Autoregressive Stochastic Process Research Articles

Explaining Returns Through Valuation

This article develops an analytically coherent yet parsimonious framework which explains market returns in terms of contemporaneous information. It anchors on the idea that valuation (static perspective) can be connected to the dynamics that explain returns, and vice versa. The framework requires two components. First, an explicit function that maps information to an estimate of value—a valuation heuristic. Second, the framework assumes that the difference between a firm’s actual value and value-per-heuristic follows an autoregressive stochastic process with a contraction parameter and no intercept. The contraction parameter can be estimated efficiently and nonparametrically. This modeling suffices to derive implied returns. Using scaled Earnings Per Share (``EPS'') forecasts as valuation heuristics, we empirically evaluate the framework’s validity and robustness. Its explanatory power compares favorably to that of traditional ordinary least squares (``OLS'') regressions, despite only requiring a single parameter. In a setting with pooled annual data, the implied and realized returns correlations range between 64% and 73%.

Investigating temporal and spatial patterns in the stochastic component of ZTD time series over Europe

The EUREF Permanent GNSS Network (EPN) provides a unique atmospheric dataset over Europe in the form of Zenith Total Delay (ZTD) time series. These ZTD time series are estimated independently by different analysis centers, but a combined solution is also provided. Previous studies showed that changes in the processing strategy do not affect trends and seasonal amplitudes. However, its effect on the temporal and spatial variations of the stochastic component of ZTD time series has not yet been investigated. This study analyses the temporal and spatial correlations of the ZTD residuals obtained from four different datasets: one solution provided by ASI (Agenzia Spaziale Italiana Centro di Geodesia Spaziale, Italy), two solutions provided by GOP (Geodetic Observatory Pecny, Czech Republic), and one combined solution resulting from the EPN’s second reprocessing campaign. We find that the ZTD residuals obtained from the three individual solutions can be modeled using a first-order autoregressive stochastic process, which is less significant and must be completed by an additional white noise process in the combined solution. Although the combination procedure changes the temporal correlation in the ZTD residuals, it neither affects its spatial correlation structure nor its time-variability, for which an annual modulation is observed for stations up to 1,000 km apart. The main spatial patterns in the ZTD residuals also remain identical. Finally, we compare two GOP solutions, one of which only differs in the modeling of non-tidal atmospheric loading at the observation level, and conclude that its modeling has a negligible effect on ZTD values.

A high throughput generative vector autoregression model for stochastic synapses.

By imitating the synaptic connectivity and plasticity of the brain, emerging electronic nanodevices offer new opportunities as the building blocks of neuromorphic systems. One challenge for large-scale simulations of computational architectures based on emerging devices is to accurately capture device response, hysteresis, noise, and the covariance structure in the temporal domain as well as between the different device parameters. We address this challenge with a high throughput generative model for synaptic arrays that is based on a recently available type of electrical measurement data for resistive memory cells. We map this real-world data onto a vector autoregressive stochastic process to accurately reproduce the device parameters and their cross-correlation structure. While closely matching the measured data, our model is still very fast; we provide parallelized implementations for both CPUs and GPUs and demonstrate array sizes above one billion cells and throughputs exceeding one hundred million weight updates per second, above the pixel rate of a 30 frames/s 4K video stream.

Measuring Financial Impacts of the Renewable Energy Based Fiscal Policy in Colombia under Electricity Price Uncertainty

This paper analyses the financial implications, from the point of view of an investor in renewable energy, which sells the energy for an uncertain price of electricity and decides to take advantage of the Colombian tax policy over the renewable energy. The policy, known as Investment Tax Allowance (ITA), encourages installation of renewable projects in a country traditionally dominated by hydro power. Price is modeled as a non-stationary autoregressive stochastic process with normally distributed error terms. Costs, and uncertain revenue and taxes are considered to assess the financial impact on a solar project when the policy is implemented. Since impact varies according to project ownership, two cases are evaluated: a generation company (GENCO-1) that only owns the solar project; and, an existent generation company (GENCO-2) that owns a portfolio of projects. Results indicate that if ITA is applied, it is likely that the GENCO-1 cannot take the full advantage of the incentive, as opposed to the GENCO-2. Although this policy might not satisfy planner objectives since it does not guarantee the construction of significantly high capacity of new renewable energy projects, it definitely represents an attractive mechanism to decrease tax obligations at the GENCO-2 level. Finally, a theoretical analysis shows that investment cost affects the mean of the present value; whereas tax rates impacts both its mean and standard deviation.

