Beta seasonal autoregressive moving average models

In this paper, we introduce the class of beta seasonal autoregressive moving average (βSARMA) models for modelling and forecasting time series data that assume values in the standard unit interval. It generalizes the class of beta autoregressive moving average models [Rocha AV and Cribari-Neto F. Beta autoregressive moving average models. Test. 2009;18(3):529–545] by incorporating seasonal dynamics to the model dynamic structure. Besides introducing the new class of models, we develop parameter estimation, hypothesis testing inference, and diagnostic analysis tools. We also discuss out-of-sample forecasting. In particular, we provide closed-form expressions for the conditional score vector and for the conditional Fisher information matrix. We also evaluate the finite sample performances of conditional maximum likelihood estimators and white noise tests using Monte Carlo simulations. An empirical application is presented and discussed.     

Asymptotic Properties of the Empirical Spatial Extremogram

The extremogram is a useful tool for measuring extremal dependence and checking model adequacy in a time series. We define the extremogram in the spatial domain when the data is observed on a lattice or at locations distributed as a Poisson point process in d‐dimensional space. We establish a central limit theorem for the empirical spatial extremogram. We show these conditions are applicable for max‐moving average processes and Brown–Resnick processes and illustrate the empirical extremogram's performance via simulation. We also demonstrate its practical use with a data set related to rainfall in a region in Florida and ground‐level ozone in the eastern United States.     

Forecasting Macroeconomic Variables Under Model Instability

We compare different approaches to accounting for parameter instability in the context of macroeconomic forecasting models that assume either small, frequent changes versus models whose parameters exhibit large, rare changes. An empirical out-of-sample forecasting exercise for U.S. gross domestic product (GDP) growth and inflation suggests that models that allow for parameter instability generate more accurate density forecasts than constant-parameter models although they fail to produce better point forecasts. Model combinations deliver similar gains in predictive performance although they fail to improve on the predictive accuracy of the single best model, which is a specification that allows for time-varying parameters and stochastic volatility. Supplementary materials for this article are available online.     

Kalman filter-based modelling and forecasting of stochastic volatility with threshold

We propose a parametric nonlinear time-series model, namely the Autoregressive-Stochastic volatility with threshold (AR-SVT) model with mean equation for forecasting level and volatility. Methodology for estimation of parameters of this model is developed by first obtaining recursive Kalman filter time-update equation and then employing the unrestricted quasi-maximum likelihood method. Furthermore, optimal one-step and two-step-ahead out-of-sample forecasts formulae along with forecast error variances are derived analytically by recursive use of conditional expectation and variance. As an illustration, volatile all-India monthly spices export during the period January 2006 to January 2012 is considered. Entire data analysis is carried out using EViews and matrix laboratory (MATLAB) software packages. The AR-SVT model is fitted and interval forecasts for 10 hold-out data points are obtained. Superiority of this model for describing and forecasting over other competing models for volatility, namely AR-Generalized autoregressive conditional heteroscedastic, AR-Exponential GARCH, AR-Threshold GARCH, and AR-Stochastic volatility models is shown for the data under consideration. Finally, for the AR-SVT model, optimal out-of-sample forecasts along with forecasts of one-step-ahead variances are obtained.     

Space-time short- to medium-term wind speed forecasting

Accurate wind power forecasts depend on reliable wind speed forecasts. Numerical weather predictions utilize huge amounts of computing time, but still have rather low spatial and temporal resolution. However, stochastic wind speed forecasts perform well in rather high temporal resolution settings. They consume comparably little computing resources and return reliable forecasts, if forecasting horizons are not too long. In the recent literature, spatial interdependence is increasingly taken into consideration. In this paper we propose a new and quite flexible multivariate model that accounts for neighbouring weather stations’ information and as such, exploits spatial data at a high resolution. The model is applied to forecasting horizons of up to 1 day and is capable of handling a high resolution temporal structure. We use a periodic vector autoregressive model with seasonal lags to account for the interaction of the explanatory variables. Periodicity is considered and is modelled by cubic B-splines. Due to the model’s flexibility, the number of explanatory variables becomes huge. Therefore, we utilize time-saving shrinkage methods like lasso and elastic net for estimation. Particularly, a relatively newly developed iteratively re-weighted lasso and elastic net is applied that also incorporates heteroscedasticity. We compare our model to several benchmarks. The out-of-sample forecasting results show that the exploitation of spatial information increases the forecasting accuracy tremendously, in comparison to models in use so far.     

