Alessandro Cardinali

A statistical multiscale approach to image segmentation and fusion

We propose an algorithm to adaptively segment and fuse images by alternating wavelet packet and local cosine transforms each containing best basis selection and thresholding. Within segmented regions fusion is informed by multiple hypothesis testing based on a log-linear factorial model. This fusion identifies homogenous regions from which to select wavelet or local cosine packets, possibly from the original images. The successful performance of the fusion algorithm and segmentation is demonstrated on some multispectral thematic mapper imagery.

Costationarity of Locally Stationary Time Series

Given more than one locally stationary (LS) time series, this article describes a method to discover time-varying linear combinations of the LS series that are stationary. Systems for which this can occur are called costationary, and the associated time-varying linear combinations are called costationary vectors. Costationary systems are interesting for a number of reasons. The costationary vectors shed light on the nature and strength of a potentially interesting relationship between the LS series. The derived stationary series, which is the time-varying combination of the LS series, is often of independent interest and use. The article discusses why a spectral approach is often preferred to the time-domain and why costationary vectors need to be complexity constrained, and it also demonstrates an interesting error-correction formulae which shows how costationary systems must evolve to maintain stationarity in response to system shocks. We illustrate our methodology with two examples: one from asset allocation in financial portfolio construction and the other which mitigates intermittency in wind power management. In the former, a stationary synthetic asset is constructed using market index data and is shown to have superior Sharpe ratios to two established portfolio selectors. In the latter, power outputs from separate wind series are dynamically combined to provide a power output which has smaller intermittency than the individual inputs.

Soluble ST2 Is Regulated by p75 Neurotrophin Receptor and Predicts Mortality in Diabetic Patients With Critical Limb Ischemia

Objective—The p75 neurotrophin receptor (p75NTR) contributes to diabetes mellitus−induced defective postischemic neovascularization. The interleukin-33 receptor ST2 is expressed as transmembrane (ST2L) and soluble (sST2) isoforms. Here, we studied the following: (1) the impact of p75NTR in the healing of ischemic and diabetic calf wounds; (2) the link between p75NTR and ST2; and (3) circulating sST2 levels in critical limb ischemia (CLI) patients. Methods and Results—Diabetes mellitus was induced in p75NTR knockout (p75KO) mice and wild-type (WT) littermates by streptozotocin. Diabetic and nondiabetic p75KO and WT mice received left limb ischemia induction and a full-thickness wound on the ipsilateral calf. Diabetes mellitus impaired wound closure and angiogenesis and increased ST2 expression in WT, but not in p75KO wounds. In cultured endothelial cells, p75NTR promoted ST2 (both isoforms) expression through p38MAPK/activating transcription factor 2 pathway activation. Next, sST2 was measured in the serum of patients with CLI undergoing either revascularization or limb amputation and in the 2 nondiabetic groups (with CLI or nonischemic individuals). Serum sST2 increased in diabetic patients with CLI and was directly associated with higher mortality at 1 year from revascularization. Conclusion—p75NTR inhibits the healing of ischemic lower limb wounds in diabetes mellitus and promotes ST2 expression. Circulating sST2 predicts mortality in diabetic CLI patients.

A GENERALIZED MULTISCALE ANALYSIS OF THE PREDICTIVE CONTENT OF EURODOLLAR IMPLIED VOLATILITIES

It is widely believed that implied volatilities contains information that would enable prediction of spot volatility for a wide range of financial assets. Lead-lag analysis based on the Discrete Wavelet Transform has been proposed as one method for identifying and extracting that predictive information. Unfortunately this approach can fail to identify periodic components that are not proportional to an increasing dyadic scale. We propose a multiscale analysis of the Eurodollar realized volatility and at-the-money (ATM) implied volatilities. After filtering the long memory components we produce a decomposition of cross-correlation by using wavelet packet methods. A threshold cost functional based on asymptotic confidence intervals was used along with the best basis algorithm in order to select an adaptive frequency partition of the sample cross-correlation. We found substantial evidence that Eurodollar implied volatilities contain predictive information about realized volatilities. Moreover, in our analysis the new technique outperforms the lead-lag analysis based on the nondecimated Discrete Wavelet Transform. Therefore we contend that the proposed technique will improve detection of predictive information and recommend further testing in a range of applied contexts.

