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12
Multiple local Whittle estimation in stationary systems
 ANNALS OF STATISTICS
, 2007
"... Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (), at the frequency of principal interest, zero; for short memory series = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differenci ..."
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Cited by 19 (4 self)
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Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (), at the frequency of principal interest, zero; for short memory series = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differencing" case = ( 2 1) =2; where 1; 2 are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the consequent properties of crossautocovariances to ones of the (possibly bilateral) moving average representation which, with martingale difference innovations of arbitrary dimension, is used in asymptotic theory for local Whittle parameter estimates depending on a single smoothing number. Incorporating also a regression parameter ( ) which, when nonzero, indicates cointegration, the consistency proof of these implicitlyde…ned estimates is nonstandard due to the estimate converging faster than the others. We also establish joint asymptotic normality of the estimates, and indicate how this outcome can apply in statistical inference on several questions of interest. Issues of implemention are discussed, along with implications of knowing and of correct or incorrect specification of; and possible extensions to higherdimensional systems and nonstationary series.
An analysis of the variance and distribution of commodity pricechanges
 Australian Journal of Management
, 1979
"... A method of jointly estimating the timedependent variance of daily commodity price changes and their distribution is presented. The data are copper spot prices (196674) and sugar futures prices (196173), for London contracts. Much of the leptokurtosis observed in the price chanqe distributions is ..."
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Cited by 2 (0 self)
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A method of jointly estimating the timedependent variance of daily commodity price changes and their distribution is presented. The data are copper spot prices (196674) and sugar futures prices (196173), for London contracts. Much of the leptokurtosis observed in the price chanqe distributions is shown to result from the mixinq of nonnormal distributions whose variances differ substantially. There are important consequences for conventional autocorrelation tests, which falsely assume a constant variance. The usefulness of the logarithmic transformation of prices is assessed statisticall ~ and it is found that the transformation does help to equalise the variance of price changes. Keywords:
GOODNESS OF FIT FOR LATTICE PROCESSES
"... Abstract. The paper discusses tests for the correct speci…cation of a model when data is observed in a ddimensional lattice, extending previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distribution of the tests are functionals of a ..."
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Cited by 1 (1 self)
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Abstract. The paper discusses tests for the correct speci…cation of a model when data is observed in a ddimensional lattice, extending previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distribution of the tests are functionals of a Gaussian sheet process, say B (), 2 [0; ] d. Because it is not easy to …nd a time transformation h ( ) such that B (h ()) becomes the standard Brownian sheet, a consequence is that the critical values are di ¢ cult, if at all possible, to obtain. So, to overcome the problem of its implementation, we propose to employ a bootstrap approach, showing its validity in our context. JEL Classi…cation: C21, C23. 1.
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, 2014
"... This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has ..."
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This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has
The Suntory Centre Suntory and Toyota International Centres for Economics and Related Disciplines
"... Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (γ), at the frequency of principal interest, zero; for short memory series γ = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differe ..."
Abstract
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Moving from univariate to bivariate jointly dependent long memory time series introduces a phase parameter (γ), at the frequency of principal interest, zero; for short memory series γ = 0 automatically. The latter case has also been stressed under long memory, along with the "fractional differencing " case γ = ( δ2 − δ1) π/ 2; where 1, δ2 δ are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the consequent properties of crossautocovariances to ones of the (possibly bilateral) moving average representation which, with martingale difference innovations of arbitrary dimension, is used in asymptotic theory for local Whittle parameter estimates depending on a single smoothing number. Incorporating also a regression parameter (β) which, when nonzero, indicates cointegration, the consistency proof of these implicitlydefined estimates is nonstandard due to the β estimate converging faster than the others. We also establish joint asymptotic normality of the estimates, and indicate how this outcome can apply in statistical inference on several questions of interest. Issues of implementation are discussed, along with implications of knowing β and of correct or incorrect specification of γ, and possible extensions to higherdimensional systems and nonstationary series.
Dependence Estimation for High Frequency Sampled Multivariate CARMA Models
"... The paper considers high frequency sampled multivariate continuoustime ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior of the crosscovariances between different components of the ..."
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The paper considers high frequency sampled multivariate continuoustime ARMA (MCARMA) models, and derives the asymptotic behavior of the sample autocovariance function to a normal random matrix. Moreover, we obtain the asymptotic behavior of the crosscovariances between different components of the model. We will see that the limit distribution of the sample autocovariance function has a similar structure in the continuoustime and in the discretetime model. As special case we consider a CARMA (onedimensional MCARMA) process. For a CARMA process we prove Bartlett's formula for the sample autocorrelation function. Bartlett's formula has the same form in both models, only the sums in the discretetime model are exchanged by integrals in the continuoustime model. Finally, we present limit results for multivariate MA processes as well which are not known in this generality in the multivariate setting yet.
Title of project: Generalized Autoregressive Conditional Heteroscedastic Time Series Models
, 2003
"... ii Autoregressive and Moving Average time series models and their combination are reviewed. Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models are extensions of these models. These are dened and compared to the class of Autoreg ..."
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ii Autoregressive and Moving Average time series models and their combination are reviewed. Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models are extensions of these models. These are dened and compared to the class of Autoregressive Moving Average models. Maximum likelihood estimation of parameters is examined. Conditions for existence and stationarity of GARCH models are discussed and the moments of the observations and the conditional variance are derived. Characteristics of low order GARCH models are explored further through simulations with dierent initial parameter values. As examples, GARCH models with dierent orders are tted to the Standard & Poor's 500 Stock Price Index. iii Acknowledgments First, I would like to thank Derek for encouraging me to apply for the M.Sc. program