Time-varying ARMA Model Research Articles

The Predictive Power of Monetary Policy on International Stock Market Returns—Evidence From TV-ARMAX Model

In this paper, we apply the time-varying ARMA model with exogenous variable (TV-ARMAX) to examine the predictive power of monetary policy on international stock returns. This method allows time-varying coefficient estimates and uses time-dependent cumulated variation penalty to filter noisy outlier data points. Based on a wide range of 31 countries, our method robustly outperforms other popular methods including the simple linear-regression model (SLM), the vector autoregression and its variants (VAR, TV-VAR, and VARX) and the ARMA model with exogenous variable (ARMAX).

基于时变ARMA模型的MEMS陀螺随机误差补偿技术

基于时变ARMA模型的MEMS陀螺随机误差补偿技术

A multivariate time-frequency approach for tracking QT variability changes unrelated to heart rate variability.

The beat-to-beat variability of the QT interval (QTV) is a marker of ventricular repolarization (VR) dynamics and it has been suggested as an index of sympathetic ventricular outflow and cardiac instability. However, QTV is also affected by RR (or heart rate) variability (RRV), and QTV due to RRV may reduce QTV specificity as a VR marker. Therefore, it would be desirable to separate QTV due to VR dynamics from QTV due to RRV. To do that, previous work has mainly focused on heart rate corrections or time-invariant autoregressive models. This paper describes a novel framework that extends classical multiple inputs/single output theory to the time-frequency (TF) domain to quantify QTV and RRV interactions. Quadratic TF distributions and TF coherence function are utilized to separate QTV into two partial (conditioned) spectra representing QTV related and unrelated to RRV, and to provide an estimates of intrinsic VR dynamics. In a simulation study, a time-varying ARMA model was used to generate signals representing realistic RRV and VR dynamics with controlled instantaneous frequencies and powers. The results demonstrated that the proposed methodology is able to accurately track changes in VR dynamics, with a correlation between theoretical and estimated patterns higher than 0.88. Data from healthy volunteers undergoing a tilt table test were analyzed and representative examples are discussed. Results show that the QTV unrelated to RRV dynamics quickly increased during orthostatic challenge.

Synthesis of HRV signals characterized by predetermined time-frequency structure by means of time-varying ARMA models

AbstractIn this paper we present two methodologies to generate heart rate variability (HRV) signals characterized by controlled and real-like time-frequency (TF) structure to be used to assess different methods of non-stationary HRV analysis. The synthesized signals are stochastic processes whose TF structure is predetermined by choosing either the time-course of the instantaneous frequencies and powers or the shape of the TF model function. They consist of three steps: (a) choice of the desired TF structure of the signals by choosing a set of design parameters; (b) automatic identification of the parameters of the corresponding models via simple closed-form expressions; (c) synthesis of the desired stochastic signals. Two measures to evaluate the goodness of the simulated signals are also given. Using this framework we were able to model the wide range of non-stationarities observed in heart rate modulation during exercise stress testing and experiments of music-induced emotions. We used the proposed methodology to assess the capability of the smoothed pseudo Wigner–Ville distribution (SPWVD) to quantify HRV patterns. We observed that the SPWVD followed the temporal evolution of the spectral components even when sudden and sharp transitions occur.

Parameter Estimation and Application of Time-varying FARIMA Model

The prediction model of network traffic has been a hot research spot. In this paper, a time-varying FARIMA model is proposed based on the traditional FARIMA model, in which the parameter d is changed into time-varying parameter d(t) and the time-varying parameters are estimated combined with time-varying ARMA model. The new model overcomes the fractal information loss caused by the global average and improves the accuracy of parameter estimation. Finally, the model's application in the anomaly detection of network traffic is analyzed.

Gear fault diagnosis via non-stationary adaptive MARTIN distance

In this paper, a new method of gear fault diagnosis is proposed based on a combination of the time synchronized averaging method (TSA), time-varying ARMA model and MARTIN distance. This method contains three major steps. In the first step, a TSA method is proposed for averaging the gearbox signal. The second step deals with selection of a proper ARMA model for a signal produced via a gearbox and using an adaptive filter (with a weighted least square algorithm) for identifying the time-varying parameters of the model. In the last step, a new time-varying distance is defined for gear fault diagnosis. The proposed distance is an extension of the MARTIN distance. Finally, as the case study, the method is used on a YAMAHA gearbox for identifying gear faults. The results of the diagnosis are satisfactory.

Instantaneous spectrum estimation of earthquake ground motions based on unscented Kalman filter method

Representing earthquake ground motion as time varying ARMA model, the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model. In this paper, unscented Kalman filter is applied to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter, and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.

Estimation of time-varying ARMA models with Markovian changes in regime

In this paper, we consider the estimation of time-varying ARMA models subject to Markovian changes in regime. We give explicit conditions ensuring consistency and asymptotic normality, as well as the limiting covariance matrix, of least squares and quasi-generalized least-squares estimators.

Estimation de modèles ARMA à changements de régime récurrents

This Note considers estimation of time-varying ARMA models. We focus on models with recurrent but non-periodic changes in regime. Conditions ensuring the consistency and the asymptotic normality of two sequences of least squares estimators are given. These conditions are made explicit when the regime generated process is a Markov chain. To cite this article: C. Francq, A. Gautier, C. R. Acad. Sci. Paris, Ser. I 339 (2004).

