Periodic Heteroskedastic RegARFIMA models for daily electricity spot prices

In this paper we consider different periodic extensions of regression models with autoregressive fractionally integrated moving average disturbances for the analysis of daily spot prices of electricity. We show that day-of-the-week periodicity and long memory are important determinants for the dynamic modelling of the conditional mean of electricity spot prices. Once an effective description of the conditional mean of spot prices is empirically identified, focus can be directed towards volatility features of the time series. For the older electricity market of Nord Pool in Norway, it is found that a long memory model with periodic coefficients is required to model daily spot prices effectively. Further, strong evidence of conditional heteroskedasticity is found in the mean corrected Nord Pool series. For daily prices at three emerging electricity markets that we consider (APX in The Netherlands, EEX in Germany and Powernext in France) periodicity in the autoregressive coefficients is also stablished, but evidence of long memory is not found and existence of dynamic behaviour in the variance of the spot prices is less pronounced. The novel findings in this paper can have important consequences for the modelling and forecasting of mean and variance functions of spot prices for electricity and associated contingent assetsGARCH, Long Memory

A Note on the Effect of Seasonal Dummies on the Periodogram Regression

We discuss how prior regression on seasonal dummies leads to singularities in periodogram regression procedures for the detection of long memory. We suggest a modified procedure. We illustrate the problems using monthly inflation data from Hassler and Wolters (1995)

Long Memory Modelling of Inflation with Stochastic Variance and Structural Breaks

We investigate changes in the time series characteristics of postwar U.S. inflation. In a model-based analysis the conditional mean of inflation is specified by a long memory autoregressive fractionally integrated moving average process and the conditional variance is modelled by a stochastic volatility process. We develop a Monte Carlo maximum likelihood method to obtain efficient estimates of the parameters using a monthly data-set of core inflation for which we consider different subsamples of varying size. Based on the new modelling framework and the associated estimation technique, we find remarkable changes in the variance, in the order of integration, in the short memory characteristics and in the volatility of volatility

A seasonal periodic long memory model for monthly river flows

Based on simple time series plots and periodic sample autocorrelations, we document that monthly river flow data display long memory, in addition to pronounced seasonality. In fact, it appears that the long memory characteristics vary with the season. To describe these two properties jointly, we propose a seasonal periodic long memory model and fit it to the well-known Fraser river data (to be obtained from Statlib at http://lib.stat.cmu.edu/datasets/. We provide a statistical analysis and provide impulse response functions to show that shocks in certain months of the year have a longer lasting impact than those in other months

A periodic long memory model for quarterly UK inflation

We consider an extension of the fractionally integrated ARIMA(0, d, 0) model for quarterly UK inflation, where we allow the fractional integration parameter d to vary with the season s. This periodic ARFIMA(0, d, 0) model does not only provide an informative in-sample description, it may also be useful for out-of-sample forecasting. The main result is that the integration parameter in the first two quarters is significantly larger than that in the last two quarters

Did men of taste and civilization save the stage? Theatre-going in Rotterdam, 1860-1916. A statistical analysis of ticket sales

This essay deals with Dutch theater history of the second half of the 19th century (1860—1916). It statistically tests, whether the dominant opinion in Dutch theater writing, that after 1870 the stage recovered from a half century of decline, due to a renewed interest in it by the city elite, occupying the first ranks with a taste for civilized modern drama, and that, hence, a sharp cleft became visible between lower-rank tastes and upper-rank tastes. We test the tenability of this position on the basis of the Rotterdam Grand Theater archives, which contain ticket sales per rank per performance from 1776 till 1916, and the play bills of the performances. We analyze aggregated behavior of an anonymous theater consumers subdivided into price classes, hypothesizing that differences in attendance to high and low quality plays (as the critics judged them) over the different ranks, might reveal class-based divisions of taste. A long-memory time series analysis confirms that there is a significant gradual change of quality in the theater during the period 1860—1881, but this change is hardly rank- (and by implication likely class-) based. A second time series analysis, analyzing the impact of the repertoire and companies controlled for season and dynamics of the time series over the years 1860—1887 and 1887—1916, hardly sustains the narrative of recovery for most products as related to ranks. Only in a few telling instances, there was a clear opposition between low-rank tastes and upper-rank tastes. Hence, the recovery thesis must on the whole be rejected. This research will be followed-up by a prosopographical analysis of season-ticket and coupon holders in the Rotterdam theaters from 1773—1916, in which more detailed information on the social backgrounds and particularly on social class division of not anonymous theater audiences in `the long 19th century' is central

Inflation, Forecast Intervals and Long Memory Regression Models

We examine recursive out-of-sample forecasting of monthly postwar U.S. core inflation and log price levels. We use the autoregressive fractionally integrated moving average model with explanatory variables (ARFIMAX). Our analysis suggests a significant explanatory power of leading indicators associated with macroeconomic activity and monetary conditions for forecasting horizons up to two years. Even after correcting for the effect of explanatory variables, there is conclusive evidence of both fractional integration and structural breaks in the mean and variance of inflation in the 1970s and 1980s and we incorporate these breaks in the forecasting model for the 1980s and 1990s. We compare the results of the fractionally integrated ARFIMA(0,d,0) model with those for ARIMA(1,d,1) models with fixed order of d=0 and d=1 for inflation. Comparing mean squared forecast errors, we find that the ARMA(1,1) model performs worse than the other models over our evaluation period 1984-1999. The ARIMA(1,1,1) model provides the best forecasts, but its multi-step forecast intervals are too large

Loss of HR6B ubiquitin-conjugating activity results in damaged synaptonemal complex structure and increased crossing-over frequency during the male meiotic prophase.

