Selective Linear Segmentation for Detecting Relevant Parameter Changes*

2020 ◽  
Author(s):  
Arnaud Dufays ◽  
Elysee Aristide Houndetoungan ◽  
Alain Coën
Keyword(s):  
Time Series ◽  
Hedge Fund ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Relevant Parameter ◽  
Time Varying ◽  
Long Time ◽  
Model Selection Uncertainty ◽  
Penalized Likelihood Approach ◽  
Changes Over Time

Abstract Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of fourteen hedge fund (HF) strategies, using an asset-based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns.

Cosinor Analysis for Temperature Time Series Data of Long Duration

2007 ◽  
Vol 9 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Nikhil S. Padhye ◽  
Sandra K. Hanneman
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Model Fit ◽  
Series Data ◽  
Model Parameters ◽  
Cosinor Analysis ◽  
Long Time ◽  
Improved Model ◽  
Data Length ◽  
Cosinor Models

The application of cosinor models to long time series requires special attention. With increasing length of the time series, the presence of noise and drifts in rhythm parameters from cycle to cycle lead to rapid deterioration of cosinor models. The sensitivity of amplitude and model-fit to the data length is demonstrated for body temperature data from ambulatory menstrual cycling and menopausal women and from ambulatory male swine. It follows that amplitude comparisons between studies cannot be made independent of consideration of the data length. Cosinor analysis may be carried out on serial-sections of the series for improved model-fit and for tracking changes in rhythm parameters. Noise and drift reduction can also be achieved by folding the series onto a single cycle, which leads to substantial gains in the model-fit but lowers the amplitude. Central values of model parameters are negligibly changed by consideration of the autoregressive nature of residuals.

Time-Varying Delay Estimation Applied to the Surface Electromyography Signals Using the Parametric Approach

2018 ◽  
Vol 17 (02) ◽  
pp. 1850015 ◽  
Author(s):  
Gia Thien Luu ◽  
Abdelbassit Boualem ◽  
Tran Trung Duy ◽  
Philippe Ravier ◽  
Olivier Butteli
Keyword(s):  
Parametric Method ◽  
Optimization Technique ◽  
Likelihood Estimation ◽  
Model Parameters ◽  
Fiber Direction ◽  
Time Varying ◽  
Time Varying Delay ◽  
Power Spectral ◽  
Changes Over Time ◽  
Varying Delay

Muscle Fiber Conduction Velocity (MFCV) can be calculated from the time delay between the surface electromyographic (sEMG) signals recorded by electrodes aligned with the fiber direction. In order to take into account the non-stationarity during the dynamic contraction (the most daily life situation) of the data, the developed methods have to consider that the MFCV changes over time, which induces time-varying delays and the data is non-stationary (change of Power Spectral Density (PSD)). In this paper, the problem of TVD estimation is considered using a parametric method. First, the polynomial model of TVD has been proposed. Then, the TVD model parameters are estimated by using a maximum likelihood estimation (MLE) strategy solved by a deterministic optimization technique (Newton) and stochastic optimization technique, called simulated annealing (SA). The performance of the two techniques is also compared. We also derive two appropriate Cramer–Rao Lower Bounds (CRLB) for the estimated TVD model parameters and for the TVD waveforms. Monte-Carlo simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the variance obtained is close to the derived CRBs. A comparison with non-parametric approaches of the TVD estimation is also presented and shows the superiority of the method proposed.

