Bivariate Autoregressive Model Research Articles

Causal linear parametric model for baroreflex gain assessment in patients with recent myocardial infarction.

Spectral and cross-spectral analysis of R-R interval and systolic arterial pressure (SAP) spontaneous fluctuations have been proposed for noninvasive evaluation of baroreflex sensitivity (BRS). However, results are not in good agreement with clinical measurements. In this study, a bivariate parametric autoregressive model with exogenous input (ARXAR model), able to divide the R-R variability into SAP-related and -unrelated parts, was used to quantify the gain (alpha(ARXAR)) of the baroreflex regulatory mechanism. For performance assessing, two traditional noninvasive methods based on frequency domain analysis [spectral, baroreflex gain by autogressive model (alpha(AR)); cross-spectral, baroreflex gain by bivariate autoregressive model (alpha(2AR))] and one based on the time domain [baroreflex gain by sequence analysis (alpha(SEQ))] were considered and compared with the baroreflex gain by phenylephrine test (alpha(PHE)). The BRS evaluation was performed on 30 patients (61 +/- 10 yr) with recent (10 +/- 3 days) myocardial infarction. The ARXAR model allowed dividing the R-R variability (950 +/- 1,099 ms(2)) into SAP-related (256 +/- 418 ms(2)) and SAP-unrelated (694 +/- 728 ms(2)) parts. alpha(AR) (12.2 +/- 6.1 ms/mmHg) and alpha(2AR) (8.9 +/- 5.6 ms/mmHg) as well as alpha(SEQ) (12.6 +/- 7.1 ms/mmHg) overestimated BRS assessed by alpha(PHE) (6.4 +/- 4.7 ms/mmHg), whereas the ARXAR index gave a comparable value (alpha(ARXAR) = 5.4 +/- 3.3 ms/mmHg). All noninvasive methods were significantly correlated to alpha(PHE) (alpha(ARXAR) and alpha(SEQ) were more correlated than the other indexes). Thus the baroreflex gain obtained describing the causal dependence of R-R interval on SAP showed a good agreement with alpha(PHE) and may provide additional information regarding the gain estimation in the frequency domain.

Bivariate autoregressive models for the time series of significant wave height and mean period

This paper generalises the application of univariate models of the long-term time series of significant wave height to the case of the bivariate series of significant wave height and mean period. A brief review of the basic features of multivariate autoregressive models is presented, and then applications are made to the wave time series of Figueira da Foz, in Portugal. It is demonstrated that the simulated series from these models exhibit the correlation between the two parameters a feature that univariate series cannot reproduce. An application to two series of significant wave height from two neighbouring stations shows the applicability of this type of models to other type of correlated data sets.

Spectral properties of EEG fast activity ictal discharges associated with infantile spasms

Objective: The aim of this study was to evaluate the characteristics of the ictal EEG event accompanying infantile spasms.Methods: Quantitative analysis was used, based on the application of a bivariate autoregressive (AR) parametric model; autospectra, coherence, phase functions and inter-hemispheric time differences were estimated on homologous EEG channels in 18 infants presenting with either cryptogenic or symptomatic West syndrome.Results: The AR analysis of the 500 ms EEG epochs preceding spasm onset revealed the presence of a short discharge of fast activity restricted to a narrow frequency band in 13 of the 18 cases included in the study. The fast discharge peaked at 17.5±2.1 Hz, with rather low inter-hemispheric coherence values (0.52±0.17) and asymmetric amplitude on homologous EEG derivations. It persisted briefly after spasm onset, reaching a higher coherence value (0.71±0.16). The inter-hemispheric time difference, estimated in those cases with the coherence values significantly different from zero, ranged from 9.1 to 14.3 ms (11.4±1.9) in the epoch preceding spasm onset.Conclusion: The data obtained from the analysis of the ictal EEG events, compared with clinical and interictal EEG features, indicate that an asymmetric EEG pattern (mainly consisting of a rhythmic burst of fast activity) consistently preceded both symmetric and asymmetric spasms, thus suggesting a localized cortical origin of the ictal discharge giving rise to the spasms.

Bootstrap order selection for autoregressive models

This paper proposes the use of the bootstrap when an order selection criteria is used for stationary autoregressive (AR) models. Monte Carlo simulations are conducted for a number of univariate and bivariate AR models to evaluate small sample performance of bootstrap order selection. It is found that the bootstrap can substantially improve small sample performance of AR order selection. Empirical frequencies of bootstrap orders are in general more concentrated at the true order (or approximate AR order when the true order is non-existent) than those of asymptotic orders.