Forecasting time series of economic processes by model averaging across data frames of various lengths

This paper presents an extension of mean-squared forecast error (MSFE) model averaging for integrating linear regression models computed on data frames of various lengths. Proposed method is considered to be a preferable alternative to best model selection by various efficiency criteria such as Bayesian information criterion (BIC), Akaike information criterion (AIC), F-statistics and mean-squared error (MSE) as well as to Bayesian model averaging (BMA) and naïve simple forecast average. The method is developed to deal with possibly non-nested models having different number of observations and selects forecast weights by minimizing the unbiased estimator of MSFE. Proposed method also yields forecast confidence intervals with a given significance level what is not possible when applying other model averaging methods. In addition, out-of-sample simulation and empirical testing proves efficiency of such kind of averaging when forecasting economic processes.     

A Bayesian kriged Kalman model for short-term forecasting of air pollution levels

Summary.  Short-term forecasts of air pollution levels in big cities are now reported in news-papers and other media outlets. Studies indicate that even short-term exposure to high levels of an air pollutant called atmospheric particulate matter can lead to long-term health effects. Data are typically observed at fixed monitoring stations throughout a study region of interest at different time points. Statistical spatiotemporal models are appropriate for modelling these data. We consider short-term forecasting of these spatiotemporal processes by using a Bayesian kriged Kalman filtering model. The spatial prediction surface of the model is built by using the well-known method of kriging for optimum spatial prediction and the temporal effects are analysed by using the models underlying the Kalman filtering method. The full Bayesian model is implemented by using Markov chain Monte Carlo techniques which enable us to obtain the optimal Bayesian forecasts in time and space. A new cross-validation method based on the Mahalanobis distance between the forecasts and observed data is also developed to assess the forecasting performance of the model implemented.     

An Algorithm for Enhancing Spreadsheet Regression with Out-of-Sample Statistics

An innovative algorithm is developed for obtaining spreadsheet regression measures used in computing out-of-sample statistics. This algorithm alleviates the leave-one-out computational simulation complexity and memory size problems perceived in computing these statistics. Hence, the purpose of this article is to describe a computationally enhanced algorithm that gives spreadsheet users advanced regression capabilities thereby adding a new dimension to spreadsheet regression operations. These statistics include diagonals of the hat matrix, legitimate forecasting intervals, and PRESS residuals. These computational innovations promote learning while eliminating spreadsheet inadequacies thereby making spreadsheet regression attractive to academicians in teaching and practitioners in acquiring further application competence.     

Predictive Inference for Big,Spatial, Non‐Gaussian Data: MODIS Cloud Data and its Change‐of‐Support

Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non‐Gaussian in distribution. To overcome computational challenges, we use the reduced‐rank spatial random effects (SRE) model in a statistical analysis of cloud‐mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite. Parameterisations of cloud processes are the biggest source of uncertainty and sensitivity in different climate models’ future projections of Earth's climate. An accurate quantification of the spatial distribution of clouds, as well as a rigorously estimated pixel‐scale clear‐sky‐probability process, is needed to establish reliable estimates of cloud‐distributional changes and trends caused by climate change. Here we give a hierarchical spatial‐statistical modelling approach for a very large spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud‐mask data, and we use spatial change‐of‐Support relationships to estimate cloud fraction at coarser resolutions. Our model is non‐Gaussian; it postulates a hidden process for the clear‐sky probability that makes use of the SRE model, EM‐estimation, and optimal (empirical Bayes) spatial prediction of the clear‐sky‐probability process. Measures of prediction uncertainty are also given.     

