Autoregressive Function Research Articles

Moderate deviation principle in nonlinear bifurcating autoregressive models

Recently, nonparametric techniques have been proposed to study bifurcating autoregressive processes. One can build Nadaraya–Watson type estimators of the two autoregressive functions as in Bitseki Penda et al. (2017) and Bitseki Penda and Olivier (2017). In the present work, we prove moderate deviation principle for these estimators.

A battle tank simulator for eye and hand coordination tasks under horizontal whole-body vibration

This paper describes the development of a simulator to reproduce gunner’s target tracking tasks in a main battle tank, under whole-body vibration conditions. For specifying the vibration and tracking conditions, three-degree-of-freedom acceleration was measured in a tracked armored vehicle, equipped with a 105 mm cannon, running in a battlefield test track. The electrohydraulic dynamics of the turret systems was experimentally identified as black-box autoregressive functions. A pneumatic actuation system and a real-time control software were designed to reproduce horizontal, single-axis periodic motion with the dominant frequency observed in field measurements. The control software displays the target and sight points and acquires the turret pointing command from an adapted gunner’s handle joystick. The root mean square error between target and simulated turret position allows assessing gunner’s target acquisition and tracking performance under periodic vibration.

Dependence Structures and Systemic Risk of Government Securities Markets in Central and Eastern Europe: A CoVaR-Copula Approach

In this study, we proposed a new empirical method by combining generalized autoregressive score functions and a copula model with high-frequency data to model the conditional time-varying joint distribution of the government bond yields between Poland/Czech Republic/Hungary, and Germany. Capturing the conditional time-varying joint distribution of these bond yields allowed us to precisely measure the dependence of the government securities markets. In particular, we found a high dependence of these government securities markets in the long term, but a low dependence in the short term. In addition, we report that the Czech Republic showed the highest dependence with Germany, while Hungary showed the lowest. Moreover, we found that the systemic risk dynamics were consistent with the idea that the global financial crisis not only had spillover effects on countries with weak economic fundamentals (e.g., Hungary, which had the highest systemic risk), but also had contagion effects for both CEEC-3 countries and Germany. Finally, we confirm that three major market events, namely the EU accession, the global financial crisis, and the European debt crisis, caused structural changes to the dynamic correlation.

TESTS FOR TAR MODELS VS. STAR MODELS--A SEPARATE FAMILY OF HYPOTHESES APPROACH

The threshold autoregressive (TAR) model and the smooth threshold autoregressive (STAR) model have been popular parametric nonlinear time series models for the past three decades or so. As yet there is no formal statistical test in the literature for one against the other. The two models are fundamentally different in their autoregressive functions, the TAR model being generally discontinuous while the STAR model is smooth (except in the limit of infinitely fast switching for some cases). Following the approach initiated by Cox (1961, 1962), we treat the test problem as one of separate families of hypotheses. The test statistic under a STAR model is shown to follow asymptotically a chi-squared distribution, and the one under a TAR model can be expressed as a functional of a chi-squared process. We present numerical results with both simulated and real data to assess the performance of our procedure.

About Local Projection Impulse Response Function Reliability

I compare the performance of the vector autoregressive (VAR) model impulse response function estimator with the Jorda (2005) local projection (LP) methodology. In a Monte Carlo experiment, I demonstrate that when the data generating process is a well-specified VAR, the standard impulse response function estimator is the best option. However, when the sample size is small, and the model lag-length is misspecified, I prove that the local projection estimator is a competitive alternative. Finally, I show how to improve the local projection performance by fixing the lag-length at each horizon.

Analysis of autoregressive models with symmetric stable innovations

ABSTRACTThis paper develops algorithms for fitting autoregressive models with symmetric stable innovations using auto-covariation function. A recursive algorithm is proposed for generalized Yule-Walker estimation of autoregressive coefficients and partial auto-covariation function. It also introduces a new information criterion, useful for consistent order selection. Applications of the proposed methods are illustrated using observations simulated from autoregressive models with symmetric stable innovations as well as by analysing a set of real data.

Transportation and concentration inequalities for bifurcating Markov chains

We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful concentration inequalities. We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive function.

