Autocorrelation | EPFL Graph Search

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. Auto-

Robust Multivariate and Nonlinear Time Series Models

Time series modeling and analysis is central to most financial and econometric data modeling. With increased globalization in trade, commerce and finance, national variables like gross domestic productivity (GDP) and unemployment rate, market variables like indices and stock prices and global variables like commodity prices are more tightly coupled than ever before. This translates to the use of multivariate or vector time series models and algorithms in analyzing and understanding the relationships that these variables share with each other. Autocorrelation is one of the fundamental aspects of time series modeling. However, traditional linear models, that arise from a strong observed autocorrelation in many financial and econometric time series data, are at times unable to capture the rather nonlinear relationship that characterizes many time series data. This necessitates the study of nonlinear models in analyzing such time series. The class of bilinear models is one of the simplest nonlinear models. These models are able to capture temporary erratic fluctuations that are common in many financial returns series and thus, are of tremendous interest in financial time series analysis. Another aspect of time series analysis is homoscedasticity versus heteroscedasticity. Many time series data, even after differencing, exhibit heteroscedasticity. Thus, it becomes important to incorporate this feature in the associated models. The class of conditional heteroscedastic autoregressive (ARCH) models and its variants form the primary backbone of conditional heteroscedastic time series models. Robustness is a highly underrated feature of most time series applications and models that are presently in use in the industry. With an ever increasing amount of information available for modeling, it is not uncommon for the data to have some aberrations within itself in terms of level shifts and the occasional large fluctuations. Conventional methods like the maximum likelihood and least squares are well known to be highly sensitive to such contaminations. Hence, it becomes important to use robust methods, especially in this age with high amounts of computing power readily available, to take into account such aberrations. While robustness and time series modeling have been vastly researched individually in the past, application of robust methods to estimate time series models is still quite open. The central goal of this thesis is the study of robust parameter estimation of some simple vector and nonlinear time series models. More precisely, we will briefly study some prominent linear and nonlinear models in the time series literature and apply the robust S-estimator in estimating parameters of some simple models like the vector autoregressive (VAR) model, the (0, 0, 1, 1) bilinear model and a simple conditional heteroscedastic bilinear model. In each case, we will look at the important aspect of stationarity of the model and analyze the asymptotic behavior of the S-estimator.

EPFL2010

Nonlinear feature transformations for noise robust speech recognition

Shajith Ikbal

Robustness against external noise is an important requirement for automatic speech recognition (ASR) systems, when it comes to deploying them for practical applications. This thesis proposes and evaluates new feature-based approaches for improving the ASR noise robustness. These approaches are based on nonlinear transformations that, when applied to the spectrum or feature, aim to emphasize the part of the speech that is relatively more invariant to noise and/or deemphasize the part that is more sensitive to noise. Spectral peaks constitute high signal-to-noise ratio part of the speech. Thus an efficient parameterization of the components only from the peak locations is expected to improve the noise robustness. An evaluation of this requires estimation of the peak locations. Two methods proposed in this thesis for the peak estimation task are: 1) frequency-based dynamic programming (DP) algorithm, that uses the spectral slope values of single time frame, and 2) HMM/ANN based algorithm, that uses distinct time-frequency (TF) patterns in the spectrogram (thus imposing temporal constraints during the peak estimation). The learning of the distinct TF patterns in an unsupervised manner makes the HMM/ANN based algorithm sensitive to energy fluctuations in the TF patterns, which is not the case with frequency-based DP algorithm. For an efficient parameterization of spectral components around the peak locations, parameters describing activity pattern (energy surface) within local TF patterns around the spectral peaks are computed and used as features. These features, referred to as spectro-temporal activity pattern (STAP) features, show improved noise robustness, however they are inferior to the standard features in clean speech. The main reason for this is the complete masking of the non-peak regions in the spectrum, which also carry significant information required for clean speech recognition. This leads to a development of a new approach that utilizes a soft-masking procedure instead of discarding the non-peak spectral components completely. In this approach, referred to as phase autocorrelation (PAC) approach, the noise robustness is actually addressed in the autocorrelation domain (time-domain Fourier equivalent of the power spectral domain). It uses phase (i.e., angle) variation of the signal vector over time as a measure of correlation, as opposed to the regular autocorrelation which uses dot product. This alternative measure of autocorrelation is referred to as PAC, and is motivated by the fact that angle gets less disturbed by the additive disturbances than the dot product. Interestingly, the use of PAC has an effect of emphasizing the peaks and smoothing out the valleys, in the spectral domain, without explicitly estimating the peak locations. PAC features exhibit improved noise robustness. However, even the soft masking strategy tends to degrade the clean speech recognition performance. This points to the fact that externally designed transformations, which do not take a complete account of underlying complexity of the speech signal, may not be able to improve the robustness without hurting the clean speech recognition. A better approach in this case will be to learn the transformation from the speech data itself in a data-driven manner, compromising between improving the noise robustness while keeping the clean performance intact. An existing data-driven approach called TANDEM is analyzed to validate this. In TANDEM approach, a multi-layer perceptron (MLP) used to perform a data-driven transformation of the input features, learns the transformation by getting trained in a supervised, discriminative mode, with phoneme labels as output classes. Such a training makes the MLP to perform a nonlinear discriminant analysis in the input feature space and thus makes it to learn a transformation that projects the input features onto a sub-space of maximum class discriminatory information. This projection is able to suppress the noise related variability, while keeping the speech discriminatory information intact. An experimental evaluation of the TANDEM approach shows that it is effective in improving the noise robustness. Interestingly, TANDEM approach is able to further improves the noise robustness of the STAP and PAC features, and also improve their clean speech recognition performance. The analysis of noise robustness of TANDEM has also lead to another interesting aspect of it namely, using it as an integration tool for adaptively combining multiple feature streams. The validity of the various noise robust approaches developed in this thesis is shown by evaluating them on OGI Numbers95 database added with noises from Noisex92, and also with Aurora-2 database. A combination of robust features developed in this thesis along with standard features, in a TANDEM framework, result in a system that is reasonably robust in all conditions.

EPFL2004

Infrequent Rebalancing, Return Autocorrelation, and Seasonality

Vincent Jean Bogousslavsky

A model of infrequent rebalancing can explain specific predictability patterns in the time series and cross-section of stock returns. First, infrequent rebalancing produces return autocorrelations that are consistent with empirical evidence from intraday returns and new evidence from daily returns. Autocorrelations can switch sign and become positive at the rebalancing horizon. Second, the cross-sectional variance in expected returns is larger when more traders rebalance. This effect generates seasonality in the cross-section of stock returns, which can help explain available empirical evidence.

Wiley-Blackwell2016

Robust Multivariate and Nonlinear Time Series Models

EPFL2010

Nonlinear feature transformations for noise robust speech recognition

Shajith Ikbal

EPFL2004