Locally Stationary Wavelet Packet Processes

For non-stationary time series, the fixed Fourier basis is no longer canonical. Rather than limit our basis choice to wavelet or Fourier functions, we propose the use of a library of non-decimated wavelet packets from which we select a suitable basis (frame). Non-decimated packets are preferred to decimated basis libraries so as to prevent information ‘loss’ at scales coarser than the finest. This article introduces a new class of locally stationary wavelet packet processes and a method to fit these to time series. We also provide new material on the boundedness of the inverse of the inner product operator of autocorrelation wavelet packet functions. We demonstrate the effectiveness of our modelling and basis selection on simulated series and Standard and Poors 500 index series.

Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting

For non-stationary time series, the fixed Fourier basis is no longer canonical. Rather than limit our basis choice to wavelet or Fourier functions, we propose the use of a library of non-decimated wavelet packets from which we select a suitable basis (frame). Non-decimated packets are preferred to decimated basis libraries so as to prevent information ‘loss’ at scales coarser than the finest. This article introduces a new class of locally stationary wavelet packet processes and a method to fit these to time series. We also provide new material on the boundedness of the inverse of the inner product operator of autocorrelation wavelet packet functions. We demonstrate the effectiveness of our modelling and basis selection on simulated series and Standard and Poors 500 index series.

Locally Stationary Wavelet Packet Processes: Basis Selection and Model Fitting: LOCALLY STATIONARY WAVELET PACKET PROCESSES

For non-stationary time series, the fixed Fourier basis is no longer canonical. Rather than limit our basis choice to wavelet or Fourier functions, we propose the use of a library of non-decimated wavelet packets from which we select a suitable basis (frame). Non-decimated packets are preferred to decimated basis libraries so as to prevent information ‘loss’ at scales coarser than the finest. This article introduces a new class of locally stationary wavelet packet processes and a method to fit these to time series. We also provide new material on the boundedness of the inverse of the inner product operator of autocorrelation wavelet packet functions. We demonstrate the effectiveness of our modelling and basis selection on simulated series and Standard and Poors 500 index series.

Local Covariance Estimation Using Costationarity

In this paper we propose a novel estimator for the time-varying covariance of locally stationary time series. This new approach is based on costationary combinations, that is, time-varying deterministic combinations of locally stationary time series that are second-order stationary. We show with a simulation example that the new estimator has smaller variance than other approaches exclusively based on the evolutionary cross-periodogram, and can therefore be appealing in a large number of applications.

Estimating volatility from ATM options with lognormal stochastic variance and long memory

In this article we propose a nonlinear state space representation to model At-The-Money (ATM) implied volatilities and to estimate the unobserved Stochastic Volatility (SVOL) for the underlying asset. We derive a polynomial measurement model relating fractionally cointegrated implied and spot volatilities. We then use our state space representation to obtain Maximum Likelihood (ML) estimates of the short-memory model parameters, and for filtering the fractional spot volatility. We are also able to estimate the average volatility risk premia. We applied our methodology to implied volatilities on eurodollar options, from which we filter the unobserved spot local variance. These data arise from Over The Counter (OTC) transactions that account for high liquidity. For these data, we estimated a positive average volatility risk premia, which is consistent with the Intertemporal Capital Asset Pricing Model (ICAPM) setup of Merton (1973). We also had evidence of highly nonlinear relation between eurodollar spot and implied volatilities. From a methodological and computational point of view, the likelihood function, and all the iterative procedures associated with it, converged uniformly in the parameter space at very little computational expense. We illustrated the effectiveness of our approach by evaluating the approximated Information matrix, the Hotellings T 2 test along with other diagnostic procedures.