Urbanization, democracy, bureaucratic quality, and environmental degradation

The study examines the relationship between urbanization and environment degradation while controlling for political environment in 38 African countries over the period 1970–2011. Using panel cointegration and causality analyses, we find that urbanization, environmental degradation (CO2 emissions) and political economy variables (democracy and bureaucratic quality) are cointegrated. Second, democracy and bureaucratic quality are effective in reducing environmental degradation in the long-run. Third, there are positive bi-directional relationships between CO2 emissions and affluence and population as shown by panel vector autoregressive and impulse response functions. However, a negative uni-directional relationship runs from CO2 emissions to bureaucratic quality. These results suggest that political economy variables are important in explaining the relationship between urbanization and environmental degradation.

Varying coefficient functional autoregressive model with application to the U.S. treasuries

The functional autoregressive (FAR) model belongs to an important class of models for dependent functional data analysis (FDA) and has been investigated intensively in many applications, especially for modeling the autoregressive dynamics of high-volume time series data. In this paper, we extend the classical FAR model to address the intrinsic local stationarity of a process through a varying-coefficient (VC) FAR model which characterizes nonconstant dependence between the functional predictors and the functional responses with a time-varying operator. We express the nonparametric models under sieves, whereas the time-varying operator is estimated by a local regression technique. The asymptotic properties of the estimated operator are established in this paper. Our simulation study points to a substantial gain from the VC-FAR modeling as the underlying smooth structural changes can be captured precisely. As an application, we consider the yield curves of the U.S. government bonds with different maturities. Our proposed model provides a reasonable interpretation of the dynamic transition consistent to the economic events triggering the evolution shifts, and performs more accurately on forecasting actual yield data at both short and long horizons, compared with various standard benchmark forecasts.

Forecasting Limit Order Book Liquidity Supply-Demand Curves with Functional Autoregressive Dynamics

We develop a dynamic model to simultaneously characterize the liquidity demand and supply in limit order book. The joint dynamics is modelled in a unified Vector Functional AutoRegressive (VFAR) framework. We derive a closed-form maximum likelihood estimator under sieves and establish asymptotic consistency of the proposed method under mild conditions. We find the VFAR model presents strong interpretability and accurate out-of-sample forecast. In application to limit order book records of 12 stocks in NASDAQ traded from 2 Jan 2015 to 6 Mar 2015, the VFAR model yields R2 values as high as 98.5 percent for in-sample estimation and 98.2 percent in out-of-sample forecast experiments. It produces accurate 5-, 25- and 50-$minute forecasts, with RMSE as low as 0.09 to 0.58 and MAPE as low as 0.3 to 4.5 percent. The predictive power stably reduces trading cost in the order splitting strategies and achieves excess gains of 31 basis points on average.

Functional Autoregression for Sparsely Sampled Data

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with nonnegligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with broader applicability and improved computational efficiency over standard Gaussian process models. We prove finite-sample forecasting and interpolation optimality properties of the proposed model, which remain valid with the Gaussian assumption relaxed. An efficient Gibbs sampling algorithm is developed for estimation, inference, and forecasting, with extensions for FAR(p) models with model averaging over the lag p. Extensive simulations demonstrate substantial improvements in forecasting performance and recovery of the autoregressive surface over competing methods, especially under sparse designs. We apply the proposed methods to forecast nominal and real yield curves using daily U.S. data. Real yields are observed more sparsely than nominal yields, yet the proposed methods are highly competitive in both settings. Supplementary materials, including R code and the yield curve data, are available online.

An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves

We propose an adaptive functional autoregressive (AFAR) forecast model to predict electricity price curves. With time-varying operators, the AFAR model can be safely used in both stationary and nonstationary situations. A closed-form maximum likelihood (ML) estimator is derived under stationarity. The result is further extended for nonstationarity, where the time-dependent operators are adaptively estimated under local homogeneity. We provide theoretical results of the ML estimator and the adaptive estimator. Simulation study illustrates nice finite sample performance of the AFAR modeling. The AFAR model also exhibits a superior accuracy in the forecast exercise of the California electricity daily price curves compared to several alternatives.

An integrated population model for bird monitoring in North America.

