The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform

K.j. Ray Liu - One of the best experts on this subject based on the ideXlab platform.

  • Robust median filtering forensics using an Autoregressive Model
    IEEE Transactions on Information Forensics and Security, 2013
    Co-Authors: Xiangui Kang, Anjie Peng, Matthew C. Stamm, K.j. Ray Liu
    Abstract:

    In order to verify the authenticity of digital images, researchers have begun developing digital forensic techniques to identify image editing. One editing operation that has recently received increased attention is median filtering. While several median filtering detection techniques have recently been developed, their performance is degraded by JPEG compression. These techniques suffer similar degradations in performance when a small window of the image is analyzed, as is done in localized filtering or cut-and-paste detection, rather than the image as a whole. In this paper, we propose a new, robust median filtering forensic technique. It operates by analyzing the statistical properties of the median filter residual (MFR), which we define as the difference between an image in question and a median filtered version of itself. To capture the statistical properties of the MFR, we fit it to an Autoregressive (AR) Model. We then use the AR coefficients as features for median filter detection. We test the effectiveness of our proposed median filter detection techniques through a series of experiments. These results show that our proposed forensic technique can achieve important performance gains over existing methods, particularly at low false-positive rates, with a very small dimension of features.

Soren Johansen - One of the best experts on this subject based on the ideXlab platform.

  • the cointegrated vector Autoregressive Model with general deterministic terms
    Journal of Econometrics, 2017
    Co-Authors: Soren Johansen, Morten Orregaard Nielsen
    Abstract:

    Abstract In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive Model X t = γ Z t + Y t , where Z t belongs to a large class of deterministic regressors and Y t is a zero-mean CVAR. We suggest an extended Model that can be estimated by reduced rank regression, and give a condition for when the additive and extended Models are asymptotically equivalent, as well as an algorithm for deriving the additive Model parameters from the extended Model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are χ 2 -distributed.

  • the cointegrated vector Autoregressive Model with general deterministic terms
    CREATES Research Papers, 2016
    Co-Authors: Soren Johansen, Morten Orregaard Nielsen
    Abstract:

    In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive Model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class of deterministic regressors and Y(t) is a zero-mean CVAR. We suggest an extended Model that can be estimated by reduced rank regression and give a condition for when the additive and extended Models are asymptotically equivalent, as well as an algorithm for deriving the additive Model parameters from the extended Model parameters. We derive asymptotic properties of the maximum likelihood estimators and discuss tests for rank and tests on the deterministic terms. In particular, we give conditions under which the estimators are asymptotically (mixed) Gaussian, such that associated tests are khi squared distributed.

  • least squares estimation in a simple random coefficient Autoregressive Model
    Journal of Econometrics, 2013
    Co-Authors: Soren Johansen, Theis Lange
    Abstract:

    The question we discuss is whether a simple random coefficient Autoregressive Model with infinite variance can create the long swings, or persistence, which are observed in many macroeconomic variables. The Model is defined by yt=stρyt−1+et,t=1,…,n, where st is an i.i.d. binary variable with p=P(st=1), independent of et i.i.d. with mean zero and finite variance. We say that the process yt is persistent if the Autoregressive coefficient ρˆn of yt on yt−1 is close to one. We take p<1random variables with infinite variance to find the order of magnitude of ∑t=1nyt−12 and ∑t=1nytyt−1 and hence the limit of ρˆn.

  • likelihood inference for a fractionally cointegrated vector Autoregressive Model
    CREATES Research Papers, 2010
    Co-Authors: Soren Johansen, Morten Orregaard Nielsen
    Abstract:

    We consider Model based inference in a fractionally cointegrated (or cofractional) vector Autoregressive Model based on the conditional Gaussian likelihood. The Model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors s for which s'X_{t} is fractional of order d-b. The parameters d and b satisfy either d=b=1/2, d=b=1/2, or d=d_{0}=b=1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2=b=d=d_{1} for any d_{1}=d_{0}. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of s is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

  • likelihood inference for a nonstationary fractional Autoregressive Model
    Research Papers in Economics, 2007
    Co-Authors: Soren Johansen, Morten Orregaard Nielsen
    Abstract:

    This paper discusses Model based inference in an Autoregressive Model for fractional processes based on the Gaussian likelihood. The Model allows for the process to be fractional of order d or d – b; where d ≥ b > 1/2 are parameters to be estimated. We Model the data X , …, Xт given the initial values Xo-n, n = 0, 1, …, under the assumption that the errors are i.i.d. Gaussian. We consider the likelihood and its derivatives as stochastic processes in the parameters, and prove that they converge in distribution when the errors are i.i.d. with suitable moment conditions and the initial values are bounded. We use this to prove existence and consistency of the local likelihood estimator, and to find the asymptotic distribution of the estimators and the likelihood ratio test of the associated fractional unit root hypothesis, which contains the fractional Brownian motion of type II.

Pentti Saikkonen - One of the best experts on this subject based on the ideXlab platform.

