6,008 research outputs found
Spectral analysis for nonstationary audio
A new approach for the analysis of nonstationary signals is proposed, with a
focus on audio applications. Following earlier contributions, nonstationarity
is modeled via stationarity-breaking operators acting on Gaussian stationary
random signals. The focus is on time warping and amplitude modulation, and an
approximate maximum-likelihood approach based on suitable approximations in the
wavelet transform domain is developed. This paper provides theoretical analysis
of the approximations, and introduces JEFAS, a corresponding estimation
algorithm. The latter is tested and validated on synthetic as well as real
audio signal.Comment: IEEE/ACM Transactions on Audio, Speech and Language Processing,
Institute of Electrical and Electronics Engineers, In pres
Filtered derivative with p-value method for multiple change-points detection
This paper deals with off-line detection of change points for time series of
independent observations, when the number of change points is unknown. We
propose a sequential analysis like method with linear time and memory
complexity. Our method is based at first step, on Filtered Derivative method
which detects the right change points but also false ones. We improve Filtered
Derivative method by adding a second step in which we compute the p-values
associated to each potential change points. Then we eliminate as false alarms
the points which have p-value smaller than a given critical level. Next, our
method is compared with the Penalized Least Square Criterion procedure on
simulated data sets. Eventually, we apply Filtered Derivative with p-Value
method to segmentation of heartbeat time series
A test for second-order stationarity of time series based on unsystematic sub-samples
In this paper, we introduce a new method for testing the stationarity of time
series, where the test statistic is obtained from measuring and maximising the
difference in the second-order structure over pairs of randomly drawn
intervals. The asymptotic normality of the test statistic is established for
both Gaussian and a range of non-Gaussian time series, and a bootstrap
procedure is proposed for estimating the variance of the main statistics.
Further, we show the consistency of our test under local alternatives. Due to
the flexibility inherent in the random, unsystematic sub-samples used for test
statistic construction, the proposed method is able to identify the intervals
of significant departure from the stationarity without any dyadic constraints,
which is an advantage over other tests employing systematic designs. We
demonstrate its good finite sample performance on both simulated and real data,
particularly in detecting localised departure from the stationarity
Wavelet Method for Locally Stationary Seasonal Long Memory Processes
Long memory processes have been extensively studied over the past decades. When dealing with the financial and economic data, seasonality and time-varying long-range dependence can often be observed and thus some kind of non-stationarity can exist inside financial data sets. To take into account this kind of phenomena, we propose a new class of stochastic process : the locally stationary k-factor Gegenbauer process. We describe a procedure of estimating consistently the time-varying parameters by applying the discrete wavelet packet transform (DWPT). The robustness of the algorithm is investigated through simulation study. An application based on the error correction term of fractional cointegration analysis of the Nikkei Stock Average 225 index is proposed.Discrete wavelet packet transform ; Gegenbauer process ; Nikkei Stock Average 225 index ; non-stationarity ; ordinary least square estimation
LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R
Locally stationary process representations have recently been proposed and applied to both time series and image analysis applications. This article describes an implementation of the locally stationary two-dimensional wavelet process approach in R. This package permits construction of estimates of spatially localized spectra and localized autocovariance which can be used to characterize structure within images.
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