Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting

Wind power forecasts with lead times of up to a few hours are essential to the optimal and economical operation of power systems and markets. Vector autoregression (VAR) is a framework that has been shown to be well suited to predicting for several wind farms simultaneously by considering the spatio-temporal dependencies in their time series. Lasso penalisation yields sparse models and can avoid overfitting the large numbers of coefficients in higher dimensional settings. However, estimation in VAR models usually does not account for changes in the spatio-temporal wind power dynamics that are related to factors such as seasons or wind farm setup changes, for example. This paper tackles this problem by proposing a time-adaptive lasso estimator and an efficient coordinate descent algorithm for updating the VAR model parameters recursively online. The approach shows good abilities to track changes in the multivariate time series dynamics on simulated data. Furthermore, in two case studies it shows clearly better predictive performances than the non-adaptive lasso VAR and univariate autoregression.     

A note on autoregressive error components models

The purpose of this paper is to shed some light on the asymptotic behavior of a wide class of estimators for a dynamic error components model when only the number of individuals tends to infinity, the number of time periods being kept fixed. In particular, it is shown that this asymptotic behavior is highly dependent on the assumption about the initial observations and that it offers very good approximations to the small sample behavior of the various estimators under consideration.     

GEFCom2012: Electric load forecasting and backcasting with semi-parametric models

We sum up the methodology of the team tololo for the Global Energy Forecasting Competition 2012: Load Forecasting. Our strategy consisted of a temporal multi-scale model that combines three components. The first component was a long term trend estimated by means of non-parametric smoothing. The second was a medium term component describing the sensitivity of the electricity demand to the temperature at each time step. We use a generalized additive model to fit this component, using calendar information as well. Finally, a short term component models local behaviours. As the factors that drive this component are unknown, we use a random forest model to estimate it.     

Estimation and model adequacy checking for multivariate seasonal autoregressive time series models with periodically varying parameters

We introduce a class of multivariate seasonal time series models with periodically varying parameters, abbreviated by the acronym SPVAR. The model is suitable for multivariate data, and combines a periodic autoregressive structure and a multiplicative seasonal time series model. The stationarity conditions (in the periodic sense) and the theoretical autocovariance functions of SPVAR stochastic processes are derived. Estimation and checking stages are considered. The asymptotic normal distribution of the least squares estimators of the model parameters is established, and the asymptotic distributions of the residual autocovariance and autocorrelation matrices in the class of SPVAR time series models are obtained. In order to check model adequacy, portmanteau test statistics are considered and their asymptotic distributions are studied. A simulation study is briefly discussed to investigate the finite-sample properties of the proposed test statistics. The methodology is illustrated with a bivariate quarterly data set on travelers entering in to Canada.     

Macroeconomic forecasting using approximate factor models with outliers

In this paper we consider estimating an approximate factor model in which candidate predictors are subject to sharp spikes such as outliers or jumps. Given that these sharp spikes are assumed to be rare, we formulate the estimation problem as a penalized least squares problem by imposing a norm penalty function on those sharp spikes. Such a formulation allows us to disentangle the sharp spikes from the common factors and estimate them simultaneously. Numerical values of the estimates can be obtained by solving a principal component analysis (PCA) problem and a one-dimensional shrinkage estimation problem iteratively. In addition, it is easy to incorporate methods for selecting the number of common factors in the iterations. We compare our method with PCA by conducting simulation experiments in order to examine their finite-sample performances. We also apply our method to the prediction of important macroeconomic indicators in the U.S., and find that it can deliver performances that are comparable to those of the PCA method.     

A two-step approach for identifying seasonal autoregressive time series forecasting models

One of the most powerful and widely used methodologies for forecasting economic time series is the class of models known as seasonal autoregressive processes. In this article we present a new approach not only for identifying seasonal autoregressive models, but also the degree of differencing required to induce stationarity in the data. The identification method is iterative and consists in systematically fitting increasing order models to the data, and then verifying that the resulting residuals behave like white noise using a two stage autoregressive order determination criterion. Once the order of the process is determined the identified structure is tested to see if it can be simplified. The identification performance of this procedure is contrasted with other order selection procedures for models with ‘gaps.' We also illustrate the forecast performance of the identification method using monthly and quarterly economic data.     