COV-OBS.x2: 180 years of geomagnetic field evolution from ground-based and satellite observations

We present the geomagnetic field model COV-OBS.x2 that covers the period 1840–2020. It is primarily constrained by observatory series, satellite data, plus older surveys. Over the past two decades, we consider annual differences of 4-monthly means at ground-based stations (since 1996), and virtual observatory series derived from magnetic data of the satellite missions CHAMP (over 2001–2010) and Swarm (since 2013). A priori information is needed to complement the constraints carried by geomagnetic records and solve the ill-posed geomagnetic inverse problem. We use for this purpose temporal cross-covariances associated with auto-regressive stochastic processes of order 2, whose parameters are chosen so as to mimic the temporal power spectral density observed in paleomagnetic and observatory series. We aim this way to obtain as far as possible realistic posterior model uncertainties. These can be used to infer for instance the core dynamics through data assimilation algorithms, or an envelope for short-term magnetic field forecasts. We show that because of the projection onto splines, one needs to inflate the formal model error variances at the most recent epochs, in order to account for unmodeled high frequency core field changes. As a by-product of the core field model, we co-estimate the external magnetospheric dipole evolution on periods longer than 2 years. It is efficiently summarized as the sum of a damped oscillator (of period 10.5 years and decay rate 55 years), plus a short-memory (6 years) damped random walk.

Parametric recurrence quantification analysis of autoregressive processes for pattern recognition in multichannel electroencephalographic data

Recurrence quantification analysis (RQA) is an acknowledged method for the characterization of experimental time series. We propose a parametric version of RQA, pRQA, allowing a fast processing of spatial arrays of time series, once each is modeled by an autoregressive stochastic process. This method relies on the analytical derivation of asymptotic expressions for five current RQA measures as a function of the model parameters. By avoiding the construction of the recurrence plot of the time series, pRQA is computationally efficient. As a proof of principle, we apply pRQA to pattern recognition in multichannel electroencephalographic (EEG) data from a patient with a brain tumor.

Relative income dynamics of individuals in New Zealand

This paper reports estimates of simple models of income dynamics, using longitudinal income data for 1994 to 2012 from New Zealand Inland Revenue. Income changes are described using a simple autoregressive stochastic process in which Galtonian regression is combined with serial correlation in the stochastic term. The parameters of the model have convenient interpretations. Substantial regression towards the mean combined with negative serial correlation is observed, with remarkable parameter stability over the whole period. The estimates imply that, on average, relatively high income individuals have lower proportional increases in income from year to year compared with lower income individuals, and those with large increases in one year are more likely to experience decreases the following year. These dynamics are shown to be sufficient to ensure that cross-sectional indices of inequality fall as the accounting period increases.

Validation of PARX Models for Default Count Prediction.

The growing importance of financial technology platforms, based on interconnectedness, makes necessary the development of credit risk measurement models that properly take contagion into account. Evaluating the predictive accuracy of these models is achieving increasing importance to safeguard investors and maintain financial stability. The aim of this paper is two-fold. On the one hand, we provide an application of Poisson autoregressive stochastic processes to default data with the aim of investigating credit contagion; on the other hand, focusing on the validation aspects, we assess the performance of these models in terms of predictive accuracy using both the standard metrics and a recently developed criterion, whose main advantage is being not dependent on the type of predicted variable. This new criterion, already validated on continuous and binary data, is extended also to the case of discrete data providing results which are coherent to those obtained with the classical predictive accuracy measures. To shed light on the usefulness of our approach, we apply Poisson autoregressive models with exogenous covariates (PARX) to the quarterly count of defaulted loans among Italian real estate and construction companies, comparing the performance of several specifications. We find that adding a contagion component leads to a decisive improvement in model accuracy with respect to the only autoregressive specification.

Minimum Cost SDN Routing With Reconfiguration Frequency Constraints

Software-defined network (SDN) controllers include mechanisms to globally reconfigure the network in order to respond to a changing environment. As demands arrive or leave the system, the globally optimum flow configuration changes over time. Although the optimum configuration can be computed with standard iterative methods, convergence may be slower than system variations, and hence it may be preferable to interrupt the solver and restart. In this paper, we focus on the class of iterative solvers with an exponential decrease over time in the optimality gap. Assuming dynamic arrivals and departures of demands, the computed optimality gap at each iteration Q(t) is described by an auto-regressive stochastic process. At each time slot, the controller may choose to: 1) stop the iterative solver and apply the best found configuration to the network or 2) allow the solver to continue the iterations keeping the network in its suboptimal form. Choice 1) reduces the optimality gap leading to smaller routing costs but requires flow reconfiguration which hurts QoS and system stability. To limit the negative impact of reconfigurations, we propose two control policies that minimize the time-average routing cost while respecting a network reconfiguration budget. We experiment with realistic network settings using standard linear programming tools from SDN industry. In the experiments conducted over the GEANT networks and fat tree networks, our policies provide a practical means of keeping the routing cost small within a given reconfiguration constraint.

