Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain, Research Methods/ Statistical Methods,

Monitoring for Disruptions in Financial Markets

Historical and sequential CUSUM change-point tests for strongly dependent nonlinear processes are studied. These tests are used to monitor the conditional variance of asset returns and to provide early information regarding instabilities or disruptions in financial risk. Data-driven monitoring schemes are investigated. Since the processes are strongly dependent several novel issues require special attention. One such issue is the sampling frequency. We study the power of detection as sampling frequencies vary. Analytical local power results are obtained for historical CUSUM tests and simulation evidence is presented for sequential tests. Finally, a prediction-based statistic is introduced that reduces the detection delay considerably. The prediction based formula is based on a local Brownian bridge approximation argument and provides an assessment of the likelihood of change-points. Nous étudions les tests CUSUM historiques et séquentiels pour des séries dépendantes avec des applications en finance. Pour les processus temporels, une nouvelle dimension se présente : l'effet du choix de la fréquence des observations. Un nouveau test est également proposé. Ce test est basé sur une formule de prévision locale d'un pont brownien.structural change, CUSUM, GARCH, quadratic variation, power variation, high frequency data, Brownian bridge, boundary crossing, sequential tests, local power, changement structurel, CUSUM, GARCH, variation quadratique, 'power variation', données de haute fréquence, pont Brownien, puissance locale, tests séquentiels

25 Years of IIF Time Series Forecasting: A Selective Review

We review the past 25 years of time series research that has been published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982-1985; International Journal of Forecasting 1985-2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on possible future research directions in this field.Accuracy measures; ARCH model; ARIMA model; Combining; Count data; Densities; Exponential smoothing; Kalman Filter; Long memory; Multivariate; Neural nets; Nonlinearity; Prediction intervals; Regime switching models; Robustness; Seasonality; State space; Structural models; Transfer function; Univariate; VAR.

Study of phase transition on a temporal network, and application to epidemiology

In this work we address the problem of assessing the vulnerability of a system of interacting individuals targeted with a disease. The disease is modelled using the SIS compartmental model, for which people can be either susceptible S or infectious I. The transition S→I takes place with probability λ, if a S meets an I; the I→S recovery happens spontaneously with probability μ. We dispose of a data-set regarding the interactions of a bipartite community whose contacts change in time. To encode this dynamics we exploit the formalism of temporal networks. We have focused on the so called epidemic threshold (e.t.) in order to give a quantification of the vulnerability of the system. In infinite size systems, the epidemic threshold is the value of diseases's parameters μ, so that for μ >μc the number of infectious people in the stationary state is non zero, while in the other case reaches the disease-free state. We carry out the analysis of the threshold both numerically and analytically. In order to compute the e.t. , we exploit the findings of a recent work on temporal networks coupled with disease dynamics. This work demonstrates that, when it comes to the determination of the epidemic threshold on a temporal network, the microscopic stochastic simulation of a disease-spreading can be replaced with a simpler and faster computation of the spectral radius of a suitable matrix, the so called Infection Propagator. This matrix encodes the coupled dynamics of disease and network in a finite period of time. Using this approach, we evaluate the phase-transition diagram threshold μc(λ) in various portion of the temporal data set. As this system regards woman-man interactions relative to sexual contacts, we also allow for men and women to have different λ, as medical studies show. We find that the impact of the two categories on the threshold is symmetric, and that the present system is largely non vulnerable with respect to the most common STDs. We then address the question of which is the main temporal or topological feature that drives the disease on the network. We brake some properties of the network in order to see their impact on the e.t., and we conclude that the aggregated network is the structure one needs to preserve in order to capture the dynamic of the disease. To tackle the problem analytically, we test on our network three analytical models that allow to write an explicit expression for the e.t. , generalising them to a bipartite structure. Only the time averaged approximation of the temporal network works fine. Lastly, we try to ameliorate this approximation introducing a stochastic correction. We write a N- dimensional Langevin equation for the evolution of the state of probability of infection per each node, p(t), when close to the disease-free state, i.e. p(t)~0. The deterministic part of the equation is the same that describes the time-average regime. The stochastic part includes a Wiener noise-matrix that aims to reproduce the fluctuations of the temporal contact matrix of the network respect to the annealed matrix. The resulting equation is a N-dimensional geometric Brownian motion. By extending the findings for the asymptotic state of a one dimensional GBM, we find an epidemic threshold very close to the actual one. For the future, it would be interesting to delve more into this stochastic approach and test its validity on other networks and on synthetic models; and maybe on other types of noises , such as the Poissonian or shot noise, that resembles more to the real behaviour of human contact dynamics

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1