  • a mixture Autoregressive Model based on student s t distribution
    Communications in Statistics-theory and Methods, 2021
    Co-Authors: Mika Meitz, Daniel P A Preve, Pentti Saikkonen
    Abstract:

    A new mixture Autoregressive Model based on Student’s t–distribution is proposed. A key feature of our Model is that the conditional t–distributions of the component Models are based on autoregress...

  • a mixture Autoregressive Model based on student s t distribution
    Social Science Research Network, 2018
    Co-Authors: Mika Meitz, Daniel P A Preve, Pentti Saikkonen
    Abstract:

    A new mixture Autoregressive Model based on Student’s t-distribution is proposed. A key feature of our Model is that the conditional t-distributions of the component Models are based on autoregressions that have multivariate t-distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component Model is a linear function of past observations and the conditional variance is also time varying. Compared to previous mixture Autoregressive Models our Model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear Autoregressive Models. An empirical example employing a realized kernel series constructed from S&P 500 high-frequency intraday data shows that the proposed Model performs well in volatility forecasting. Our methodology is implemented in the freely available StMAR Toolbox for MATLAB.

  • a mixture Autoregressive Model based on student s t distribution
    Research Papers in Economics, 2018
    Co-Authors: Mika Meitz, Daniel P A Preve, Pentti Saikkonen
    Abstract:

    A new mixture Autoregressive Model based on Student's $t$-distribution is proposed. A key feature of our Model is that the conditional $t$-distributions of the component Models are based on autoregressions that have multivariate $t$-distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component Model is a linear function of past observations and the conditional variance is also time varying. Compared to previous mixture Autoregressive Models our Model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear Autoregressive Models. An empirical example employing a realized kernel series based on S&P 500 high-frequency data shows that the proposed Model performs well in volatility forecasting.

  • a gaussian mixture Autoregressive Model for univariate time series
    Journal of Time Series Analysis, 2015
    Co-Authors: Leena Kalliovirta, Mika Meitz, Pentti Saikkonen
    Abstract:

    type="main" xml:id="jtsa12108-abs-0001"> The Gaussian mixture Autoregressive Model studied in this article belongs to the family of mixture Autoregressive Models, but it differs from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the definition of the Model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear Autoregressive Models. Another major advantage is that, for a pth-order Model, explicit expressions of the stationary distributions of dimension p + 1 or smaller are known and given by mixtures of Gaussian distributions with constant mixing weights. In contrast, the conditional distribution given the past observations is a Gaussian mixture with time-varying mixing weights that depend on p lagged values of the series in a natural and parsimonious way. Because of the known stationary distribution, exact maximum likelihood estimation is feasible and one can assess the applicability of the Model in advance by using a non-parametric estimate of the stationary density. An empirical example with interest rate series illustrates the practical usefulness and flexibility of the Model, particularly in allowing for level shifts and temporary changes in variance. Copyright © 2014 Wiley Publishing Ltd

  • a gaussian mixture Autoregressive Model for univariate time series
    Journal of Time Series Analysis, 2015
    Co-Authors: Leena Kalliovirta, Mika Meitz, Pentti Saikkonen
    Abstract:

    This paper presents a general formulation for the univariate nonlinear autore- gressive Model discussed by Glasbey (Journal of the Royal Statistical Society: Series C, 50(2001), 143-154) in the …rst order case, and provides a more thorough treat- ment of its theoretical properties and practical usefulness. The Model belongs to the family of mixture Autoregressive Models but it diers from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the de…- nition of the Model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in non- linear Autoregressive Models. Moreover, for a pth order Model an explicit expression of the (p+ 1)-dimensional stationary distribution is known and given by a mixture of Gaussian distributions with constant mixing weights. Lower dimensional sta- tionary distributions have a similar form whereas the conditional distribution given the past observations is a Gaussian mixture with time varying mixing weights that depend on p lagged values of the series in a natural way. Due to the known sta- tionary distribution exact maximum likelihood estimation is feasible, and one can assess the applicability of the Model in advance by using a nonparametric estimate of the density function. An empirical example with interest rate series illustrates the practical usefulness of the Model. � The …rst and third authors thank the Academy of Finland and the OP-Pohjola Group Research

Xiangui Kang - One of the best experts on this subject based on the ideXlab platform.

  • Robust median filtering forensics using an Autoregressive Model
    IEEE Transactions on Information Forensics and Security, 2013
    Co-Authors: Xiangui Kang, Anjie Peng, Matthew C. Stamm, K.j. Ray Liu
    Abstract:

    In order to verify the authenticity of digital images, researchers have begun developing digital forensic techniques to identify image editing. One editing operation that has recently received increased attention is median filtering. While several median filtering detection techniques have recently been developed, their performance is degraded by JPEG compression. These techniques suffer similar degradations in performance when a small window of the image is analyzed, as is done in localized filtering or cut-and-paste detection, rather than the image as a whole. In this paper, we propose a new, robust median filtering forensic technique. It operates by analyzing the statistical properties of the median filter residual (MFR), which we define as the difference between an image in question and a median filtered version of itself. To capture the statistical properties of the MFR, we fit it to an Autoregressive (AR) Model. We then use the AR coefficients as features for median filter detection. We test the effectiveness of our proposed median filter detection techniques through a series of experiments. These results show that our proposed forensic technique can achieve important performance gains over existing methods, particularly at low false-positive rates, with a very small dimension of features.