Out-of-Sample Forecast Tests Robust to the Choice of Window Size

This article proposes new methodologies for evaluating economic models’ out-of-sample forecasting performance that are robust to the choice of the estimation window size. The methodologies involve evaluating the predictive ability of forecasting models over a wide range of window sizes. The study shows that the tests proposed in the literature may lack the power to detect predictive ability and might be subject to data snooping across different window sizes if used repeatedly. An empirical application shows the usefulness of the methodologies for evaluating exchange rate models’ forecasting ability.     

Parameter estimation and inference with spatial lags and cointegration

This article studies dynamic panel data models in which the long run outcome for a particular cross-section is affected by a weighted average of the outcomes in the other cross-sections. We show that imposing such a structure implies a model with several cointegrating relationships that, unlike in the standard case, are nonlinear in the coe?cients to be estimated. Assuming that the weights are exogenously given, we extend the dynamic ordinary least squares methodology and provide a dynamic two-stage least squares estimator. We derive the large sample properties of our proposed estimator under a set of low-level assumptions. Then our methodology is applied to US financial market data, which consist of credit default swap spreads, as well as firm-specific and industry data. We construct the economic space using a “closeness” measure for firms based on input–output matrices. Our estimates show that this particular form of spatial correlation of credit default swap spreads is substantial and highly significant.     

Emulator-assisted reduced-rank ecological data assimilation for nonlinear multivariate dynamical spatio-temporal processes

As ecological data sets increase in spatial and temporal extent with the advent of new remote sensing platforms and long-term monitoring networks, there is increasing interest in forecasting ecological processes. Such forecasts require realistic initial conditions over complete spatial domains. Typically, data sources are incomplete in space, and the processes include complicated dynamical interactions across physical and biological variables. This suggests that data assimilation, whereby observations are fused with mechanistic models, is the most appropriate means of generating complete initial conditions. Often, the mechanistic models used for these procedures are very expensive computationally. We demonstrate a rank-reduced approach for ecological data assimilation whereby the mechanistic model is based on a statistical emulator. Critically, the rank-reduction and emulator construction are linked and, by utilizing a hierarchical framework, uncertainty associated with the dynamical emulator can be accounted for. This provides a so-called “weak-constraint” data assimilation procedure. This approach is demonstrated on a high-dimensional multivariate coupled biogeochemical ocean process.     

Threshold knot selection for large-scale spatial models with applications to the Deepwater Horizon disaster

Large spatial datasets are typically modelled through a small set of knot locations; often these locations are specified by the investigator by arbitrary criteria. Existing methods of estimating the locations of knots assume their number is known a priori, or are otherwise computationally intensive. We develop a computationally efficient method of estimating both the location and number of knots for spatial mixed effects models. Our proposed algorithm, Threshold Knot Selection (TKS), estimates knot locations by identifying clusters of large residuals and placing a knot in the centroid of those clusters. We conduct a simulation study showing TKS in relation to several comparable methods of estimating knot locations. Our case study utilizes data of particulate matter concentrations collected during the course of the response and clean-up effort from the 2010 Deepwater Horizon oil spill in the Gulf of Mexico.     

变权重组合预测模型的局部加权最小二乘解法

随着科学技术的不断进步，预测方法也得到了很大的发展，常见的预测方法就有数十种之多。而组合预测是将不同的预测方法组合起来，综合利用各个方法所提供的信息，其效果往往优于单一的预测方法，故得到了广泛的应用。而基于变系数模型的思想研究了组合预测模型，将变权重的求取转化为变系数模型中系数函数的估计问题，从而可以基于局部加权最小二乘方法求解，利用交叉证实法选取光滑参数。其结果表明所提方法预测精度很高，效果优于其他方法。     

Spatial modeling of extreme rainfall in northeast Thailand

It is well recognized that the generalized extreme value (GEV) distribution is widely used for any extreme events. This notion is based on the study of discrete choice behavior; however, there is a limit for predicting the distribution at ungauged sites. Hence, there have been studies on spatial dependence within extreme events in continuous space using recorded observations. We model the annual maximum daily rainfall data consisting of 25 locations for the period from 1982 to 2013. The spatial GEV model that is established under observations is assumed to be mutually independent because there is no spatial dependency between the stations. Furthermore, we divide the region into two regions for a better model fit and identify the best model for each region. We show that the regional spatial GEV model reflects the spatial pattern well compared with the spatial GEV model over the entire region as the local GEV distribution. The advantage of spatial extreme modeling is that more robust return levels and some indices of extreme rainfall can be obtained for observed stations as well as for locations without observed data. Thus, the model helps to determine the effects and assessment of vulnerability due to heavy rainfall in northeast Thailand.     

