First-order Autoregression Research Articles

Establishment and application of a fractional difference-autoregressive model for daily runoff time series forecasting based on wavelet analysis

ABSTRACTThe daily runoff is a complicated hydrological time-series, its extreme changes will affect not only the safety of the ships underway but also the dispatching of water transportation. Daily runoff forecast is a hot topic in hydrologic analysis and water transport planning. The fractional difference-autoregressive model based on wavelet analysis (WFIAR) is used to forecast the daily runoff. The daily runoff time series from 2002 to 2013 of Hankou Hydrologic Station are decomposed by the orthogonal db4 wavelet function into a series of stationary high-frequency sub-sequences and a non-stationary low frequency subsequence. According to the Hurst exponent of the low frequency subsequence, the appropriate difference order is determined and fractional difference is made. The differenced low-frequency part and high-frequency parts set up autoregressive models separately. These models are combined to forecast the daily runoff time series in 2014 and 2015 separately. The first-order difference autoregression (DIAR) model and the first-order autoregression (WDIAR) model based on wavelet analysis are also established to compare the forecasting accuracy of different models. The results show that the prediction accuracy of WFIAR is higher than the other two models that reveal the advantage of WDIAR model in daily runoff forecast.

The First-Order Nonlinear Autoregressive Model with Skew Normal Innovations: A Semiparametric Approach

In this paper, we consider a nonlinear autoregressive model of order one with skew normal innovations. This allows a flexible treatment of asymmetry and heavy tails in the conditional distribution of the data. A semiparametric method is proposed to estimate the nonlinear regression function by using the conditional least squares method for parametric estimation and the nonparametric kernel approach by using the nonparametric factor that is derived by a local L2-fitting criterion for the regression adjustment estimation. Some strong and weak consistency of the semiparametric estimators in this model are presented. Furthermore, in a simulation study, the accuracy of the proposed method is verified. Also the method is applied for annual ring width data of the Pinus Eldarica trees of Kelardasht site in the north of Iran to show the applicability of the proposed model.

Standard Errors of Risk and Performance Estimators with Serially Correlated Returns

A new method for computing the standard errors of returns-based risk and performance estimators for serially correlated returns is developed. The method uses the fact that any such estimator can be represented as the sum of returns that are transformed using the estimator’s influence function, and the fact that the variance of such a sum can be estimated by estimating the zero-frequency value of the spectral density of the influence function transformed returns. The spectral density is estimated by fitting a polynomial to the periodogram using a generalized linear model for exponential distributions, with elastic net regularization. An adaptive prewhitening is used to obtain good performance for large as well as small serial correlation of returns. We show that the method works much better in comparison to conventional standard error computational methods, for a collection of 13 hedge funds whose returns have varying degrees of serial correlation. Extensive Monte Carlo mean-squared error performance studies for a number of commonly used risk and performance estimators, using first-order autoregression returns, show that the new method delivers good performance for serial correlations ranging from 0.0 to 0.9, over which range it has better performance than alternative Newey-West methods. Simulations also show that the new method works well for Garch(1,1) returns processes

The challenge of estimating a residual spatial autocorrelation from forest inventory data

Estimates of stand averages are needed by forest management for planning purposes. In forest enterprise inventories supported by remotely sensed auxiliary data, these estimates are typically derived exclusively from a model that does not consider stand effects in the study variable. Variance estimators for these means may seriously underestimate uncertainty, and confidence intervals may be too narrow when a model used for computing a stand mean omits a nontrivial stand effect in one or more of the model parameters, a nontrivial spatial distance dependent autocorrelation in the model residuals, or both. In simulated sampling from 36 populations with stands of different sizes and differing with respect to (i) the correlation between a study variable (Y) and two auxiliary variables (X), (ii) the magnitude of stand effects in the intercept of a linear population model linking X to Y, and (iii) a first-order autoregression in Y and X, we learned that none of the tested designs provided reliable estimates of the within-stand autocorrelation among model residuals. More-reliable estimates were possible from stand-wide predictions of Y. The anticipated bias in an estimated autoregression parameter had a modest influence on estimates of variance and coverage of nominal 95% confidence intervals for a synthetic stand mean.

Multichannel Sequential Detection—Part I: Non-i.i.d. Data

We consider the problem of sequential signal detection in a multichannel system assuming that the number and location of signals are either unknown or only partially known a priori . We focus on the design and analysis of two sequential hypothesis tests: the generalized sequential likelihood ratio test and the mixture sequential likelihood ratio test. We develop an asymptotic theory for a general stochastic model, where the various data streams can be coupled and correlated, and the data in each stream can be dependent and non-identically distributed. Specifically, we show that the two proposed sequential detection procedures asymptotically minimize the expected sample size and even higher moments of the sample size in the class of hypothesis tests with given probabilities of errors under weak distributional assumptions. We also propose efficient importance sampling algorithms for estimating error probabilities of the sequential tests by Monte Carlo simulation. The general theory is illustrated with several practical examples, such as the detection of signals, in Gaussian hidden Markov models, white Gaussian noises with unknown intensity, and testing of the first-order autoregression’s correlation coefficient. Finally, we illustrate our asymptotic results and compare the two proposed procedures with a simulation study.