A Time-Varying Causality Formalism Based on the Liang–Kleeman Information Flow for Analyzing Directed Interactions in Nonstationary Climate Systems

2019 ◽  
Vol 32 (21) ◽  
pp. 7521-7537 ◽  
Author(s):  
Daniel Fiifi Tawia Hagan ◽  
Guojie Wang ◽  
X. San Liang ◽  
Han A. J. Dolman
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Information Flow ◽  
Air Temperature ◽  
Land Surface ◽  
Full Range ◽  
Accurate Estimation ◽  
Time Varying ◽  
Long Time Series ◽  
Long Time

Abstract The interaction between the land surface and the atmosphere is of significant importance in the climate system because it is a key driver of the exchanges of energy and water. Several important relations to heat waves, floods, and droughts exist that are based on the interaction of soil moisture and, for instance, air temperature and humidity. Our ability to separate the elements of this coupling, identify the exact locations where they are strongest, and quantify their strengths is, therefore, of paramount importance to their predictability. A recent rigorous causality formalism based on the Liang–Kleeman (LK) information flow theory has been shown, both theoretically and in real-world applications, to have the necessary asymmetry to infer the directionality and magnitude within geophysical interactions. However, the formalism assumes stationarity in time, whereas the interactions within the land surface and atmosphere are generally nonstationary; furthermore, it requires a sufficiently long time series to ensure statistical sufficiency. In this study, we remedy this difficulty by using the square root Kalman filter to estimate the causality based on the LK formalism to derive a time-varying form. Results show that the new formalism has similar properties compared to its time-invariant form. It is shown that it is also able to capture the time-varying causality structure within soil moisture–air temperature coupling. An advantage is that it does not require very long time series to make an accurate estimation. Applying a wavelet transform to the results also reveals the full range of temporal scales of the interactions.

scholarly journals A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems

2010 ◽  
Vol 23 (10) ◽  
pp. 2759-2781 ◽  
Author(s):  
Martin P. Tingley ◽  
Peter Huybers
Keyword(s):  
Time Series ◽  
Covariance Matrix ◽  
Expectation Maximization Algorithm ◽  
Covariance Structure ◽  
Model Parameters ◽  
Data Types ◽  
Spatial Covariance ◽  
Bayesian Algorithm ◽  
Climate Anomalies ◽  
Instrumental Values

Abstract Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a “calibration” interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage. A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as “observation equations” describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series. This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation–maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.

scholarly journals A Modeling Study on the Estimation of COVID-19 Daily and Weekly Cases and Reproduction Number Using the Adaptive Kalman Filter: The Example of Ziraat Bank, Turkey

2021 ◽  
pp. 15-27
Author(s):  
İlker Met ◽  
Levent Özbek ◽  
Himmet Aksoy ◽  
Ayfer Erkoç
Keyword(s):  
Time Series ◽  
Kalman Filter ◽  
Reproduction Number ◽  
Jel Classification ◽  
Model Parameters ◽  
Time Varying ◽  
Adaptive Kalman Filter ◽  
Human Race ◽  
Time Varying Parameter ◽  
Case Number

Abstract Since the beginning of 2020, the world has been struggling with a viral epidemic (COVID-19), which poses a serious threat to the collective health of the human race. Mathematical modeling of epidemics is critical for developing such policies, especially during these uncertain times. In this study, the reproduction number and model parameters were predicted using AR(1) (autoregressive time-series model of order 1) and the adaptive Kalman filter (AKF). The data sample used in the study consists of the weekly and daily number of cases amongst the Ziraat Bank personnel between March 11, 2020, and April 19, 2021. This sample was modeled in the state space, and the AKF was used to estimate the number of cases per day. It is quite simple to model the daily and weekly case number time series with the time-varying parameter AR(1) stochastic process and to estimate the time-varying parameter with online AKF. Overall, we found that the weekly case number prediction was more accurate than the daily case number (R2 = 0.97), especially in regions with a low number of cases. We suggest that the simplest method for reproduction number estimation can be obtained by modeling the daily cases using an AR(1) model. JEL classification numbers: C02, C22, C32. Keywords: COVID-19, Modeling, Reproduction number estimation, AR(1), Kalman filter.

scholarly journals Multi-Step Solar Irradiance Forecasting and Domain Adaptation of Deep Neural Networks

