Very short term irradiance forecasting using the lasso

We find an application of the lasso (least absolute shrinkage and selection operator) in sub-5-min solar irradiance forecasting using a monitoring network. Lasso is a variable shrinkage and selection method for linear regression. In addition to the sum of squares error minimization, it considers the sum of ℓ1-norms of the regression coefficients as penalty. This bias–variance trade-off very often leads to better predictions.<p></p> One second irradiance time series data are collected using a dense monitoring network in Oahu, Hawaii. As clouds propagate over the network, highly correlated lagged time series can be observed among station pairs. Lasso is used to automatically shrink and select the most appropriate lagged time series for regression. Since only lagged time series are used as predictors, the regression provides true out-of-sample forecasts. It is found that the proposed model outperforms univariate time series models and ordinary least squares regression significantly, especially when training data are few and predictors are many. Very short-term irradiance forecasting is useful in managing the variability within a central PV power plant.<p></p&gt

Restricted Likelihood Ratio Testing in Linear Mixed Models with General Error Covariance Structure

We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to derive the (approximate) test distribution for the restricted likelihood ratio test statistic in the case of a general error covariance structure. The proposed test proves its value in simulations and is finally applied to an interesting question in the field of well-being economics

A Comparison of Five Statistical Methods for Predicting Stream Temperature Across Stream Networks

The health of freshwater aquatic systems, particularly stream networks, is mainly influenced by water temperature, which controls biological processes and influences species distributions and aquatic biodiversity. Thermal regimes of rivers are likely to change in the future, due to climate change and other anthropogenic impacts, and our ability to predict stream temperatures will be critical in understanding distribution shifts of aquatic biota. Spatial statistical network models take into account spatial relationships but have drawbacks, including high computation times and data pre-processing requirements. Machine learning techniques and generalized additive models (GAM) are promising alternatives to the SSN model. Two machine learning methods, gradient boosting machines (GBM) and Random Forests (RF), are computationally efficient and can automatically model complex data structures. However, a study comparing the predictive accuracy among a variety of widely-used statistical modeling techniques has not yet been conducted. My objectives for this study were to 1) compare the accuracy among linear models (LM), SSN, GAM, RF, and GBM in predicting stream temperature over two stream networks and 2) provide guidelines in choosing a prediction method for practitioners and ecologists. Stream temperature prediction accuracies were compared with the test-set root mean square error (RMSE) for all methods. For the actual data, SSN had the highest predictive accuracy overall, which was followed closely by GBM and GAM. LM had the poorest performance overall. This study shows that although SSN appears to be the most accurate method for stream temperature prediction, machine learning methods and GAM may be suitable alternatives

Forecasting with Spatial Panel Data

This paper compares various forecasts using panel data with spatial error correlation. The true data generating process is assumed to be a simple error component regression model with spatial remainder disturbances of the autoregressive or moving average type. The best linear unbiased predictor is compared with other forecasts ignoring spatial correlation, or ignoring heterogeneity due to the individual effects, using Monte Carlo experiments. In addition, we check the performance of these forecasts under misspecification of the spatial error process, various spatial weight matrices, and heterogeneous rather than homogeneous panel data models.forecasting, BLUP, panel data, spatial dependence, heterogeneity

Bayesian Multivariate Time Series Methods for Empirical Macroeconomics

Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as time-varying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over-parameterization problems may arise. Bayesian methods have become increasingly popular as a way of overcoming these problems. In this monograph, we discuss VARs, factor augmented VARs and time-varying parameter extensions and show how Bayesian inference proceeds. Apart from the simplest of VARs, Bayesian inference requires the use of Markov chain Monte Carlo methods developed for state space models and we describe these algorithms. The focus is on the empirical macroeconomist and we offer advice on how to use these models and methods in practice and include empirical illustrations. A website provides Matlab code for carrying out Bayesian inference in these models.Empirical macroeconometrics, Bayesian estimation, MCMC, vector autoregressions, factor models, time-varying parameters