Testing the compounding structure of the CP-INARCH model

A statistical test to distinguish between a Poisson INARCH model and a Compound Poisson INARCH model is proposed, based on the form of the probability generating function of the compounding distribution of the conditional law of the model. For first-order autoregression, the normality of the test statistics’ asymptotic distribution is established, either in the case where the model parameters are specified, or when such parameters are consistently estimated. As the test statistics’ law involves the moments of inverse conditional means of the Compound Poisson INARCH process, the analysis of their existence and calculation is performed by two approaches. For higher-order autoregressions, we use a bootstrap implementation of the test. A simulation study illustrating the finite-sample performance of this test methodology in what concerns its size and power concludes the paper.

Graph-Based Transform for 2D Piecewise Smooth Signals With Random Discontinuity Locations.

The graph-based block transform recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, in existing methods, overheads are required to describe the graph of the block, from which the decoder has to calculate the transform via time-consuming eigendecomposition. To address these problems, in this paper, we aim to develop a single graph-based transform for a class of 2D piecewise smooth signals with similar discontinuity patterns. We first consider the deterministic case with a known discontinuity location in each row. We propose a 2D first-order autoregression (2D AR1) model and a 2D graph for this type of signals. We show that the closed-form expression of the inverse of a biased Laplacian matrix of the proposed 2D graph is exactly the covariance matrix of the proposed 2D AR1 model. Therefore, the optimal transform for the signal are the eigenvectors of the proposed graph Laplacian. Next, we show that similar results hold in the random case, where the locations of the discontinuities in different rows are randomly distributed within a confined region, and we derive the closed-form expression of the corresponding optimal 2D graph Laplacian. The theory developed in this paper can be used to design both pre-computed transforms and signal-dependent transforms with low complexities. Finally, depth image coding experiments demonstrate that our methods can achieve similar performance to the state-of-the-art method, but our complexity is much lower.

Sampling Schemes by Variables Inspection for the First-Order Autoregressive Model between Linear Profiles

We present four new sampling schemes by variables inspection to deal with the first-order autoregressive model between linear profiles. The first plan is based on exponentially weighted moving average (EWMA) and the rest of three plans are using the resubmitted sampling, repetitive group sampling (RGS), and multiple dependent state (MDS) sampling schemes. The nonlinear optimization problem is developed to find the number of profiles and the corresponding acceptance criteria, such that the producer’s and consumer’s risk are satisfied simultaneously. The efficiency of the proposed plans is compared with the conventional single sampling plan in terms of average sample number and the probability of acceptance. The result implies that all of the proposed sampling plans are superior to the single acceptance sampling plan by variables. In addition, the EWMA method appeared to be better than the others. The applications of proposed plans are shown with the help of industrial examples taken from calibration of an optical imaging system, and tire cornering stiffness test.

Linear Mixed Model for Analyzing Longitudinal Data: A Simulation Study of Children Growth Differences

Growth developmental research is one example of the application of longitudinal data that have correlated value over time. Linear Mixed Model (LMM) is an extension of classic statistical procedures that provides flexibility analysis in correlated longitudinal data and allows researcher to model the covariance structures that represent its random effects. This paper briefly describes growth curves model as a single LMM that represent two levels of observation, which focused on modeling its covariance structure to capture correlated information over time of individual performance. We apply LMM and model different types of its covariance structure in the simulation study of children’s growth differences based on the feeding methods. We perform simulation scenario using MIXED procedure in SAS system, based on three fit indices (-2RLL, AIC and SBC) and p-value significance level, we obtain Unstructured (UN) covariance is always be the best fit in presenting the characteristic of data but not the best choice considering inefficient numbers of parameters while Heterogeneous First-order Autoregressive (ARH(1)) is a proper alternative covariance structure with ease of data interpretation from fewer numbers of estimated parameters.

