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Elements of Forecasting
"... Most good texts arise from the desire to leave one's stamp on a discipline by training future generations of students, coupled with the recognition that existing texts are inadequate in various respects. My motivation is no different. There is a real need for a concise and modern introductory f ..."
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Cited by 88 (4 self)
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Most good texts arise from the desire to leave one's stamp on a discipline by training future generations of students, coupled with the recognition that existing texts are inadequate in various respects. My motivation is no different. There is a real need for a concise and modern introductory forecasting text. A number of features distinguish this book. First, although it uses only elementary mathematics, it conveys a strong feel for the important advances made since the work of Box and Jenkins more than thirty years ago. In addition to standard models of trend, seasonality, and cycles, it touches – sometimes extensively – upon topics such as: data mining and insample overfitting statistical graphics and exploratory data analysis model selection criteria recursive techniques for diagnosing structural change nonlinear models, including neural networks regimeswitching models unit roots and stochastic trends
On the meaning and use of kurtosis
 Psychological Methods
, 1997
"... For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurto ..."
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Cited by 78 (0 self)
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For symmetric unimodal distributions, positive kurtosis indicates heavy tails and peakedness relative to the normal distribution, whereas negative kurtosis indicates light tails and flatness. Many textbooks, however, describe or illustrate kurtosis incompletely or incorrectly. In this article, kurtosis is illustrated with wellknown distributions, and aspects of its interpretation a d misinterpretation are discussed. The role of kurtosis in testing univariate and multivariate normality; as a measure of departures from normality; in issues of robustness, outliers, and bimodality; in generalized tests and estimators, as well as limitations of and alternatives to the kurtosis measure [32, are discussed. It is typical ly noted in introductory statistics courses that distributions can be characterized in terms of central tendency, variability, and shape. With respect o shape, virtually every textbook defines and illustrates kewness. On the other hand, another aspect of shape, which is kurtosis, is either not discussed or, worse yet, is often described or illustrated incorrectly. Kurtosis is also frequently not reported in research articles, in spite of the fact that virtually every statistical package provides a measure of kurtosis. This occurs most likely because kurtosis is not well understood and because the role of kurtosis in various aspects of statistical analysis is not widely recognized. The purpose of this article is to clarify the meaning of kurtosis and to show why and how it is useful. On the Mean ing o f Kurtosis Kurtosis can be formally defined as the standardized fourth population moment about the mean, E (X IX)4 IX4
Monte Carlo test methods in econometrics
 Companion to Theoretical Econometrics’, Blackwell Companions to Contemporary Economics
, 2001
"... The authors thank three anonymous referees and the Editor Badi Baltagi for several useful comments. This work was supported by the Bank of Canada and by grants from the Canadian Network of Centres of Excellence [program on Mathematics ..."
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Cited by 37 (26 self)
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The authors thank three anonymous referees and the Editor Badi Baltagi for several useful comments. This work was supported by the Bank of Canada and by grants from the Canadian Network of Centres of Excellence [program on Mathematics
Tensorbased cortical surface morphometry via weighted spherical harmonic representation
 IEEE Transactions on Medical Imaging
, 2008
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Exact skewnesskurtosis tests for multivariate normality and goodnessoffit in multivariate regressions with application to asset pricing models
, 2003
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Mixed normal conditional heteroskedasticity
 Journal of Financial Econometrics
, 2004
"... Both unconditional mixednormal distributions and GARCH models with fattailed conditional distributions have been employed for modeling financial return data. We consider a mixednormal distribution coupled with a GARCHtype structure which allows for conditional variance in each of the components ..."
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Cited by 19 (4 self)
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Both unconditional mixednormal distributions and GARCH models with fattailed conditional distributions have been employed for modeling financial return data. We consider a mixednormal distribution coupled with a GARCHtype structure which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. An empirical application to NASDAQindex data indicates the appropriateness of the model class and illustrates that the approach can generate a plausible disaggregation of the conditional variance process, in which the components ’ volatility dynamics have a clearly distinct behavior that is, for example, compatible with the wellknown leverage effect.
Density Estimation Under Constraints
 J. Comput. Graph. Statist
, 1999
"... . We suggest a general method for tackling problems of density estimation under constraints. It is in effect a particular form of the weighted bootstrap, in which resampling weights are chosen so as to minimise distance from the empirical or uniform bootstrap distribution subject to the constraints ..."
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Cited by 16 (2 self)
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. We suggest a general method for tackling problems of density estimation under constraints. It is in effect a particular form of the weighted bootstrap, in which resampling weights are chosen so as to minimise distance from the empirical or uniform bootstrap distribution subject to the constraints being satisfied. A number of constraints are treated as examples. They include conditions on moments, quantiles and entropy, the latter as a device for imposing qualitative conditions such as those of unimodality or "interestingness." For example, without altering the data or the amount of smoothing we may construct a density estimator that enjoys the same mean, median and quartiles as the data. Different measures of distance give rise to slightly different results. KEYWORDS. Biased bootstrap, CressieRead distance, curve estimation, empirical likelihood, entropy, kernel methods, mode, smoothing, weighted bootstrap. SHORT TITLE. Constrained density estimation. AMS SUBJECT CLASSIFICATION. ...
HIGH MOMENT PARTIAL SUM PROCESSES OF RESIDUALS IN GARCH MODELS AND THEIR APPLICATIONS 1
, 2006
"... In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of kth powers of residuals, CUSUM processes and selfnormalized partial sum processes. The kth power partial sum process converges to a Brownian p ..."
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In this paper we construct high moment partial sum processes based on residuals of a GARCH model when the mean is known to be 0. We consider partial sums of kth powers of residuals, CUSUM processes and selfnormalized partial sum processes. The kth power partial sum process converges to a Brownian process plus a correction term, where the correction term depends on the kth moment µk of the innovation sequence. If µk = 0, then the correction term is 0 and, thus, the kth power partial sum process converges weakly to the same Gaussian process as does the kth power partial sum of the i.i.d. innovations sequence. In particular, since µ1 = 0, this holds for the first moment partial sum process, but fails for the second moment partial sum process. We also consider the CUSUM and the selfnormalized processes, that is, standardized by the residual sample variance. These behave as if the residuals were asymptotically i.i.d. We also study the joint distribution of the kth and (k + 1)st selfnormalized partial sum processes. Applications to changepoint problems and goodnessoffit are considered, in particular, CUSUM statistics for testing GARCH model structure change and the Jarque– Bera omnibus statistic for testing normality of the unobservable innovation distribution of a GARCH model. The use of residuals for constructing a kernel density function estimation of the innovation distribution is discussed.