A Bayesian hierarchical spatio-temporal rainfall model

ABSTRACTA Bayesian hierarchical spatio-temporal rainfall model is presented and analysed. The model has the ability to deal with extensive missing or null values, uses a sophisticated variance stabilising rainfall pre-transformation, incorporates a new elevation model and can provide sub-catchment rainfall estimation and interpolation using a sequential kriging scheme. The model uses a vector autoregressive stochastic process to represent the time dependence of the rainfall field and an exponential covariogram to model the spatial correlation of the rainfall field. The model can be readily generalised to other types of stochastic processes. In this paper, some results of applying the model to a particular rainfall catchment are presented.

Developing a Stochastic Model of Queue Length at a Signalized Intersection

This paper proposes a stochastic hybrid dynamic model of the queue-length at a signalized intersection. The flow rate along with traffic light variables are used to define the evolution of the queue-lengths and it evolves as a piecewise linear function, being the integral of the difference between arrival and departure rate; these arrival and departure rates are described by stochastic AR model with mode-dependent parameters. The mode changes are modeled by a first order 2 or 3-state Markov process. The traffic flow rate is described using a mode-dependent first autoregressive (AR) stochastic process. The technique is applied to actual traffic flow data from the city of Jakarta, Indonesia and synthetic data from VISSIM traffic simulator. The model thus obtained via EM parameter estimation is validated by using the online particle filter. This technique can be useful and practical for periodically updating the parameters of hybrid model leading to an adaptive traffic flow state estimator as crucial part for the synthesis of traffic light control.

Inflation, interest rate and output gap in the US economy: a vine copula modeling

PurposeThe purpose of this paper is to investigate the relationship between inflation, interest rate, and output gap in the US economy in the post Second World War period, without assuming any structure nor imposing any restriction on that relationship.Design/methodology/approachThe authors apply vine copula modeling to investigate asymmetry and tail behavior on both conditional and unconditional dependence among those variables. The dependence parameter is allowed to evolve over time according to a stochastic autoregressive processes. Additionally, a conditional expectation based on vine copula is used to analyze the conditional expectation of interest rate.FindingsThe results suggest that the joint distribution, both conditional and unconditional, of the interest rate and inflation is asymmetric to the left, while the pair interest rate and output gap have symmetrical distributions coupled with low persistence and high volatility. Besides the unquestionable evidence that the US monetary policy has been mostly focused on inflation stabilization, there is also indication of nonlinearity in the conditional expected interest rate and asymmetric behavior by the Federal Reserve in the long run.Originality/valueThe vine copula modeling allows for several forms of asymmetries and tail dependence, which is a flexible modeling strategy for multivariate distributions. Moreover, the conditional expectation implied by vine copulas is suitable to account for nonlinearity in the interest rate conditional on inflation and output gap.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations.

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Explaining Returns through Valuation

This paper develops an analytically coherent yet parsimonious framework which explains market returns in terms of contemporaneous information. It anchors on the idea that valuation (static perspective) can be connected to the dynamics that explains returns, and vice versa. The framework requires two components. First, an explicit function that maps information to an estimate of value—a valuation heuristic. Second, the framework assumes that the difference between a firm’s actual value and value-per-heuristic follows an autoregressive stochastic process with a contraction parameter but no intercept. The contraction parameter can be estimated efficiently and non-parametrically. This modelling suffices to correlate implied returns with realized returns. Using scaled EPS forecasts as valuation heuristics, we empirically evaluate the framework’s validity and robustness. Its explanatory power compares favorably to that of traditional OLS regressions, despite only requiring a single parameter. In a setting with pooled annual data, the implied and realized returns correlations are 73% and 64%, respectively.

Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models

The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of their popularity, MSE and RMSE lack an analytical framework allowing their calculation for known dynamic processes and cannot be reliably computed over short time series. To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state-space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales and exploits the SS parameters to quantify analytically the complexity of the process. The resulting linear MSE (LMSE) measure is first tested in simulations, both theoretically to relate the multiscale complexity of AR processes to their dynamical properties and over short process realizations to assess its computational reliability in comparison with RMSE. Then, it is applied to the time series of heart period, arterial pressure, and respiration measured for healthy subjects monitored in resting conditions and during physiological stress. This application to short-term cardiovascular variability documents that LMSE can describe better than RMSE the activity of physiological mechanisms producing biological oscillations at different temporal scales.