Energies ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3987
Author(s):  
Giorgio Guariso ◽  
Giuseppe Nunnari ◽  
Matteo Sangiorgio
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Solar Irradiance ◽  
Short Term Memory ◽  
Domain Adaptation ◽  
Model Parameters ◽  
Network Architectures ◽  
Long Time ◽  
Unique Predictor ◽  
Hidden Neurons

The problem of forecasting hourly solar irradiance over a multi-step horizon is dealt with by using three kinds of predictor structures. Two approaches are introduced: Multi-Model (MM) and Multi-Output (MO). Model parameters are identified for two kinds of neural networks, namely the traditional feed-forward (FF) and a class of recurrent networks, those with long short-term memory (LSTM) hidden neurons, which is relatively new for solar radiation forecasting. The performances of the considered approaches are rigorously assessed by appropriate indices and compared with standard benchmarks: the clear sky irradiance and two persistent predictors. Experimental results on a relatively long time series of global solar irradiance show that all the networks architectures perform in a similar way, guaranteeing a slower decrease of forecasting ability on horizons up to several hours, in comparison to the benchmark predictors. The domain adaptation of the neural predictors is investigated evaluating their accuracy on other irradiance time series, with different geographical conditions. The performances of FF and LSTM models are still good and similar between them, suggesting the possibility of adopting a unique predictor at the regional level. Some conceptual and computational differences between the network architectures are also discussed.

scholarly journals Stochastic Identification of Guided Wave Propagation under Ambient Temperature via Non-Stationary Time Series Models

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5672
Author(s):  
Shabbir Ahmed ◽  
Fotis Kopsaftopoulos
Keyword(s):  
Time Series ◽  
Wave Propagation ◽  
Guided Wave ◽  
Stationary Time Series ◽  
Model Parameters ◽  
Time Series Models ◽  
Fe Model ◽  
Time Varying ◽  
Small Temperature ◽  
Guided Wave Propagation

In the context of active-sensing guided-wave-based acousto-ultrasound structural health monitoring, environmental and operational variability poses a considerable challenge in the damage diagnosis process as they may mask the presence of damage. In this work, the stochastic nature of guided wave propagation due to the small temperature variation, naturally occurring in the ambient or environment, is rigorously investigated and modeled with the help of stochastic time-varying time series models, for the first time, with a system identification point of view. More specifically, the output-only recursive maximum likelihood time-varying auto-regressive model (RML-TAR) is employed to investigate the uncertainty in guided wave propagation by analyzing the time-varying model parameters. The steps and facets of the identification procedure are presented, and the obtained model is used for modeling the uncertainty of the time-varying model parameters that capture the underlying dynamics of the guided waves. The stochasticity inherent in the modal properties of the system, such as natural frequencies and damping ratios, is also analyzed with the help of the identified RML-TAR model. It is stressed that the narrow-band high-frequency actuation for guided wave propagation excites more than one frequency in the system. The values and the time evolution of those frequencies are analyzed, and the associated uncertainties are also investigated. In addition, a high-fidelity finite element (FE) model was established and Monte Carlo simulations on that FE model were carried out to understand the effect of small temperature perturbation on guided wave signals.

Adaptive control of time-varying non-linear plants by speed-gradient algorithms

2019 ◽  
pp. 37-44 ◽  
Author(s):  
O. P. Tomchina ◽  
D. N. Polyakhov ◽  
O. I. Tokareva ◽  
A. L. Fradkov
Keyword(s):  
Adaptive Control ◽  
Adaptive Systems ◽  
Reference Model ◽  
Maximum Deviation ◽  
Model Parameters ◽  
Time Varying ◽  
System Solution ◽  
Non Linear ◽  
Initial Uncertainty ◽  
Speed Gradient

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

scholarly journals Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Interest Rate ◽  
Algebraic Approach ◽  
Dynamical Symmetry ◽  
Bond Pricing ◽  
Model Parameters ◽  
Time Varying ◽  
Single Factor ◽  
Bond Price ◽  
Interest Rate Models ◽  
Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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