Forecasting day-ahead electricity load using a multiple equation time series approach

The quality of short-term electricity load forecasting is crucial to the operation and trading activities of market participants in an electricity market. In this paper, it is shown that a multiple equation time-series model, which is estimated by repeated application of ordinary least squares, has the potential to match or even outperform more complex nonlinear and nonparametric forecasting models. The key ingredient of the success of this simple model is the effective use of lagged information by allowing for interaction between seasonal patterns and intra-day dependencies. Although the model is built using data for the Queensland region of Australia, the method is completely generic and applicable to any load forecasting problem. The model’s forecasting ability is assessed by means of the mean absolute percentage error (MAPE). For day-ahead forecast, the MAPE returned by the model over a period of 11 years is an impressive 1.36%. The forecast accuracy of the model is compared with a number of benchmarks including three popular alternatives and one industrial standard reported by the Australia Energy Market Operator (AEMO). The performance of the model developed in this paper is superior to all benchmarks and outperforms the AEMO forecasts by about a third in terms of the MAPE criterion.

Improving GPS time series for geodynamic studies

Accurate and stable time series of geodetic parameters can be used to help in understanding the dynamic Earth and its response to global change. The Global Positioning System, GPS, has proven to be invaluable in modern geodynamic studies. In Fennoscandia the first GPS networks were set up in 1993. These networks form the basis of the national reference frames in the area, but they also provide long and important time series for crustal deformation studies. These time series can be used, for example, to better constrain the ice history of the last ice age and the Earth s structure, via existing glacial isostatic adjustment models. To improve the accuracy and stability of the GPS time series, the possible nuisance parameters and error sources need to be minimized. We have analysed GPS time series to study two phenomena. First, we study the refraction in the neutral atmosphere of the GPS signal, and, second, we study the surface loading of the crust by environmental factors, namely the non-tidal Baltic Sea, atmospheric load and varying continental water reservoirs. We studied the atmospheric effects on the GPS time series by comparing the standard method to slant delays derived from a regional numerical weather model. We have presented a method for correcting the atmospheric delays at the observational level. The results show that both standard atmosphere modelling and the atmospheric delays derived from a numerical weather model by ray-tracing provide a stable solution. The advantage of the latter is that the number of unknowns used in the computation decreases and thus, the computation may become faster and more robust. The computation can also be done with any processing software that allows the atmospheric correction to be turned off. The crustal deformation due to loading was computed by convolving Green s functions with surface load data, that is to say, global hydrology models, global numerical weather models and a local model for the Baltic Sea. The result was that the loading factors can be seen in the GPS coordinate time series. Reducing the computed deformation from the vertical time series of GPS coordinates reduces the scatter of the time series; however, the long term trends are not influenced. We show that global hydrology models and the local sea surface can explain up to 30% of the GPS time series variation. On the other hand atmospheric loading admittance in the GPS time series is low, and different hydrological surface load models could not be validated in the present study. In order to be used for GPS corrections in the future, both atmospheric loading and hydrological models need further analysis and improvements.

Diagnostic Tests Based on Quantile Residuals for Nonlinear Time Series Models

This thesis studies quantile residuals and uses different methodologies to develop test statistics that are applicable in evaluating linear and nonlinear time series models based on continuous distributions. Models based on mixtures of distributions are of special interest because it turns out that for those models traditional residuals, often referred to as Pearson's residuals, are not appropriate. As such models have become more and more popular in practice, especially with financial time series data there is a need for reliable diagnostic tools that can be used to evaluate them. The aim of the thesis is to show how such diagnostic tools can be obtained and used in model evaluation. The quantile residuals considered here are defined in such a way that, when the model is correctly specified and its parameters are consistently estimated, they are approximately independent with standard normal distribution. All the tests derived in the thesis are pure significance type tests and are theoretically sound in that they properly take the uncertainty caused by parameter estimation into account. -- In Chapter 2 a general framework based on the likelihood function and smooth functions of univariate quantile residuals is derived that can be used to obtain misspecification tests for various purposes. Three easy-to-use tests aimed at detecting non-normality, autocorrelation, and conditional heteroscedasticity in quantile residuals are formulated. It also turns out that these tests can be interpreted as Lagrange Multiplier or score tests so that they are asymptotically optimal against local alternatives. Chapter 3 extends the concept of quantile residuals to multivariate models. The framework of Chapter 2 is generalized and tests aimed at detecting non-normality, serial correlation, and conditional heteroscedasticity in multivariate quantile residuals are derived based on it. Score test interpretations are obtained for the serial correlation and conditional heteroscedasticity tests and in a rather restricted special case for the normality test. In Chapter 4 the tests are constructed using the empirical distribution function of quantile residuals. So-called Khmaladze s martingale transformation is applied in order to eliminate the uncertainty caused by parameter estimation. Various test statistics are considered so that critical bounds for histogram type plots as well as Quantile-Quantile and Probability-Probability type plots of quantile residuals are obtained. Chapters 2, 3, and 4 contain simulations and empirical examples which illustrate the finite sample size and power properties of the derived tests and also how the tests and related graphical tools based on residuals are applied in practice.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

What do hydrological time series tell about climate change?

Yhteenveto: Mitä hydrologiset mallit kertovat ilmaston muutoksesta?

Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.

Evolution in the time series of vortex velocity fluctuations across different regimes of vortex flow

Investigations of vortex velocity fluctuation in time domain have revealed a presence of low frequency velocity fluctuations which evolve with the different driven phases of the vortex state in a single crystal of 2H-NbSe2. The observation of velocity fluctuations with a characteristic low frequency is associated with the onset of nonlinear nature of vortex flow deep in the driven elastic vortex state. (C) 2009 Elsevier B.V. All rights reserved.

Block coherence: a method for measuring the interdependence between two blocks of neurobiological time series

Multisensor recordings are becoming commonplace. When studying functional connectivity between different brain areas using such recordings, one defines regions of interest, and each region of interest is often characterized by a set (block) of time series. Presently, for two such regions, the interdependence is typically computed by estimating the ordinary coherence for each pair of individual time series and then summing or averaging the results over all such pairs of channels (one from block 1 and other from block 2). The aim of this paper is to generalize the concept of coherence so that it can be computed for two blocks of non-overlapping time series. This quantity, called block coherence, is first shown mathematically to have properties similar to that of ordinary coherence, and then applied to analyze local field potential recordings from a monkey performing a visuomotor task. It is found that an increase in block coherence between the channels from V4 region and the channels from prefrontal region in beta band leads to a decrease in response time.

Diminished chaos of heart rate time series in patients with major depression

Background: Depression and anxiety have been linked to serious cardiovascular events in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate (HR) variability has been linked to sudden death. Methods: We compared LLE and nonlinearity scores of the unfiltered (UF) and filtered time series (very low, low, and high frequency; VLF, LF and HF) of HR between patients with depression (n = 14) and healthy control subjects (n = 18). Results: We found significantly lower LLE of the unfiltered series in either posture, and HF series in patients with major depression in supine posture (p < .002). LLE (LF/UF), which may indicate relative sympathetic activity was also significantly higher in supine and standing postures in patients (p < .05); LF/HF (LLE) was also higher in patients (p < .05) in either posture. Conclusions: These findings suggest that major depression is associated with decreased cardiac vagal function and a relative increase in sympathetic function, which may be related to the higher risk of cardiovascular mortality, in this group and illustrates the usefulness of nonlinear measures of chaos such as LLE in addition to the commonly used spectral measures.