Integrated population models (IPMs) provide a unified framework for simultaneously analyzing data sets of different types to estimate vital rates, population size, and dynamics; assess contributions of demographic parameters to population changes; and assess population viability. Strengths of an IPM include the ability to estimate latent parameters and improve the precision of parameter estimates. We present a hierarchical IPM that combines two broad-scale avian monitoring data sets: count data from the North American Breeding Bird Survey (BBS) and capture-recapture data from the Monitoring Avian Productivity and Survivorship (MAPS) program. These data sets are characterized by large numbers of sample sites and observers, factors capable of inducing error in the sampling and observation processes. The IPM integrates the data sets by modeling the population abundance as a first-order autoregressive function of the previous year's population abundance and vital rates. BBS counts were modeled as a log-linear function of the annual index of population abundance, observation effects (observer identity and first survey year), and overdispersion. Vital rates modeled included adult apparent survival, estimated from a transient Cormack-Jolly-Seber model using MAPS data, and recruitment (surviving hatched birds from the previous season+dispersing adults) estimated as a latent parameter. An assessment of the IPM demonstrated it could recover true parameter values from 200 simulated data sets. The IPM was applied to data sets (1992-2008) of two bird species, Gray Catbird (Dumetella carolinensis) and Wood Thrush (Hylocichla mustelina) in the New England/Mid-Atlantic coastal Bird Conservation Region of the United States. The Gray Catbird population was relatively stable (trend +0.4% per yr), while the Wood Thrush population nearly halved (trend -4.5% per yr) over the 17-yr study period. IPM estimates of population growth rates, adult survival, and detection and residency probabilities were similar and as precise as estimates from the stand-alone BBS and CJS models. A benefit of using the IPM was its ability to estimate the latent recruitment parameter. Annual growth rates for both species correlated more with recruitment than survival, and the relationship for Wood Thrush was stronger than for Gray Catbird. The IPM's unified modeling framework facilitates integration of these important data sets.

Kernel estimates of nonparametric functional autoregression models and their bootstrap approximation

This paper considers a nonparametric functional autoregression model of order one. Existing contributions addressing the problem of functional time series prediction have focused on the linear model and literatures are rather lacking in the context of nonlinear functional time series. In our nonparametric setting, we define the functional version of kernel estimator for the autoregressive operator and develop its asymptotic theory under the assumption of a strong mixing condition on the sample. The results are general in the sense that high-order autoregression can be naturally written as a first-order AR model. In addition, a component-wise bootstrap procedure is proposed that can be used for estimating the distribution of the kernel estimation and its asymptotic validity is theoretically justified. The bootstrap procedure is implemented to construct prediction regions that achieve good coverage rate. A supporting simulation study is presented in the end to illustrate the theoretical advances in the paper.

A Sequential Semiparametric Estimation for Nonlinear Function in the Functional Autoregressive Model

Background/Objectives: The study aimed to predict regression function using semi-recursive kernel method in the first order functional auto regressive model through semiparametric estimation. Methods/Statistical Analysis: The parametric estimation by conditional nonlinear least squares method conducted; further, regression adjustment has been estimated by recursive smooth kernel approach and then investigate weak consistencies of the estimator; In this case, simulated results are presented using recursive kernel method for the semiparametric estimation. The Average Squared Error (ASE) computed to show the efficiency of the proposed estimation method. Finding: Updating causes considerably less computations in the semiparametric estimation when a sample of size n-1 changes to one of size n, this paper for estimating the adjustment factor proposed the recursive kernel method. The accuracy of the suggested method was tested by results of simulated study. Applications: The first order functional autoregressive model is currently used in financial and econometric studies. We propose semi-recursive semi parametric method for estimating this model and the results show that the semiparametric estimator of the auto regression function performs well.