Prediction from ARFIMA models: Comparisons between MLE and semiparametric estimation procedures

This paper considers the effects on multi-step prediction of using semiparametric local Whittle estimators rather than MLE for long memory ARFIMA models. We consider various representations of the minimum MSE predictor with known parameters. We then conduct a detailed simulation study for when the true parameters are replaced with estimates. The predictor based on MLE is found to be superior, in the MSE sense, to the predictor based on the two-step local Whittle estimation. The “optimal” bandwidth local Whittle estimator produces worse predictions than the local Whittle using an agnostic bandwidth of the square root of the sample size.     

A critical overview of privacy-preserving approaches for collaborative forecasting

Cooperation between different data owners may lead to an improvement in forecast quality—for instance, by benefiting from spatiotemporal dependencies in geographically distributed time series. Due to business competitive factors and personal data protection concerns, however, said data owners might be unwilling to share their data. Interest in collaborative privacy-preserving forecasting is thus increasing. This paper analyzes the state-of-the-art and unveils several shortcomings of existing methods in guaranteeing data privacy when employing vector autoregressive models. The methods are divided into three groups: data transformation, secure multi-party computations, and decomposition methods. The analysis shows that state-of-the-art techniques have limitations in preserving data privacy, such as (i) the necessary trade-off between privacy and forecasting accuracy, empirically evaluated through simulations and real-world experiments based on solar data; and (ii) iterative model fitting processes, which reveal data after a number of iterations.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

Restricted forecasting with VAR models: An analysis of a test for joint compatibility between restrictions and forecasts

A restricted forecasting compatibility test for Vector Autoregressive Error Correction models is analyzed in this work. It is shown that a variance–covariance matrix associated with the restrictions can be used to cancel out model dynamics and interactions between restrictions. This allows us to interpret the joint compatibility test as a composition of the corresponding single restriction compatibility tests. These tests are useful for appreciating the contribution of each and every restriction to the joint compatibility between the whole set of restrictions and the unrestricted forecasts. An estimated process adjustment for the test is derived and the resulting feasible joint compatibility test turns out to have better performance than the original one. An empirical illustration of the usefulness of the proposed test makes use of Mexican macroeconomic data and the targets proposed by the Mexican Government for the year 2003.     

基于RBF神经网络的股票价格预测

由于股票的价格是非线性的时间序列,文章提出了基于RBF神经网络的个股价格预测模型,该模型优于传统的股市技术分析方法,又避免了BP算法容易陷入局部极小点和收敛速度慢的缺点。根据实验的仿真结果显示,该模型对于个股价格的短期预测效果较好。     

A two–stage approach to additive time series models

For nonlinear additive time series models, an appealing approach used in the literature to estimate the nonparametric additive components is the projection method. In this paper, it is demonstrated that the projection method might not be efficient in an asymptotic sense. To estimate additive components efficiently, a two–stage approach is proposed together with a local linear fitting and a new bandwidth selector based on the nonparametric version of the Akaike information criterion. It is shown that the two–stage method not only achieves efficiency but also makes bandwidth selection relatively easier. Also, the asymptotic normality of the resulting estimator is established. A small simulation study is carried out to illustrate the proposed methodology and the two–stage approach is applied to a real example from econometrics.     

Automatic Interpretable Retail forecasting with promotional scenarios

Budgeting and planning processes require medium-term sales forecasts with marketing scenarios. The complexity in modern retailing necessitates consistent, automatic forecasting and insight generation. Remedies to the high dimensionality problem have drawbacks; black box machine learning methods require voluminous data and lack insights, while regularization may bias causal estimates in interpretable models.The proposed FAIR (Fully Automatic Interpretable Retail forecasting) method supports the retail planning process with multi-step-ahead category-store level forecasts, scenario evaluations, and insights. It considers category-store specific seasonality, focal- and cross-category marketing, and adaptive base sales while dealing with regularization-induced confounding.We show, with three chains from the IRI dataset involving 30 categories, that regularization-induced confounding decreases forecast accuracy. By including focal- and cross-category marketing, as well as random disturbances, forecast accuracy is increased. FAIR is more accurate than the black box machine learning method Boosted Trees and other benchmarks while also providing insights that are in line with the marketing literature.     