Non-parametric Sampling Approximation via Voronoi Tessellations

In this article we propose a novel non-parametric sampling approach to estimate posterior distributions from parameters of interest. Starting from an initial sample over the parameter space, this method makes use of this initial information to form a geometrical structure known as Voronoi tessellation over the whole parameter space. This rough approximation to the posterior distribution provides a way to generate new points from the posterior distribution without any additional costly model evaluations. By using a traditional Markov Chain Monte Carlo (MCMC) over the non-parametric tessellation, the initial approximate distribution is refined sequentially. We applied this method to a couple of climate models to show that this hybrid scheme successfully approximates the posterior distribution of the model parameters.     

Spatial Mallows model averaging for geostatistical models

Important progress has been made with model averaging methods over the past decades. For spatial data, however, the idea of model averaging has not been applied well. This article studies model averaging methods for the spatial geostatistical linear model. A spatial Mallows criterion is developed to choose weights for the model averaging estimator. The resulting estimator can achieve asymptotic optimality in terms of L₂ loss. Simulation experiments reveal that our proposed estimator is superior to the model averaging estimator by the Mallows criterion developed for ordinary linear models [Hansen, 2007] and the model selection estimator using the corrected Akaike's information criterion, developed for geostatistical linear models [Hoeting et al., 2006]. The Canadian Journal of Statistics 47: 336–351; 2019 © 2019 Statistical Society of Canada     

New HEAVY Models for Fat-Tailed Realized Covariances and Returns

ABSTRACT

We develop a new score-driven model for the joint dynamics of fat-tailed realized covariance matrix observations and daily returns. The score dynamics for the unobserved true covariance matrix are robust to outliers and incidental large observations in both types of data by assuming a matrix-F distribution for the realized covariance measures and a multivariate Student's t distribution for the daily returns. The filter for the unknown covariance matrix has a computationally efficient matrix formulation, which proves beneficial for estimation and simulation purposes. We formulate parameter restrictions for stationarity and positive definiteness. Our simulation study shows that the new model is able to deal with high-dimensional settings (50 or more) and captures unobserved volatility dynamics even if the model is misspecified. We provide an empirical application to daily equity returns and realized covariance matrices up to 30 dimensions. The model statistically and economically outperforms competing multivariate volatility models out-of-sample. Supplementary materials for this article are available online.     

Forecasting Performance of an Open Economy DSGE Model

This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1–2002Q4. We compare the DSGE model and a few variants of this model to various reduced-form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and two different Bayesian approaches, and traditional benchmark models, e.g., the random walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.     

Forecasting Performance of an Open Economy DSGE Model

This paper analyzes the forecasting performance of an open economy dynamic stochastic general equilibrium (DSGE) model, estimated with Bayesian methods, for the Euro area during 1994Q1-2002Q4. We compare the DSGE model and a few variants of this model to various reduced-form forecasting models such as vector autoregressions (VARs) and vector error correction models (VECM), estimated both by maximum likelihood and two different Bayesian approaches, and traditional benchmark models, e.g., the random walk. The accuracy of point forecasts, interval forecasts and the predictive distribution as a whole are assessed in an out-of-sample rolling event evaluation using several univariate and multivariate measures. The results show that the open economy DSGE model compares well with more empirical models and thus that the tension between rigor and fit in older generations of DSGE models is no longer present. We also critically examine the role of Bayesian model probabilities and other frequently used low-dimensional summaries, e.g., the log determinant statistic, as measures of overall forecasting performance.