  • Robust median filtering forensics based on the Autoregressive Model of median filtered residual
    Proceedings of The 2012 Asia Pacific Signal and Information Processing Association Annual Summit and Conference, 2012
    Co-Authors: Xiangui Kang, Matthew C. Stamm, Anjie Peng
    Abstract:

    One important aspect of multimedia forensics is exposing an image's processing history. Median filtering is a popular noise removal and image enhancement tool. It is also an effective tool in anti-forensics recently. An image is usually saved in a compressed format such as the JPEG format. The forensic detection of median filtering from a JPEG compressed image remains challenging, because typical filter characteristics are suppressed by JPEG quantization and blocking artifacts. In this paper, we introduce a robust median filtering detection scheme based on the Autoregressive Model of median filtered residual. Median filtering is first applied on a test image and the difference between the initial image and the filtered output image is called the median filtered residual (MFR). The MFR is used as the forensic fingerprint. Thus, the interference from the image edge and texture, which is regarded as a limitation of the existing forensic methods, can be reduced. Because the overlapped window filtering introduces correlation among the pixels of MFR, an Autoregressive (AR) Model of the MFR is calculated and the AR coefficients are used by a support vector machine (SVM) for classification. Experimental results show that the proposed median filtering detection method is very robust to JPEG post-compression with a quality factor as low as 30. It distinguishes well between median filtering and other manipulations, such as Gaussian filtering, average filtering, and rescaling and performs well on low-resolution images of size 32 × 32. The proposed method achieves not only much better performance than the existing state-of-the-art methods, but also has very small dimension of feature, i.e., 10-D.

Anjie Peng - One of the best experts on this subject based on the ideXlab platform.

  • Robust median filtering forensics using an Autoregressive Model
    IEEE Transactions on Information Forensics and Security, 2013
    Co-Authors: Xiangui Kang, Anjie Peng, Matthew C. Stamm, K.j. Ray Liu
    Abstract:

    In order to verify the authenticity of digital images, researchers have begun developing digital forensic techniques to identify image editing. One editing operation that has recently received increased attention is median filtering. While several median filtering detection techniques have recently been developed, their performance is degraded by JPEG compression. These techniques suffer similar degradations in performance when a small window of the image is analyzed, as is done in localized filtering or cut-and-paste detection, rather than the image as a whole. In this paper, we propose a new, robust median filtering forensic technique. It operates by analyzing the statistical properties of the median filter residual (MFR), which we define as the difference between an image in question and a median filtered version of itself. To capture the statistical properties of the MFR, we fit it to an Autoregressive (AR) Model. We then use the AR coefficients as features for median filter detection. We test the effectiveness of our proposed median filter detection techniques through a series of experiments. These results show that our proposed forensic technique can achieve important performance gains over existing methods, particularly at low false-positive rates, with a very small dimension of features.

  • Robust median filtering forensics based on the Autoregressive Model of median filtered residual
    Proceedings of The 2012 Asia Pacific Signal and Information Processing Association Annual Summit and Conference, 2012
    Co-Authors: Xiangui Kang, Matthew C. Stamm, Anjie Peng
    Abstract:

    One important aspect of multimedia forensics is exposing an image's processing history. Median filtering is a popular noise removal and image enhancement tool. It is also an effective tool in anti-forensics recently. An image is usually saved in a compressed format such as the JPEG format. The forensic detection of median filtering from a JPEG compressed image remains challenging, because typical filter characteristics are suppressed by JPEG quantization and blocking artifacts. In this paper, we introduce a robust median filtering detection scheme based on the Autoregressive Model of median filtered residual. Median filtering is first applied on a test image and the difference between the initial image and the filtered output image is called the median filtered residual (MFR). The MFR is used as the forensic fingerprint. Thus, the interference from the image edge and texture, which is regarded as a limitation of the existing forensic methods, can be reduced. Because the overlapped window filtering introduces correlation among the pixels of MFR, an Autoregressive (AR) Model of the MFR is calculated and the AR coefficients are used by a support vector machine (SVM) for classification. Experimental results show that the proposed median filtering detection method is very robust to JPEG post-compression with a quality factor as low as 30. It distinguishes well between median filtering and other manipulations, such as Gaussian filtering, average filtering, and rescaling and performs well on low-resolution images of size 32 × 32. The proposed method achieves not only much better performance than the existing state-of-the-art methods, but also has very small dimension of feature, i.e., 10-D.