A data-driven approach to forecasting ground-level ozone concentration

The ability to forecast the concentration of air pollutants in an urban region is crucial for decision-makers wishing to reduce the impact of pollution on public health through active measures (e.g. temporary traffic closures). In this study, we present a machine learning approach applied to forecasts of the day-ahead maximum value of ozone concentration for several geographical locations in southern Switzerland. Due to the low density of measurement stations and to the complex orography of the use-case terrain, we adopted feature selection methods instead of explicitly restricting relevant features to a neighborhood of the prediction sites, as common in spatio-temporal forecasting methods. We then used Shapley values to assess the explainability of the learned models in terms of feature importance and feature interactions in relation to ozone predictions. Our analysis suggests that the trained models effectively learned explanatory cross-dependencies among atmospheric variables. Finally, we show how weighting observations helps to increase the accuracy of the forecasts for specific ranges of ozone’s daily peak values.     

A consistent nonparametric test of parametric regression functional form in fixed effects panel data models

We propose a consistent test for a linear functional form against a nonparametric alternative in a fixed effects panel data model. We show that the test has a limiting standard normal distribution under the null hypothesis, and show that the test is a consistent test. We also establish the asymptotic validity of a bootstrap procedure which is used to better approximate the finite sample null distribution of the test statistic. Simulation results show that the proposed test performs well for panel data with a large number of cross-sectional units and a finite number of observations across time.     

A note on forecasting international tourism demand in Spain

This paper considers the extent to which price and income proxy variables help in forecasting tourist demand in Spain. Contrary to some recent studies, we found that the inputs' contribution in terms of fitting and forecasting is nil when compared with alternative univariate models. Whether these findings are the results of the restrictions embedded in building the proxy inputs or in a poor specification of the dynamics of these models remains to be seen. We also contend that when dealing with medium, long-term forecasting comparisons, the use of the traditional aggregate accuracy measures like RMSE and MAPE help very little in discriminating among competing models. In these situations, predicted annual growth rates may be a better alternative.     

Maximum likelihood estimation for dynamic factor models with missing data

This paper concerns estimating parameters in a high-dimensional dynamic factor model by the method of maximum likelihood. To accommodate missing data in the analysis, we propose a new model representation for the dynamic factor model. It allows the Kalman filter and related smoothing methods to evaluate the likelihood function and to produce optimal factor estimates in a computationally efficient way when missing data is present. The implementation details of our methods for signal extraction and maximum likelihood estimation are discussed. The computational gains of the new devices are presented based on simulated data sets with varying numbers of missing entries.     

Evaluating the forecasting performance of econometric models of air passenger traffic flows using multiple error measures

Airline traffic forecasting is important to airlines and regulatory authorities. This paper examines a number of approaches to forecasting short- to medium-term air traffic flows. It contributes as a rare replication, testing a variety of alternative modelling approaches. The econometric models employed include autoregressive distributed lag (ADL) models, time-varying parameter (TVP) models and an automatic method for econometric model specification. A vector autoregressive (VAR) model and various univariate alternatives are also included to deliver unconditional forecast comparisons. Various approaches for taking into account interactions between contemporaneous air traffic flows are examined, including pooled ADL models and the enhanced models with the addition of a “world trade” variable. Based on the analysis of a number of forecasting error measures, it is concluded that pooled ADL models that include the “world trade” variable outperform the alternatives, and in particular univariate methods; and, second, that automatic modelling procedures are enhanced through judgmental intervention. In contrast to earlier results, the TVP models do not improve accuracy. Depending on the preferred error measure, the difference in accuracy may be substantial.     

基于BP神经网络的时间序列预测研究

建立了基于BP网络的时间序列预测模型,将模型应用于实际算例,设计了模型的网络结构、初始权值和偏差,结果验证了模型的有效性。