Measure of bullwhip effect in supply chains with first-order bivariate vector autoregression time-series demand model

With supply chains becoming increasingly global, the issue of bullwhip effect, a phenomenon attributable to demand fluctuation in the upstream section of the supply chains, has received greater attention from many researchers. However, most existing research studies on quantifying the bullwhip effect were conducted under the first-order autoregressive [AR(1)] incoming demand process or its variants as the fundamental demand process, thereby failing to account for the retailer demand dependency. This research work thus examined the bullwhip effect for the first-order bivariate vector autoregression [VAR(1)] demand process in a two-stage supply chain consisting of one supplier and two retailers. The impacts of the correlation parameters of the demand process, the correlation coefficient between the two error terms, and the variances of the error terms on the bullwhip effect were investigated. As such, the measure of the bullwhip effect was established using an analytical approach in which the minimum mean square error (MMSE) forecasting method and the base stock policy were applied to all members of the supply chain. Numerical experiments were then conducted to illustrate the behavior of the bullwhip effect with respect to various parameters of the demand processes to see in which situations the bullwhip effect would be absent. In addition, an evaluation of the inventory variance ratio was analyzed.

Thoracoscopic Vertebrectomy for Thoracolumbar Junction Fractures and Tumors: Surgical Technique and Evaluation of the Learning Curve.

Retrospective study. The authors evaluated the surgical technique and learning curve for video-assisted thoracoscopic surgery (VATS) for treating thoracolumbar junction burst fractures and bony tumors by examining surgical data and outcome for the first 30 VATS procedures performed by a single surgeon at a training institution. VATS is commonly used in the treatment of early-stage lung cancer. Widespread use of this technique among neurosurgeons is limited by the lack of cases and the steep learning curve. This study was a retrospective case series of the first 30 T12 and L1 thoracoscopic vertebrectomies from 2003 to 2008. The sample was limited to 1 surgeon and 1 region of the spine to minimize the potential variation so that a learning curve could be assessed. Surgical data and outcomes were analyzed. Estimated blood loss and operation time were analyzed using a linear generalized estimating equation model with a first-order autoregression correlation structure. The average operative time for thoracoscopic corpectomy was 270±65 minutes (range, 160-416 min). Operating room time decreased significantly after the first 3 operations. The authors observed a stable linear decrease in operating time over the course of the study. The average blood loss during the thoracoscopic procedure was 433±330 mL (range, 100-1500 mL) and did not change as the series progressed. Complications and conversions to open procedures occurred in 2 patients and were evenly distributed throughout the series. Thoracoscopic vertebrectomy at the thoracolumbar junction has a relatively long learning curve. In this series, operating room time improved dramatically after the first 3 cases but continued to improve subsequently. The learning curve can be accomplished without an increase in blood loss, complications, rate of conversion to open procedures, or frequency of misplaced instrumentation.

Periodic autoregressive stochastic volatility

This paper proposes a stochastic volatility model (PAR-SV) in which the log-volatility follows a first-order periodic autoregression. This model aims at representing time series with volatility displaying a stochastic periodic dynamic structure, and may then be seen as an alternative to the familiar periodic GARCH process. The probabilistic structure of the proposed PAR-SV model such as periodic stationarity and autocovariance structure are first studied. Then, parameter estimation is examined through the quasi-maximum likelihood (QML) method where the likelihood is evaluated using the prediction error decomposition approach and Kalman filtering. In addition, a Bayesian MCMC method is also considered, where the posteriors are given from conjugate priors using the Gibbs sampler in which the augmented volatilities are sampled from the Griddy Gibbs technique in a single-move way. As a-by-product, period selection for the PAR-SV is carried out using the (conditional) deviance information criterion (DIC). A simulation study is undertaken to assess the performances of the QML and Bayesian Griddy Gibbs estimates in finite samples while applications of Bayesian PAR-SV modeling to daily, quarterly and monthly S&P 500 returns are considered.

Persistence in the long-run expected rate of return for corporate pension plans

Abstract Firms that sponsor a defined benefit pension plan are suspected of managing earnings through the choice of the expected long-run rate of return to pension assets. However, data on this rate show it to be quite persistent with more than 50% of firms leaving their ERR unchanged from one year to the next. To capture this persistence, I model the rate using a first-order autoregression. Asset allocation information is included in the model. Endogeneity bias is addressed by estimating the dynamic panel data model using a system GMM estimator. No evidence of earnings management, measured by the relative size of the pension plan to net income and by acquisition activity, was found.

The Natural History of Kidney Graft Cortical Microcirculation Determined by Real-Time Contrast-Enhanced Sonography (RT-CES).