Habitat Use and Selection by Giant Pandas

Animals make choices about where to spend their time in complex and dynamic landscapes, choices that reveal information about their biology that in turn can be used to guide their conservation. Using GPS collars, we conducted a novel individual-based analysis of habitat use and selection by the elusive and endangered giant pandas (Ailuropoda melanoleuca). We constructed spatial autoregressive resource utilization functions (RUF) to model the relationship between the pandas' utilization distributions and various habitat characteristics over a continuous space across seasons. Results reveal several new insights, including use of a broader range of habitat characteristics than previously understood for the species, particularly steep slopes and non-forest areas. We also used compositional analysis to analyze habitat selection (use with respect to availability of habitat types) at two selection levels. Pandas selected against low terrain position and against the highest clumped forest at the at-home range level, but no significant factors were identified at the within-home range level. Our results have implications for modeling and managing the habitat of this endangered species by illustrating how individual pandas relate to habitat and make choices that differ from assumptions made in broad scale models. Our study also highlights the value of using a spatial autoregressive RUF approach on animal species for which a complete picture of individual-level habitat use and selection across space is otherwise lacking.

Experimental modal analysis of electrical submersible pumps

The dynamic behaviour of an electrical submersible pump (ESP) under operational conditions installed in a test well is investigated by identification of its natural frequency and damping parameters. The study is conducted using an experimental modal analysis technique, the Least Square Complex Exponential (LSCE) method. The excitation was generated at one single point, because of the boundary conditions, by an impact hammer (i.e., single-input, multiple-output, or SIMO, analysis was performed), and the response signals were acquired by accelerometers fixed over the pump housing, thereby characterizing output-only processes. To evaluate the complex exponential function to fit the autoregressive function used to model the impact response function (IRF), auxiliary criteria, the averaged normalised power spectrum density (ANPSD) were used. Results have shown that the ESPs would have natural frequencies within the operational frequency range, from 30 to 62Hz, leading to the operation in resonance conditions.

A County‐Level Risk Assessment of the Deep Water Horizon Oil Spill in the Gulf of Mexico

This paper undertakes a risk assessment of coastal counties in the Gulf of Mexico impacted by the 2010 Deep Water Horizon oil spill. The study evaluates hazard risk from the perspective of community resilience, social capital, and access to resources. The proposed hazard risk location model re‐specifies risk as a function of hazard, exposure, and coping ability. The model employs an autoregressive function and a threshold analysis to develop a place‐based risk assessment. The results indicate that spatial variation in risk levels coincides with locational differences in social capital across the study area. Geographical proximity to the spill, population density, and unemployment rate are also key factors in determining overall risk. Furthermore, temporal variation in risk levels is determined by exposure to previous hazard events and changes in the business cycle.

Handling boundaries with the one‐dimensional first‐order recursive filter

In variational data assimilation, a crucial task is to determine the background‐error covariance matrix B. The effect of B on a field is often modelled through a series of operators among which is a correlation operator. The recursive filter, when properly normalized to ensure the maximum of the solution is 1, is a convenient correlation operator and is widely used as such. Often, multi‐dimensional operators are constructed from the product of one‐dimensional operators. When their coefficients are calculated appropriately, the normalized one‐dimensional first‐order recursive filter applied N times models an autoregressive function of order N.In ocean data assimilation, an extra difficulty is to handle, within the correlation operator, the boundaries formed by the different coastlines or the bathymetry. Handling the east/west wrapping or polar folds in global configurations are also part of the issue. The purpose of this article is to set up a mathematical framework for using the recursive filter in ocean data assimilation and properly accounting for boundaries. Generally, these problems are dealt with by calculating proper normalization factors using costly methods, or extending the grid near boundaries. It is shown that the normalization factors can be calculated inexpensively through an analytical formula with a corrective term to handle properly the boundary when Neumann or Dirichlet boundary conditions are used.In its classical formulation however, the recursive filter uses Robin (third type) boundary conditions. This formulation can be slightly modified in order to account for Neumann, Dirichlet or periodic boundary conditions. To do so, extra coefficients are calculated through a simple recursive formula. In a global 1/4° analysis framework, this new formulation is shown to be less expensive and more accurate than the classical formulation associated with an appropriate grid extension.

Autoregressive functions estimation in nonlinear bifurcating autoregressive models

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymp-totic and asymptotic behavior of the Nadaraya-Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by Tn, up to the depth n. Estimators achieve the classical rate |Tn| −β/(2β+1) in quadratic loss over Holder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth and a moderate deviations principle. Our proofs rely on specific techniques used to study bifurcating Markov chains. Finally, we address the question of asymmetry and develop an asymptotic test for the equality of the two autoregressive functions.