In this paper, we extend the heterogeneous panel data stationarity test of Hadri ["Econometrics Journal", Vol. 3 (2000) pp. 148-161] to the cases where breaks are taken into account. Four models with different patterns of breaks under the null hypothesis are specified. Two of the models have been already proposed by Carrion-i-Silvestre "et al." ["Econometrics Journal", Vol. 8 (2005) pp. 159-175]. The moments of the statistics corresponding to the four models are derived in closed form via characteristic functions. We also provide the exact moments of a modified statistic that do not asymptotically depend on the location of the break point under the null hypothesis. The cases where the break point is unknown are also considered. For the model with breaks in the level and no time trend and for the model with breaks in the level and in the time trend, Carrion-i-Silvestre "et al." ["Econometrics Journal", Vol. 8 (2005) pp. 159-175] showed that the number of breaks and their positions may be allowed to differ across individuals for cases with known and unknown breaks. Their results can easily be extended to the proposed modified statistic. The asymptotic distributions of all the statistics proposed are derived under the null hypothesis and are shown to be normally distributed. We show by simulations that our suggested tests have in general good performance in finite samples except the modified test. In an empirical application to the consumer prices of 22 OECD countries during the period from 1953 to 2003, we found evidence of stationarity once a structural break and cross-sectional dependence are accommodated. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2008.

In this paper, we reexamine two important aspects of the dynamics of relative primary commodity prices, namely the secular trend and the short run volatility. To do so, we employ 25 series, some of them starting as far back as 1650 and powerful panel data stationarity tests that allow for endogenous multiple structural breaks. Results show that all the series are stationary after allowing for endogeneous multiple breaks. Test results on the Prebisch-Singer hypothesis, which states that relative commodity prices follow a downward secular trend, are mixed but with a majority of series showing negative trends. We also make a first attempt at identifying the potential drivers of the structural breaks. We end by investigating the dynamics of the volatility of the 25 relative primary commodity prices also allowing for endogenous multiple breaks. We describe the often time-varying volatility in commodity prices and show that it has increased in recent years.

In this paper, we propose new cointegration tests for single equations and panels. In both cases, the asymptotic distributions of the tests, which are derived with N fixed and T → ∞, are shown to be standard normals. The effects of serial correlation and cross-sectional dependence are mopped out via long-run variances. An effective bias correction is derived which is shown to work well in finite samples; particularly when N is smaller than T. Our panel tests are robust to possible cointegration across units.JEL classification: C12, C15, C22, C23.

In this article, we propose a simple estimator of cross‐covariance matrices for a multi‐variate time series with an unknown mean based on a linear combination of the circular sample cross‐covariance estimator. Our estimator is exactly unbiased when the data generating process follows a vector moving average (VMA) model with an order less than one half of the sampling period, and is nearly unbiased if such VMA model can approximate the data generating process well. In addition, our estimator is shown to be asymptotically equivalent to the conventional sample cross‐covariance estimator. Via simulation, we show that the proposed estimator can to a large extent eliminate the finite sample bias of cross‐covariance estimates, while not necessarily increase the mean squared error.

As more and more unconventional energy sources are being applied in the field of power generation, the frequency fluctuation of power system becomes more and more serious. The frequency modulation of thermal power unit has disadvantages such as long response time and slow climbing speed. Battery energy storage has gradually become a research hotspot in power system frequency modulation due to its quick response and flexible regulation. This article first introduced the control method based on the signal of ACE (Area Control Error), which is the basic way of secondary frequency modulation and analyzed the features of the basic control mode. Then it zoned the signal of ACE and SOC of the battery energy storage system. On this basis, different frequency modulation methods were proposed according to the requirements of frequency modulation and the characteristics of the output of different regions. In addition, the fuzzy controller is used to smooth the output of the energy storage system under the normal adjustment of the regional control deviation and the normal charging and discharging state of SOC. Finally, a two-region interconnection simulation system was established based on the MATLAB simulation platform, and the simulation results verified the effectiveness of the proposed control strategy.