Univariate Conditional Distributions of an Open-Loop TAR Stochastic Process

<p>Clusters of large values are observed in sample paths of certain open-loop threshold autoregressive (TAR) stochastic processes. In order to characterize the stochastic mechanism that generates this empirical stylized fact, three types of marginal conditional distributions of the underlying stochastic process are analyzed in this paper. One allows us to find the conditional variance function that explains the aforementioned stylized fact. As a by-product, we are able to derive a sufficient condition to have asymptotic weak stationarity in an open-loop TAR stochastic process.</p>

Visibility graph analysis for re-sampled time series from auto-regressive stochastic processes

Visibility graph (VG) and horizontal visibility graph (HVG) play a crucial role in modern complex network approaches to nonlinear time series analysis. However, depending on the underlying dynamic processes, it remains to characterize the exponents of presumably exponential degree distributions. It has been recently conjectured that there is a critical value of exponent λc=ln3/2, which separates chaotic from correlated stochastic processes. Here, we systematically apply (H)VG analysis to time series from autoregressive (AR) models, which confirms the hypothesis that an increased correlation length results in larger values of λ > λc. On the other hand, we numerically find a regime of negatively correlated process increments where λ < λc, which is in contrast to this hypothesis. Furthermore, by constructing graphs based on re-sampled time series, we find that network measures show non-trivial dependencies on the autocorrelation functions of the processes. We propose to choose the decorrelation time as the maximal re-sampling delay for the algorithm. Our results are detailed for time series from AR(1) and AR(2) processes.

Distributed acoustic signature identification using incremental adaptive networks

Considerable amount of information about objects is obtained from their acoustic signature. Since the acoustic signal is physically propagated over a geographical region, any fixed point observer records data with a limited quality. Moving sources also decreases the generality of single point modeling. In this paper, we propose employing distributed incremental adaptive networks for the aim of acoustic signature identification, as a time-varying autoregressive (TVAR) stochastic process. The distributed adaptive sensor network considers spatial and temporal challenges simultaneously and provides real-time estimations. By formulating the problem under non-stationary conditions, we proceed to show the superiority of the proposed incremental adaptive algorithm compared to the classical single point observations methods. To practically prove this merit, the proposed algorithms were implemented on and evaluated using a real sensor network dataset recorded from moving vehicles for the first time in the adaptive networks field; this is a substantial real-world validation test. The experimental results well support the claim and demonstrate the excellence and competence of distributed incremental adaptive networks for this case.

Exact Finite-Dimensional Filter for Exponential Functionals of the State of Beneš Systems

The purpose of this article is to derive finite-dimensional filters for exponential functionals of the state of nonlinear Beneš type filtering systems with correlated noises. These new filters can be applied in the state reconstruction of doubly–stochastic auto–regressive processes.

Predictability of threshold exceedances in dynamical systems

In a low-order model of the general circulation of the atmosphere we examine the predictability of threshold exceedance events of certain observables. The likelihood of such binary events–the cornerstone also for the categoric (as opposed to probabilistic) prediction of threshold exceedances–is established from long time series of one or more observables of the same system. The prediction skill is measured by a summary index of the ROC curve that relates the hit- and false alarm rates. Our results for the examined systems suggest that exceedances of higher thresholds are more predictable; or in other words: rare large magnitude, i.e., extreme, events are more predictable than frequent typical events. We find this to hold provided that the bin size for binning time series data is optimized, but not necessarily otherwise. This can be viewed as a confirmation of a counterintuitive (and seemingly contrafactual) statement that was previously formulated for more simple autoregressive stochastic processes. However, we argue that for dynamical systems in general it may be typical only, but not universally true. We argue that when there is a sufficient amount of data depending on the precision of observation, the skill of a class of data-driven categoric predictions of threshold exceedances approximates the skill of the analogous model-driven prediction, assuming strictly no model errors. Therefore, stronger extremes in terms of higher threshold levels are more predictable both in case of data- and model-driven prediction. Furthermore, we show that a quantity commonly regarded as a measure of predictability, the finite-time maximal Lyapunov exponent, does not correspond directly to the ROC-based measure of prediction skill when they are viewed as functions of the prediction lead time and the threshold level. This points to the fact that even if the Lyapunov exponent as an intrinsic property of the system, measuring the instability of trajectories, determines predictability, it does that in a nontrivial manner.