SPACE–TIME MODELLING OF SYDNEY HARBOUR WINDS

This paper develops a space‐time statistical model for local forecasting of surface‐level wind fields in a coastal region with complex topography. The statistical model makes use of output from deterministic numerical weather prediction models which are able to produce forecasts of surface wind fields on a spatial grid. When predicting surface winds at observing stations , errors can arise due to sub‐grid scale processes not adequately captured by the numerical weather prediction model , and the statistical model attempts to correct for these influences. In particular , it uses information from observing stations within the study region as well as topographic information to account for local bias. Bayesian methods for inference are used in the model , with computations carried out using Markov chain Monte Carlo algorithms. Empirical performance of the model is described , illustrating that a structured Bayesian approach to complicated space‐time models of the type considered in this paper can be readily implemented and can lead to improvements in forecasting over traditional methods.     

On the Optimal Use of Suboptimal Forecasts of Explanatory Variables

Ashley (1983) gave a simple condition for determining when a forecast of an explanatory variable (X_t ) is sufficiently inaccurate that direct replacement of X_t by the forecast yields worse forecasts of the dependent variable than does respecification of the equation to omit X_t . Many available macroeconomic forecasts were shown to be of limited usefulness in direct replacement. Direct replacement, however, is not optimal if the forecast's distribution is known. Here optimal linear forms in commercial forecasts of several macroeconomic variables are obtained by using estimates of their distributions. Although they are an improvement on the raw forecasts (direct replacement), these optimal forms are still too inaccurate to be useful in replacing the actual explanatory variables in forecasting models. The results strongly indicate that optimal forms involving several commercial forecasts will not be very useful either. Thus Ashley's (1983) sufficient condition retains its value in gauging the usefulness of a forecast of an explanatory variable in a forecasting model, even though it focuses on direct replacement.     

Cointegration and Long-Horizon Forecasting

We consider the forecasting of cointegrated variables, and we show that at long horizons nothing is lost by ignoring cointegration when forecasts are evaluated using standard multivariate forecast accuracy measures. In fact, simple univariate Box–Jenkins forecasts are just as accurate. Our results highlight a potentially important deficiency of standard forecast accuracy measures—they fail to value the maintenance of cointegrating relationships among variables—and we suggest alternatives that explicitly do so.     

Analysis and modelling of wind speed in New York

In this paper we propose an ARMA time-series model for the wind speed at a single spatial location, and estimate it on in-sample data recorded in three different wind farm regions in New York state. The data have a three-hour granularity, but based on applications to financial wind derivatives contracts, we also consider daily average wind speeds. We demonstrate that there are large discrepancies in the behaviour of daily average and three-hourly wind speed records. The validation procedure based on out-of-sample observations reflects that the proposed model is reliable and can be used for various practical applications, like, for instance, weather prediction, pricing of financial wind contracts, wind generated power, etc. Furthermore, we discuss some striking resemblances with temperature dynamics.     

Spatial–temporal model for wind speed in Lithuania

In this paper, we propose a spatial–temporal model for the wind speed (WS). We first estimate the model at the single spatial meteorological station independently on spatial correlations. The temporal model contains seasonality, a higher-order autoregressive component and a variance describing the remaining heteroskedesticity in residuals. We then model spatial dependencies by a Gaussian random field. The model is estimated on daily WS records from 18 meteorological stations in Lithuania. The validation procedure based on out-of-sample observations shows that the proposed model is reliable and can be used for various practical applications.     

Regularization and variable selection via the elastic net

Summary.  We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together. The elastic net is particularly useful when the number of predictors ( p ) is much bigger than the number of observations ( n ). By contrast, the lasso is not a very satisfactory variable selection method in the p ≫ n case. An algorithm called LARS-EN is proposed for computing elastic net regularization paths efficiently, much like algorithm LARS does for the lasso.     

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.     

Term structure forecasting in affine framework with time-varying volatility

This study extends the affine Nelson–Siegel model by introducing the time-varying volatility component in the observation equation of yield curve, modeled as a standard EGARCH process. The model is illustrated in state-space framework and empirically compared to the standard affine and dynamic Nelson–Siegel model in terms of in-sample fit and out-of-sample forecast accuracy. The affine based extended model that accounts for time-varying volatility outpaces the other models for fitting the yield curve and produces relatively more accurate 6- and 12-month ahead forecasts, while the standard affine model comes with more precise forecasts for the very short forecast horizons. The study concludes that the standard and affine Nelson–Siegel models have higher forecasting capability than their counterpart EGARCH based models for the short forecast horizons, i.e., 1 month. The EGARCH based extended models have excellent performance for the medium and longer forecast horizons.     

