http://t.co/cf1JAhai autocovariance structures for radial averages in small-angle X-ray scattering experiments http://t.co/KjKvZCqX
19 May 2012, 7:17 pm
http://t.co/cf1JAhai autocovariance structures for radial averages in small-angle X-ray scattering experiments http://t.co/KjKvZCqX

Imox: Limiting Spectral Distribution of Sample autocovariance Matrices. (arXiv:1108.3147v2 [math.PR] UPDATED)
18 April 2012, 8:41 pm
Imox Limiting Spectral Distribution of Sample autocovariance Matrices. (arXiv:1108.3147v2 [math.PR] UPDATED) - http://arxiv.org/abs/1108.3147 April 18 from math updates on arXiv.org - Comment - Like We show that the empirical spectral distribution (ESD) of the sample autocovariance matrix (ACVM) converges as the dimension increases, when the time series is a linear process with reasonable restriction on the coefficients. The limit does not depend on the distribution of the underlying driving i.i.d. sequence and its support is unbounded. This limit does not coincide with the spectral distribution of the theoretical ACVM. However, it does so if we consider a suitably tapered version of the sample ACVM. For banded sample ACVM the limit has unbounded support as long as the number of non-zero diagonals in proportion to the dimension of the matrix is bounded away from zero. If this ratio tends to zero, then the limit exists and again coincides with the spectral distribution of the theoretical ACVM. Finally we also study the LSD of a naturally modified version of the ACVM which is not non-negative definite. - Imox

Imox: Unit roots in moving averages beyond first order. (arXiv:1203.2496v1 [math.ST])
12 March 2012, 7:52 pm
Imox Unit roots in moving averages beyond first order. (arXiv:1203.2496v1 [math.ST]) - http://arxiv.org/abs/1203.2496 March 12 from math updates on arXiv.org - Comment - Like The asymptotic theory of various estimators based on Gaussian likelihood has been developed for the unit root and near unit root cases of a first-order moving average model. Previous studies of the MA(1) unit root problem rely on the special autocovariance structure of the MA(1) process, in which case, the eigenvalues and eigenvectors of the covariance matrix of the data vector have known analytical forms. In this paper, we take a different approach to first consider the joint likelihood by including an augmented initial value as a parameter and then recover the exact likelihood by integrating out the initial value. This approach by-passes the difficulty of computing an explicit decomposition of the covariance matrix and can be used to study unit root behavior in moving averages beyond first order. The asymptotics of the generalized likelihood ratio (GLR) statistic for testing unit roots are also studied. The GLR test has operating characteristics that are competitive with the locally... - Imox

Imox: Long run behaviour of the autocovariance function of ARCH($\infty$) models. (arXiv:1202.5440v1 [math.CA])
26 February 2012, 9:13 pm
Imox Long run behaviour of the autocovariance function of ARCH($\infty$) models. (arXiv:1202.5440v1 [math.CA]) - http://arxiv.org/abs/1202.5440 February 26 from math updates on arXiv.org - Comment - Like The asymptotic properties of the memory structure of ARCH($\infty$) equations are investigated. This asymptotic analysis is achieved by expressing the autocovariance function of ARCH($\infty$) equations as the solution of a linear Volterra summation equation and analysing the properties of an associated resolvent equation via the admissibility theory of linear Volterra operators. It is shown that the autocovariance function decays subexponentially (or geometrically) if and only if the kernel of the resolvent equation has the same decay property. It is also shown that upper subexponential bounds on the autocovariance function result if and only if similar bounds apply to the kernel. - Imox

Imox: On the range of validity of the autoregressive sieve bootstrap. (arXiv:1201.6211v1 [math.ST])
30 January 2012, 8:19 pm
Imox On the range of validity of the autoregressive sieve bootstrap. (arXiv:1201.6211v1 [math.ST]) - http://arxiv.org/abs/1201.6211 January 30 from math updates on arXiv.org - Comment - Like We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is... - Imox