Evidence on Structural Instability in Macroeconomic Time Series Relations

An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a sample of 76 representative U.S. monthly postwar macroeconomic time series, constituting 5700 bivariate forecasting relations. The tests indicate widespread instability in univariate and bivariate autoregressive models. However, adaptive forecasting models, in particular time varying parameter models, have limited success in exploiting this instability to improve upon fixed-parameter or recursive autoregressive forecasts.

Evidence on Structural Instability in Macroeconomic Time Series Relations

An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a sample of 76 representative U.S. monthly postwar macroeconomic time series, constituting 5700 bivariate forecasting relations. The tests indicate widespread instability in univariate and bivariate autoregressive models. However, adaptive forecasting models, in particular time varying parameter models, have limited success in exploiting this instability to improve upon fixed-parameter or recursive autoregressive forecasts.

Modelling and forecasting seasonal precipitation in Florida: A vector time‐domain approach

AbstractSome major stages of vector autoregressive (AR) modelling consisting of specification, order determination, estimation, diagnostic checking, and forecasting are described. To illustrate the utility of multivariate AR models for climate teleconnection research, the seasonal Southern Oscillation Index (SOI) and a precipitation index in Florida are modelled jointly. Two bivariate AR processes, order one and order four, are selected as candidate models to represent the joint series.To make a comparison of model performance, one‐season‐ahead forecasts of Florida precipitation are generated from the bivariate AR models, as well as from a simple regression model, for recent years that are independent from the period on which the model is constructed. Results show that seasonal forecasts from the two‐dimensional, order‐one model are somewhat better than the other two models. One new and important finding of this study is that, in addition to winter precipitation forecast skill, there is also a forecast skill for autumn precipitation. The physical mechanisms by which these teleconnections might arise are briefly discussed. Other applications of vector models are suggested.

A bivariate autoregressive model for estimation of prevalence of fasciolosis in cattle

AbstractFasciolosis is a serious economic disease of cattle and sheep with a worldwide distribution. In the annual control of the disease, it is vital that the issue of specific veterinary advice on the strategic use of control measures should be based on precise estimates of the levels of risk of the occurrence of the disease. This paper describes the construction of a mathematical model to forecast the level of risk of the disease in cattle in any year. The model has been developed in Northern Ireland using a computerized information database retrieval system for abattoir condemnation data. The information recorded by the system details the specific cause and location of all condemnations in cattle, sheep and pigs for all abattoirs in Northern Ireland. Analysis of a subset of these data (1976 to 1991) for cattle resulted in a univariate time series model for the recorded prevalence of condemnations due to fasciolosis in cattle livers. The overall mathematical forecasting model was constructed by regressing the residual terms of the univariate time series model with the corresponding time series of all the key meteorological variables. The best model (R2 =0·8) was obtained using the mean air temperature for the period fune to August inclusive. The model could be adopted for use in any region of the world where relevant abattoir condemnation and meteorological data are available.

Clinical Factors Associated with Weight Loss Related to Infection with Human Immunodeficiency Virus Type 1 in the Multicenter AIDS Cohort Study

The relation between a number of potential risk factors and change in body mass index per semester was examined in a community-based cohort of 1,809 homosexual and bisexual men seropositive for human immunodeficiency virus type 1 (HIV-1). The men were followed semiannually for up to 6.5 years between 1984 and 1990. A total of 9,735 person-semesters of observations were available for analysis. A Markov-type autoregressive model, adjusting for previous body mass index, was used to predict the change in body mass index over each person-semester. Overall, the cohort was gaining weight. An asymptomatic participant 1.8 m in height whose CD4+ cell count was > 750/microliters gained a mean of 0.5 kg each person-semester. In bivariate autoregressive models, diarrhea, fever, oral thrush, acquired immunodeficiency syndrome (AIDS), and CD4+ lymphocyte counts of < 100 and 100-199 cells/microliters were all associated with a significant decrease in body mass index. A significant inverse association was also found between change in body mass index and lymphadenopathy and herpes zoster, but when the intercept coefficient was added, no overall decrease in body mass index was seen in these models. In a final multivariate model, diarrhea was less strongly associated with a change in body mass index (p = 0.057), although AIDS (p = 0.009), fever (p = 0.006), thrush (p = 0.002), and a CD4+ lymphocyte count of < 100 cells/microliters (p < 0.001) all remained independently associated with a decrease in body mass index. Lymphadenopathy and a CD4+ lymphocyte count of 100-199 cells/microliters were also significant covariates in the final model, but neither of the beta coefficients exceeded that of the intercept, indicating that they were not independently associated with a decrease in body mass index. These findings suggest that the importance of diarrhea as a cause of HIV-related weight loss may have been over-estimated in previous clinic-based studies. AIDS and nonspecific markers of progression (fever, thrush, and a CD4+ count of < 100 cells/microliters) were the best predictors of weight loss during a semester.