BackgroundKidney transplantation is the therapy of choice for end-stage kidney disease. Graft’s life span is shorter than expected due in part to the delayed diagnosis of various complications, specifically those related to silent progression. It is recognized that serum creatinine levels and proteinuria are poor markers of mild kidney lesions, which results in delayed clinical information. There are many investigation looking for early markers of graft damage. Decreasing kidney graft cortical microcirculation has been related to poor prognosis in kidney transplantation. Cortical capillary blood flow (CCBF) can be measured by real-time contrast-enhanced sonography (RT-CES). Our aim was to describe the natural history of CCBF over time under diverse conditions of kidney transplantation, to explore the influence of donor conditions and recipient events, and to determine the capacity of CCBF for predicting renal function in medium term.Patients and MethodsRT-CES was performed in 79 consecutive kidney transplant recipients during the first year under regular clinical practice. Cortical capillary blood flow was measured. Clinical variables were analyzed. The influence of CCBF has been determined by univariate and multivariate analysis using mixed regression models based on sequential measurements for each patient over time. We used a first-order autoregression model as the structure of the covariation between measures. The post-hoc comparisons were considered using the Bonferroni correction.ResultsThe CCBF values varied significantly over the study periods and were significantly lower at 48 h and day 7. Brain-death donor age and CCBF levels showed an inverse relationship (r: -0.62, p<0.001). Living donors showed higher mean CCBF levels than brain-death donors at each point in the study. These significant differences persisted at month 12 (54.5 ± 28.2 vs 33.7 ± 30 dB/sec, living vs brain-death donor, respectively, p = 0.004) despite similar serum creatinine levels (1.5 ± 0.3 and 1.5 ± 0.5 mg/dL). A sole rejection episode was associated with lower overall CCBF values over the first year. CCBF defined better than level of serum creatinine the graft function status at medium-term.ConclusionRT-CES is a non-invasive tool that can quantify and iteratively estimate cortical microcirculation. We have described the natural history of cortical capillary blood flow under regular clinical conditions.

Dividend Yields, Dividend Growth, and Return Predictability in the Cross Section of Stocks

AbstractThere is a generalized conviction that variation in dividend yields is exclusively related to expected returns and not to expected dividend growth, for example, Cochrane’s (2011) presidential address. We show that this pattern, although valid for the aggregate stock market, is not true for portfolios of small and value stocks, where dividend yields are related mainly to future dividend changes. Thus, the variance decomposition associated with the aggregate dividend yield has important heterogeneity in the cross section of equities. Our results are robust to different forecasting horizons, econometric methodology (long-horizon regressions or first-order vector autoregression), and alternative decomposition based on excess returns.

Solving asset pricing models with stochastic volatility

This paper provides a closed-form solution for the price-dividend ratio in a standard asset pricing model with stochastic volatility. The growth rate of the endowment is a first-order Gaussian autoregression, while the stochastic volatility innovations can be drawn from any distribution for which the moment-generating function exists. The solution is useful in allowing comparisons among numerical methods used to approximate the nontrivial closed form. The closed-form solution reveals that, when using perturbation methods around the deterministic steady state, the approximate solution needs to be sixth-order accurate in order for the parameter capturing the conditional standard deviation of the stochastic volatility process to be present.

Arbitrage-Free Gaussian Affine Term Structure Model with Observable Factors

This paper analyzes a simple discrete-time affine multifactor model of the term structure of interest rates in which the pricing factors that follow a Gaussian first-order vector autoregression are observable and there are no possibilities for risk-free arbitrage. We present the theoretical results for the compatible risk-neutral dynamics of observable factors in a maximally flexible way consistent with no-arbitrage under the assumption that the factor loadings of some yields are specified exogenously.

Limit theory for an explosive autoregressive process

Large sample properties are studied for a first-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coefficient, the least-squares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error distribution, and hence an invariance principle applies. The coefficient based test and the t test have better power for testing the hypothesis of zero intercept in the explosive process than in the stationary process.

Exchange rate dynamics, forecasting and the microstructure approach: empirical evidence for an emerging market economy

This article investigates exchange rate dynamics and forecasting in an emerging market economy by incorporating elements from the market microstructure approach. The investigation finds that in the Dominican Republic imbalances between purchases and sales in the foreign exchange market are significant in explaining exchange rate dynamics over and above traditional purchasing power parity (PPP) fundamentals. The investigation runs a forecasting competition, and the preferred model beats a battery of competitors at the 3-month horizon. But an uncovered interest parity (UIP) specification outperforms the otherwise preferred model, a PPP benchmark and a first-order autoregression over 6- and 12-month forecast horizons.

INTERTEMPORAL PORTFOLIO ALLOCATION AND HEDGING DEMAND: AN APPLICATION TO SOUTH AFRICA

This paper analyses the intertemporal hedging demand for stocks and bonds in South Africa, the United Kingdom and the United States. The analysis is done using an approximate solution method for the optimal consumption and wealth portfolio problem of an infinitely long-lived investor. Investors are assumed to have Epstein-Zin-Weil-type preferences and face asset returns described by a first-order vector autoregression in returns and state variables. The results show that the mean intertemporal hedging demands for stocks are considerably smaller in SA than in the UK or the US, whilst the mean intertemporal hedging demand for bonds are not significantly different from zero in any of the countries considered. Furthermore, it is found that stocks in the US and the UK do not present a useful hedging opportunity for an investor in SA, nor do SA stocks present a useful hedging opportunity for investors from the UK or the US.