Imox: Robust estimation in time series with long and short memory properties. (arXiv:1112.6308v1 [stat.ME])
29 December 2011, 7:56 pm
Imox Robust estimation in time series with long and short memory properties. (arXiv:1112.6308v1 [stat.ME]) - http://arxiv.org/abs/1112.6308 December 29 from stat updates on arXiv.org - Comment - Like This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and L\'evy-Leduc et al. (2011a), the emphasis in this paper is given in the following directions; the influence of additive outliers in the estimation of a time series, the asymptotic properties of a robust autocovariance function and a robust semiparametric estimation method of the fractional parameter d in ARFIMA(p, d, q) models. Some simulations are used to support the use of the robust method when a time series has additive outliers. The invariance property of the estimators for the first difference in ARFIMA model with outliers is also discussed. In general, the robust long-memory estimator leads to be outlier resistant and is invariant to first differencing. - Imox

Imox: Binomial ARMA count series from renewal processes. (arXiv:1112.4554v1 [math.ST])
20 December 2011, 9:20 pm
Imox Binomial ARMA count series from renewal processes. (arXiv:1112.4554v1 [math.ST]) - http://arxiv.org/abs/1112.4554 December 20 from math updates on arXiv.org - Comment - Like This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration. An estimation method is developed for the AR(p) cases. - Imox

Imox: Asymptotic Theory of Cepstral Random Fields. (arXiv:1112.1977v1 [math.ST])
11 December 2011, 11:00 pm
Imox Asymptotic Theory of Cepstral Random Fields. (arXiv:1112.1977v1 [math.ST]) - http://arxiv.org/abs/1112.1977 December 11 from math updates on arXiv.org - Comment - Like Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. Given the importance of this topic, there has been substantial research devoted to this area. However, in spite of the tremendous research to date, outside the engineering literature, the cepstral random field model remains largely underdeveloped. We provide a comprehensive treatment of the asymptotic theory for cepstral random field models. In particular, we provide recursive formulas that connect the spatial cepstral coefficients to an equivalent moving-average random field, which facilitates easy computation of the necessary autocovariance matrix. Additionally, we establish asymptotic consistency results for Bayesian, maximum likelihood, and quasi-maximum likelihood estimation. Further, in both the maximum and quasi-maximum likelihood frameworks we derive the asymptotic distribution of our estimator. The theoretical... - Imox

Imox: Quantization of long memory processes. (arXiv:1107.4476v1 [q-fin.ST])
24 July 2011, 8:47 pm
Imox Quantization of long memory processes. (arXiv:1107.4476v1 [q-fin.ST]) - http://arxiv.org/abs/1107.4476 July 24 from stat updates on arXiv.org - Comment - Like We study how quantization, occurring when a continuously varying process is approximated by or observed on a grid of discrete values, changes the properties of a Gaussian long-memory process. By computing the asymptotic behavior of the autocovariance and of the spectral density, we find that the quantized process has the same Hurst exponent of the original process. We show that the log-periodogram regression and the Detrended Fluctuation Analysis (DFA) are severely negatively biased estimators of the Hurst exponent for quantized processes. We compute the asymptotics of the DFA for a generic long-memory process and we study them for quantized processes. - Imox

Imox: Fractional L\'{e}vy-driven Ornstein--Uhlenbeck processes and stochastic differential equations. (arXiv:1102.1830v1 [math.ST])
9 February 2011, 8:29 pm
Imox Fractional L\'{e}vy-driven Ornstein--Uhlenbeck processes and stochastic differential equations. (arXiv:1102.1830v1 [math.ST]) - http://arxiv.org/abs/1102.1830 February 9, 2011 from math updates on arXiv.org - Comment - Like Using Riemann-Stieltjes methods for integrators of bounded $p$-variation we define a pathwise integral driven by a fractional L\'{e}vy process (FLP). To explicitly solve general fractional stochastic differential equations (SDEs) we introduce an Ornstein-Uhlenbeck model by a stochastic integral representation, where the driving stochastic process is an FLP. To achieve the convergence of improper integrals, the long-time behavior of FLPs is derived. This is sufficient to define the fractional L\'{e}vy-Ornstein-Uhlenbeck process (FLOUP) pathwise as an improper Riemann-Stieltjes integral. We show further that the FLOUP is the unique stationary solution of the corresponding Langevin equation. Furthermore, we calculate the autocovariance function and prove that its increments exhibit long-range dependence. Exploiting the Langevin equation, we consider SDEs driven by FLPs of bounded $p$-variation for $p<2$ and construct solutions using the corresponding FLOUP. Finally, we consider examples... - Imox