On the grouped selection and model complexity of the adaptive elastic net

Lasso proved to be an extremely successful technique for simultaneous estimation and variable selection. However lasso has two major drawbacks. First, it does not enforce any grouping effect and secondly in some situation lasso solutions are inconsistent for variable selection. To overcome this inconsistency adaptive lasso is proposed where adaptive weights are used for penalizing different coefficients. Recently a doubly regularized technique namely elastic net is proposed which encourages grouping effect i.e. either selection or omission of the correlated variables together. However elastic net is also inconsistent. In this paper we study adaptive elastic net which does not have this drawback. In this article we specially focus on the grouped selection property of adaptive elastic net along with its model selection complexity. We also shed some light on the bias-variance tradeoff of different regularization methods including adaptive elastic net. An efficient algorithm was proposed in the line of LARS-EN, which is then illustrated with simulated as well as real life data examples.     

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.     

Statistical models for short- and long-term forecasts of snow depth

Forecasting of future snow depths is useful for many applications like road safety, winter sport activities, avalanche risk assessment and hydrology. Motivated by the lack of statistical forecasts models for snow depth, in this paper we present a set of models to fill this gap. First, we present a model to do short-term forecasts when we assume that reliable weather forecasts of air temperature and precipitation are available. The covariates are included nonlinearly into the model following basic physical principles of snowfall, snow aging and melting. Due to the large set of observations with snow depth equal to zero, we use a zero-inflated gamma regression model, which is commonly used to similar applications like precipitation. We also do long-term forecasts of snow depth and much further than traditional weather forecasts for temperature and precipitation. The long-term forecasts are based on fitting models to historic time series of precipitation, temperature and snow depth. We fit the models to data from six locations in Norway with different climatic and vegetation properties. Forecasting five days into the future, the results showed that, given reliable weather forecasts of temperature and precipitation, the forecast errors in absolute value was between 3 and 7?cm for different locations in Norway. Forecasting three weeks into the future, the forecast errors were between 7 and 16?cm.     

Dynamic Forecasts of Qualitative Variables

This article presents a new Qual VAR model for incorporating information from qualitative and/or discrete variables in vector autoregressions. With a Qual VAR, it is possible to create dynamic forecasts of the qualitative variable using standard VAR projections. Previous forecasting methods for qualitative variables, in contrast, produce only static forecasts. I apply the Qual VAR to forecasting the 2001 business recession out of sample and to analyzing the Romer and Romer narrative measure of monetary policy contractions as an endogenous variable in a VAR. Out of sample, the model predicts the timing of the 2001 recession quite well relative to the recession probabilities put forth at the time by professional forecasters. Qual VARs—which include information about the qualitative variable—can also enhance the quality of density forecasts of the other variables in the system.     

Vector and recurrent singular spectrum analysis: which is better at forecasting?

Singular spectrum analysis (SSA) is an increasingly popular and widely adopted filtering and forecasting technique which is currently exploited in a variety of fields. Given its increasing application and superior performance in comparison to other methods, it is pertinent to study and distinguish between the two forecasting variations of SSA. These are referred to as Vector SSA (SSA-V) and Recurrent SSA (SSA-R). The general notion is that SSA-V is more robust and provides better forecasts than SSA-R. This is especially true when faced with time series which are non-stationary and asymmetric, or affected by unit root problems, outliers or structural breaks. However, currently there exists no empirical evidence for proving the above notions or suggesting that SSA-V is better than SSA-R. In this paper, we evaluate out-of-sample forecasting capabilities of the optimised SSA-V and SSA-R forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures, to provide a statistically reliable answer to the question of which SSA algorithm is best for forecasting at both short and long run horizons based on several important criteria.     