Simulation of earthquake records using time-varying Arma (2,1) model

In this paper, the time-varying auto regressive moving average (ARMA) process is used as a simple yet efficient method for simulating earthquake ground motions. This model is capable of reproducing the nonstationary amplitude as well as the frequency content of the earthquake ground accelerations. The moving time-window technique is used to estimate the time variation of the model parameters from the actual earthquake records. The method is applied to synthesize the near field earthquakes, Naghan 1977, Tabas 1978, and Manjil 1990 recorded on dense soils in Iran, as well as the Mexico City 1985 earthquake recorded on a site with soft soil. It is shown that the selected ARMA (2,1) model and the algorithm used for generating the accelerograms are able to preserve the features of the real earthquake records with different frequency content. The moving time-window technique is used to estimate the time-varying ARMA parameters. Using a general guideline, it is found that a reasonable estimate of the moving window and overlapping sizes can be obtained with a few trials. The required window and overlapping sizes generally reduce, as the local soil of the site becomes stiffer. The statistical response and Fourier spectra of the simulated accelerograms are compared with those of the actual records and reasonable agreement was found. The relationship between the ARMA (2,1) model and the continuous Kanai–Tajimi model is also studied. It is shown that the parameters of the nonstationary Kanai–Tajimi model for simulation of artificial earthquakes can be evaluated using the present modeling procedure.

An ARMA order selection method with fuzzy reasoning

A fuzzy reasoning based approach for ARMA order selection is discussed in this communication. The proposed method attempts to select the optimal ARMA order of a time-varying ARMA model. This method improves model validity-criterion based order selection, such as the Akaike's information criterion and the minimum description length, by applying a fuzzy recursive reasoning method and a fuzzy c-means clustering method.

Minimum Variance Prediction for Linear Time-Varying Systems

In this paper we study the problem of minimum variance prediction for linear time- varying systems. We consider the standard time-varying ARMA model and develop a predictor which guarantees minimum variance prediction for a large class of linear time-varying systems. We also show equivalence between this input-output predictor and the Kalman predictor using an example. A simulation result is also included.

3次元地震動の時変ARMAモデルの同定

This paper presents a practical method for fitting the time-varying three-dimensional ARMA model to digitalized three-dimensionally recorded seismogram. In order to estimate the timevarying parameters of the model, a suitable time-window should be adopted and moved successively every instant. Covariance structure of the data sequence is decided by means of the AR model fitting to the locally stationary data sequence within the time-window. The ARMA model corresponding to the time-window may be fitted to the simulated time-series with the covariance structure through the recursive algorithm based on least squares method. AIC is employed to determine optimal order of the model.

Continuous adaptive speech analysis based on a time-varying ARMA model

An algorithm which estimates both the input excitation and the parameters of a time-varying ARMA speech production model by statistical approximation is proposed. A simplified form of the proposed algorithm that reduces the computational complexity to about one tenth is also proposed. >

地震記象の時系列解析の物理的意味について

A trial of looking for physical meanings of the statistical time-series model fitted to the seismogram is described. This paper shows that if a particle movement of the elastic displacement field of the Earth due to White-noise body-force equivalent to stochastic displacement discontinuity on the seismic fault plane is observed at the ground surface, the observed wave-form corresponding to the seismogram can be expressed by the innovations representation for time-varying autoregressive moving-average process i. e. the time-varying ARMA model.As briefly concluding remarks: (1) AR-coefficient matrices of the model can be interpreted as a function of eigen values of vibration of the Crust. (2) MA-coefficient matrices of the model are interpreted as a function not only of the eigen values but also of eigen-functions of vibration of the soil deposits under the observation site and of covariance function of the White-noise body-force. (3) Covariance function of the innovation sequence obtained from fitting the optimal time-varying ARMA or AR model to the digitalized seismogram has mainly relation to the covariance function of the White-noise body-force and also is influenced by both of the covariance functions of filtering and measurement errors.

Some Critical Issues on the State-Representation of Time-Varying ARMA Models

Abstract This paper deals with the problem of qualifying the class of linear dynamical systems which can be represented as time-varying ARMA models. It is proved that any r-step uniformly observable system admits an ARMA representation of order r and, conversey, an ARMA model of order r can be represented by means of an r-step observable system. Minimality of ARMA models is then discussed. It is shown that the ARMA representation of certain systems requires more parameters than the correspondent minimal state-space realization.

Return-difference and spectral factorisation relationship for the discrete-time Kalman filter

The optimal discrete-time filtering problem is considered for time-varying non-stationary signal models. A return-difference/covariance factorisation result is derived which is well known for time-invariant systems and which has implications for both the stability and optimality of the filter. A new method is described for calculating the Kalman gain matrix when the signal model is presented by a time-varying ARMA model.

Nonstationary Yule-Walker equations

A nonstationary generalization of the classical Yule-Walker equations, relating the (time-varying) autocorrelations of an autoregressive process to the coefficients of the possible models for this process, is given. The corresponding theoretical model-building (or spectral factorization) problem, i.e., that of expressing the above mentioned models in terms of the autocorrelations, is solved. This paper, as well as several others, is part of a work whose purpose is a systematic study of time-varying ARMA models.