An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves

We propose an adaptive functional autoregressive (AFAR) forecast model to predict electricity price curves. With time-varying operators, the AFAR model can be safely used in both stationary and nonstationary situations. A closed-form maximum likelihood (ML) estimator is derived under stationarity. The result is further extended for nonstationarity, where the time-dependent operators are adaptively estimated under local homogeneity. We provide theoretical results of the ML estimator and the adaptive estimator. Simulation study illustrates nice finite sample performance of the AFAR modeling. The AFAR model also exhibits a superior accuracy in the forecast exercise of the California electricity daily price curves compared to several alternatives.     

The Generalized Conditional Autoregressive Wishart Model for Multivariate Realized Volatility

It is well known that in finance variances and covariances of asset returns move together over time. Recently, much interest has been aroused by an approach involving the use of the realized covariance (RCOV) matrix constructed from high-frequency returns as the ex-post realization of the covariance matrix of low-frequency returns. For the analysis of dynamics of RCOV matrices, we propose the generalized conditional autoregressive Wishart (GCAW) model. Both the noncentrality matrix and scale matrix of the Wishart distribution are driven by the lagged values of RCOV matrices, and represent two different sources of dynamics, respectively. The GCAW is a generalization of the existing models, and accounts for symmetry and positive definiteness of RCOV matrices without imposing any parametric restriction. Some important properties such as conditional moments, unconditional moments, and stationarity are discussed. Empirical examples including sequences of daily RCOV matrices from the New York Stock Exchange illustrate that our model outperforms the existing models in terms of model fitting and forecasting.     

Weighted simulated integrated conditional moment tests for parametric conditional distributions of stationary time series processes

In this article, we propose a weighted simulated integrated conditional moment (WSICM) test of the validity of parametric specifications of conditional distribution models for stationary time series data, by combining the weighted integrated conditional moment (ICM) test of Bierens (1984 Bierens, H. J. (1984). Model specification testing of time series regressions. Journal of Econometrics 26:323–353.[Crossref], [Web of Science ®] , [Google Scholar]) for time series regression models with the simulated ICM test of Bierens and Wang (2012 Bierens, H. J., Wang, L. (2012). Integrated conditional moment tests for parametric conditional distributions. Econometric Theory 28:328–362.[Crossref], [Web of Science ®] , [Google Scholar]) of conditional distribution models for cross-section data. To the best of our knowledge, no other consistent test for parametric conditional time series distributions has been proposed yet in the literature, despite consistency claims made by some authors.     

Signal extraction goodness-of-fit diagnostic tests under model parameter uncertainty: Formulations and empirical evaluation

We present a time-domain goodness-of-fit (gof) diagnostic test that is based on signal-extraction variances for nonstationary time series. This diagnostic test extends the time-domain gof statistic of Maravall (2003 Maravall, A. (2003). A class of diagnostics in the ARIMA-model-based decomposition of a time series. Memorandum, Bank of Spain. Available at http://www.bde.es/servicio/software/tramo/diagnosticsamb.pdf [Google Scholar]) by taking into account the effects of model parameter uncertainty, utilizing theoretical results of McElroy and Holan (2009 McElroy, T., Holan, S. (2009). A local spectral approach for assessing time series model misspeci?cation. Journal of Multivariate Analysis 100:604–621.[Crossref], [Web of Science ®] , [Google Scholar]). We demonstrate that omitting this correction results in a severely undersized statistic. Adequate size and power are obtained in Monte Carlo studies for fairly short time series (10 to 15 years of monthly data). Our Monte Carlo studies of finite sample size and power consider different combinations of both signal and noise components using seasonal, trend, and irregular component models obtained via canonical decomposition. Details of the implementation appropriate for SARIMA models are given. We apply the gof diagnostic test statistics to several U.S. Census Bureau time series. The results generally corroborate the output of the automatic model selection procedure of the X-12-ARIMA software, which in contrast to our diagnostic test statistic does not involve hypothesis testing. We conclude that these diagnostic test statistics are a useful supplementary model-checking tool for practitioners engaged in the task of model-based seasonal adjustment.     

Fourier–type tests involving martingale difference processes

We develop testing procedures which detect if the observed time series is a martingale difference sequence. Furthermore, tests are developed that detect change–points in the conditional expectation of the series given its past. The test statistics are formulated following the approach of Fourier–type conditional expectations first proposed by Bierens (1982 Bierens, H. J. (1982). Consistent model speci?cation tests. J. Econometr. 20:105–134.[Crossref], [Web of Science ®] , [Google Scholar]) and have the advantage of computational simplicity. The limit behavior of the test statistics is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test. The performance of the bootstrap version of the test is compared in finite samples with other methods for the same problem. A real–data application is also included.     

Robust inference for group sequential trials

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests.     

Testing independence based on Bernstein empirical copula and copula density

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function.