Forecasting Multivariate Road Traffic Flows Using Bayesian Dynamic Graphical Models,Splines and Other Traffic Variables

Traffic flow data are routinely collected for many networks worldwide. These invariably large data sets can be used as part of a traffic management system, for which good traffic flow forecasting models are crucial. The linear multiregression dynamic model (LMDM) has been shown to be promising for forecasting flows, accommodating multivariate flow time series, while being a computationally simple model to use. While statistical flow forecasting models usually base their forecasts on flow data alone, data for other traffic variables are also routinely collected. This paper shows how cubic splines can be used to incorporate extra variables into the LMDM in order to enhance flow forecasts. Cubic splines are also introduced into the LMDM to parsimoniously accommodate the daily cycle exhibited by traffic flows. The proposed methodology allows the LMDM to provide more accurate forecasts when forecasting flows in a real high‐dimensional traffic data set. The resulting extended LMDM can deal with some important traffic modelling issues not usually considered in flow forecasting models. Additionally, the model can be implemented in a real‐time environment, a crucial requirement for traffic management systems designed to support decisions and actions to alleviate congestion and keep traffic flowing.     

Estimation of covariance matrix via the sparse Cholesky factor with lasso

In this paper, we discuss a parsimonious approach to estimation of high-dimensional covariance matrices via the modified Cholesky decomposition with lasso. Two different methods are proposed. They are the equi-angular and equi-sparse methods. We use simulation to compare the performance of the proposed methods with others available in the literature, including the sample covariance matrix, the banding method, and the L₁-penalized normal loglikelihood method. We then apply the proposed methods to a portfolio selection problem using 80 series of daily stock returns. To facilitate the use of lasso in high-dimensional time series analysis, we develop the dynamic weighted lasso (DWL) algorithm that extends the LARS-lasso algorithm. In particular, the proposed algorithm can efficiently update the lasso solution as new data become available. It can also add or remove explanatory variables. The entire solution path of the L₁-penalized normal loglikelihood method is also constructed.     

基于时空地理加权回归模型的中国碳排放驱动因素实证研究

基于2006-2011年中国省级区域面板数据,应用时空加权回归模型(GTWR)实证考察了各驱动因素对碳排放规模和碳排放强度影响的时空差异。研究结果表明:大部分解释变量的时空系数估计值显著,波动性较为稳定,符号与预期一致,各驱动因素及其外溢效应在不同区域存在较强的空间异质性,且表现出一定的空间梯度分布。若实现区域差异化碳减排,需要充分考虑空间异质性和外溢性。     

Wavelet packet transfer function modelling of nonstationary time series

This article shows how a non-decimated wavelet packet transform (NWPT) can be used to model a response time series, Y _t, in terms of an explanatory time series, X _t. The proposed computational technique transforms the explanatory time series into a NWPT representation and then uses standard statistical modelling methods to identify which wavelet packets are useful for modelling the response time series. We exhibit S-Plus functions from the freeware WaveThresh package that implement our methodology.The proposed modelling methodology is applied to an important problem from the wind energy industry: how to model wind speed at a target location using wind speed and direction from a reference location. Our method improves on existing target site wind speed predictions produced by widely used industry standard techniques. However, of more importance, our NWPT representation produces models to which we can attach physical and scientific interpretations and in the wind example enable us to understand more about the transfer of wind energy from site to site.     

Forecasting the Distribution of Economic Variables in a Data-Rich Environment

This article investigates the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semiparametric specification based on the quantile autoregressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy relative to a stochastic volatility model using the quantile score. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at long horizons and in tails of the distribution, while for the inflation variables the improved performance occurs mostly at the 6-month horizon. We also illustrate the practical relevance of predicting the distribution by considering forecasts at three dates during the last recession.     

The covariance structure of sequential forecasts obtained by regression analysis

A method is presented for evaluating the covariance matrix of a set of sequential forecasts obtained by regression analysis. The matrix can be used to derive the relation between the variance of the forecasts on the one hand, and the lead times between the forecasting time and the time at which the forecasted variables are realized, on the other hand. The determination of this relation is important whenever the optimal frequency of forecasting must be determined.     

Modelling the evolution of a random set utilizing covariate information with applications to nowcasting

ABSTRACT

We propose models that allow us to capture the evolution of objects over time and more importantly, we provide forecasts to describe an object at future unobserved states utilizing information from the current state along with covariate information. We view objects as random sets and proceed to model them in a hierarchical Bayesian framework and estimate the model parameters using a Markov chain Monte Carlo scheme. We illustrate the methodology with an application to nowcasting of severe weather precipitation fields as obtained from weather radar images, where the severe storm cells are treated as random sets and the wind velocity is used to inform the distributions of the model parameters.