The ubiquitin-conjugating enzymes HR6A and HR6B are the two mammalian homologs of Saccharomyces cerevisiae RAD6. In yeast, RAD6 plays an important role in postreplication DNA repair and in sporulation. HR6B knockout mice are viable, but spermatogenesis is markedly affected during postmeiotic steps, leading to male infertility. In the present study, increased apoptosis of HR6B knockout primary spermatocytes was detected during the first wave of spermatogenesis, indicating that HR6B performs a primary role during the meiotic prophase. Detailed analysis of HR6B knockout pachytene nuclei showed major changes in the synaptonemal complexes. These complexes were found to be longer. In addition, we often found depletion of synaptonemal complex proteins from near telomeric regions in the HR6B knockout pachytene nuclei. Finally, we detected an increased number of foci containing the mismatc

Empirical Vector Autoregressive Modeling

Chapter 2 introduces the baseline version of the VAR model, with its basic statistical assumptions that we examine in the sequel. We first check whether the variables in the VAR can be transformed to meet these assumptions. We analyze the univariate characteristics of the series. Important properties are a bounded spectrum, the order of (seasonal) integration, linearity and normality after the appropriate transformation. Subsequently, these properties are contrasted with the properties of stochastic fractional integration. We suggest data-analytic tools to check the assumption of univariate unit root integration. In an appendix we give a detailed account of unit root tests for stochastic unit root nonstationarity versus deterministic nonstationarity at frequencies of interest. Chapter 3 first discusses local and global influence analysis, which should point out the observations with the most notable impact on the estimates of location and covariance parameters. The results from this analysis can be helpful in spotting the sources of possible problems with the baseline model. After the influence analysis we discuss the merits of various statistical diagnostic tests for the adequacy of the separate regression equations. After one has estimated the unrestricted VAR one should check some overall characteristics of the system. We present several suggestions on how to do this. Chapter 4 deals with common sources of misspecification stemming from problems with seasonality and seasonal adjustment in the multivariate model. We discuss a number of univariate unobserved component models for stochastic seasonality, giving additional insight into the properties of models with unit root nonstationarity. We also suggest a modification of a simple but quite robust seasonal adjustment procedure. Some new data-analytic tools are introduced to examine the seasonal component more closely. Appendix A4.1 discusses the limitations of deterministic modeling of seasonality. Appendix A4.2 treats aspects of backforecasting in models with nonstationarity in mean. Chapter 5 introduces outlier models. We develop a testing procedure to direct and evaluate the treatment of exceptional observations in the VAR. We illustrate its application on an artificial data set that contains important characteristics of macroeconomic time series. The effect of the outliers and the effectiveness of the testing procedure is also analyzed on a four-variate set of quarterly French data, which exhibits cointegration. We compare some ready-to-use outlier correction methods in the last section. Chapter 6 deals with restrictions on the VAR model. First we discuss a number of interesting reparameterizations of the VAR under unit root restrictions. The reparameterizations lead to different interpretations, which can help to assess the plausibility of empirical outcomes. We present some straightforward transformation formulae for a number of these parameterizations and show which assumptions are essential for the equivalence of these models. We illustrate this in simple numerical examples. Next we compare VAR based methods to estimate pushing trends and pulling equilibria in multivariate time series. The predictability approach of Box and Tiao receives special attention. Finally we discuss multivariate tests for unit roots and cointegration. Chapter 7 applies the methods described in the previous chapters to analyze gross fixed capital investment in the Netherlands from 1961 to 1988 in a six-variate system. We discuss a number of economic approaches to model macroeconomic investment series. We list a number of problems in empirical applications of these models. Section 7.3 presents empirically relevant aspects of the measurement model for macroeconomic investment. Section 7.4 applies the univariate techniques of Chapters 2, 3, 4 and 5 to the investment series and five other macroeconomic with a notable dynamic relationship with investment, viz. consumption, imports, exports, the terms of trade and German industrial production. The univariate analysis clearly shows the presence of nonstationary seasonal components in a number of the series. The model is extended with a structural break on the basis of results from the univariate analysis. The subsequent multivariate analysis confirms the need for a structural break in the model for the growth rates of the multivariate series. An empirically important equilibrium relation between investment, imports and exports is seen to remain stable over the entire sample period. The partial correlation of deviations from this equilibrium and growth rates of investment is large and stable

Review of SsfPack 2.2: statistical algorithms for models in state space

SsfPack is a set of procedures with a strong link to the object-oriented matrix programming language Ox. In this review I Þrst discuss installation issues and prerequisites for a productive use of SsfPack, namely statistical and econometric knowledge, programming skills and additional software. Next I discuss the documentation and sample programs. Before concluding I discuss extensions in the direction of user-friendly programs