector form, the parameters are estimated by least squares or maximum likelihood estimation, and the interrelationship of the variables is analyzed by impulse response function. The vector autoregressive model was used to evaluate the tax-related risk of the betting agreement of Company M, and 12 factors were obtained. Among them, the factors that have more than 80% influence on tax-related risk are the lack of research on the betting agreement and the backwardness of the theoretical aspects of the handling of the betting agreement, with the influence of 87.89% and 84.98%, respectively. Therefore, the vector autoregressive model can effectively assess the tax-related risks in corporate betting agreements and provide a reference for companies diversifying into restructuring and mergers.

This paper is concerned with identification of autoregressive (AR) model parameters using observations corrupted with colored noise. A novel formulation of an auxiliary least-squares estimator is introduced so that the autocovariance functions of the colored observation noise can be estimated in a straightforward manner. With this, the colored-noise-induced estimation bias can be removed to yield the unbiased estimate of the AR parameters. The performance of the proposed unbiased estimation algorithm is illustrated by simulation results. The presented work greatly extends the author's previous methods that were developed for identification of AR signals observed in white noise.

Inverse filtering based method for estimation of noisy autoregressive signals

This paper deals with the joint symbol-channel estimation for quasi-synchronous Multi-carrier Direct-Sequence Code DivisionMultiple Access (MC-DS-CDMA) systems over Rayleigh fading channels. To solve this non-linear problem, Rao- Blackwellized particle filters have proved efficient. In this framework, our contribution is twofold. 1) Instead of using an autoregressive (AR) model which does not match the bandlimitation of the theoretical power spectrum density (PSD) of a Rayleigh channel, we suggest modeling the channel by a low-pass filtered version of the so-called stochastic sinusoidal process. It consists of sinusoids in quadrature with random magnitudes modeled as AR processes. By suitably choosing the AR parameters, this combination has the advantage of providing a stationnary process whose PSD is bandlimited and has two peaks at the maximum Doppler frequency for any AR order. 2) The estimation of the model parameters is included in the joint symbol-channel estimation process. For this purpose, a deterministic Rao-Blackewellized Particle Filter which jointly estimates the symbols and the channels is cross-coupled with a Kalman Filter which yields the AR parameters.

Increasing antibiotic resistance may reciprocally affect consumption and lead to use of broader-spectrum alternatives; a vicious cycle that may gradually limit therapeutic options. Our aim in this study was to demonstrate this vicious cycle in gram-negative bacteria and show the utility of vector autoregressive (VAR) models for time-series analysis in explanatory and dependent roles simultaneously. Monthly drug consumption data in defined daily doses per 100 bed-days and incidence densities of gram-negative bacteria (Escherichia coli, Klebsiella spp., Pseudomonas aeruginosa, and Acinetobacter baumannii) resistant to cephalosporins or to carbapenems were analyzed using VAR models. These were compared to linear transfer models used earlier. In case of all gram-negative bacteria, cephalosporin consumption led to increasing cephalosporin resistance, which provoked carbapenem use and consequent carbapenem resistance and finally increased colistin consumption, exemplifying the vicious cycle. Different species were involved in different ways. For example, cephalosporin-resistant Klebsiella spp. provoked carbapenem use less than E. coli, and the association between carbapenem resistance of P. aeruginosa and colistin use was weaker than that of A. baumannii. Colistin use led to decreased carbapenem use and decreased carbapenem resistance of P. aeruginosa but not of A. baumannii. VAR models allow analysis of consumption and resistance series in a bidirectional manner. The reconstructed resistance spiral involved cephalosporin use augmenting cephalosporin resistance primarily in E. coli. This led to increased carbapenem use, provoking spread of carbapenem-resistant A. baumannii and consequent colistin use. Emergence of panresistance is fueled by such antibiotic-resistance spirals.

In this paper, we have estimated vector autoregression (VAR), Bayesian vector autoregression (BVAR) and vector error-correction models (VECMs) using annual time-series data of South Korea for 1950-94. We find evidence supporting the view that growth of real per-capita income has been aided by income, investment and export growth, as well as government spending and exchange rate policies. The VECMs provide better forecasts of growth than do the VAR and BVAR models for both short-term and long-term predictions.