A real-time flood forecasting model based on maximum-entropy spectral analysis: II. Application

The MESA-based model, developed in the first paper, for real-time flood forecasting was verified on five watersheds from different regions of the world. The sampling time interval and forecast lead time varied from several minutes to one day. The model was found to be superior to a state-space model for all events where it was difficult to obtain prior information about model parameters. The mathematical form of the model was found to be similar to a bivariate autoregressive (AR) model, and under certain conditions, these two models became equivalent.

A bivariate autoregressive technique for analysis and classification of planar shapes

A bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes. The boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object's shape. This circular sample sequence is then represented by a vector autoregressive difference equation which models the individual Cartesian coordinate sequences as well as coordinate interdependencies. Several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed. These features are shown to be invariant to object transformations such as translation, rotation, and scaling. Laboratory experiments involving object sets representative of industrial shapes are presented. Superior classification results are demonstrated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A bivariate model for total fertility rate and mean age of childbearing

Annual U.S. total fertility rates and mean ages of childbearing, 1921–1980, are fitted to a bivariate autoregressive model which incorporates regression adjustments for the effects of World War II. The result is a transfer function model with total fertility rate as a predictor of mean age of childbearing. While contemporaneous changes in mean age of childbearing tend to be negatively correlated with changes in total fertility rate, there is a tendency for adjusments in mean age to be in the same direction as changes in total fertility in the long run. Point forecasts from the model suggest total fertility will tend to rise but stay below replacement level, and mean age of childbearing will increase very slightly.

Tests of Granger causality by the selection of the orders of a bivariate autoregressive model

The problem of testing Granger causality is considered in bivariate autoregressive systems. Some testing methods based on the statistical criteria for model selection are proposed, and their asymptoticerror probabilities are derived.

Multivariate subset autoregressive modelling with zero constraints for detecting ‘overall causality’

The necessary and sufficient condition to test for ‘overall causality’, i.e., the presence of Granger- causality and instantaneous causal relations, in a bivariate and trivariate autoregressive model with recursive form is discussed. It is argued that the conventional AR model (the reduced form AR) is a more straightforward and effective means of testing for ‘overall causality’. To detect instanta- neous causality it is proposed to select the best subset system in a residual regression system in conjunction with model selection criteria. The Canadian money-income-bank rate system is re-examined in this way and by using a previously proposed algorithm we identify the optimum multivariate subset AR with constraints to detect whether there is ‘overall causality’ in that system.

Threshing loss stochastic variabDity on combine harvesters

The stochastic variability is investigated in the experimental results from an acoustic grain loss monitor and a table auger torque sensor on a combine harvester. A bivariate first-order autoregressive first-order moving-average model is identified and used to specify optimal control systems for adjusting combine forward speed to maintain constant threshing losses. These provide upper bounds on the benefits of practical forward speed control systems.

KONSUM, EINKOMMEN UND RATIONALE ERWARTUNGEN: EMPIRISCHE ERGEBNISSE FÜR DIE SCHWEIZ

SUMMARY The life cycle hypothesis of consumption and rational (in the sense of Muth) expectations implies under certain additional, but not very restrictive, assumptions that real consumption follows an univariate first order autoregressive process. This implication was tested in the framework of bivariate autoregressive models with Swiss quarterly macroeconomic data. A slightly modified variant of the stepwise modelling approach suggested by Hsiao was applied. The hypothesis was rejected with respect to a ‘Neo-Ricardian’ definition of disposable income and real stock prices. By contrast, the test with the conventional definition of disposable income brought not significant results. These findings rise some doubts about the usual specification of macroeconometric consumption functions and their policy implications.

MONETARY AND FISCAL POLICIES AND STOCK PRICES

Investigations into business cycles have found money supply to be a lead variable to stock prices. However, some would argue that the stock market, being efficient, anticipates money supply changes and therefore, stock prices are lead variables to money supply changes. Recent developments in time series methods have facilitated the testing of these relationships through identifying bivariate and multivariate autoregressive models. However, in many cases, the results using different procedures contradict themselves and are in conflict with theoretical reasonings. In this paper the causal relationship is tested between fiscal and monetary policies and stock prices using Canadian data and bivariate andmultivariate autoregressive models.