|
Showing 1 - 2 of
2 matches in All Departments
Box and Jenkins (1970) made the idea of obtaining a stationary time
series by differencing the given, possibly nonstationary, time
series popular. Numerous time series in economics are found to have
this property. Subsequently, Granger and Joyeux (1980) and Hosking
(1981) found examples of time series whose fractional difference
becomes a short memory process, in particular, a white noise, while
the initial series has unbounded spectral density at the origin,
i.e. exhibits long memory.Further examples of data following long
memory were found in hydrology and in network traffic data while in
finance the phenomenon of strong dependence was established by
dramatic empirical success of long memory processes in modeling the
volatility of the asset prices and power transforms of stock market
returns.At present there is a need for a text from where an
interested reader can methodically learn about some basic
asymptotic theory and techniques found useful in the analysis of
statistical inference procedures for long memory processes. This
text makes an attempt in this direction. The authors provide in a
concise style a text at the graduate level summarizing theoretical
developments both for short and long memory processes and their
applications to statistics. The book also contains some real data
applications and mentions some unsolved inference problems for
interested researchers in the field.
This book presents a unified approach for obtaining the limiting distributions of minimum distance, M and R estimators corresponding to non-smooth underlying scores in a large class of dynamic non-linear models including ARCH models. It also discusses classes of goodness-of-t tests for fitting an error distribution in some of these models and/or fitting a regression-autoregressive function without assuming the knowledge of the error distribution. The main tool is the asymptotic equicontinuity of certain basic weighted residual empirical processes in the uniform and L2 metrics. The contents of this monograph should be useful to graduate students and research scholars in statistics, econometrics, and finance. This book is a an updated edition of the author's monograph Weighted Empirical Processes and Liner Models (IMS Lecture Notes-Monograph 21, 1992). The new edition differs from the previous one in many ways. To mention just a few: It includes asymptotically distribution free tests for fitting a regression and/or an autoregressive models; the asymptotic distributions of auto-regression quantiles and rank scores; and above all the weak convergence of the residual empirical processes useful in nonlinear ARCH models. Hira L. Koul is a professor of statistics at Michigan State University. He is a Fellow of the IMS and an Elected Member of the International Statistical Institute. He was awarded the prestigious Humboldt Research Award for Senior Researchers in 1995. He has been on the editorial boards of the Annals of Statistics, Sankhya, and J. Indian Statistical Association. Currently he is a Coordinating Editor of the Journal of Statistical Planning and Inference, and an Associate Editor of Statistics and Probability Letters.
|
You may like...
Poor Things
Emma Stone, Mark Ruffalo, …
DVD
R357
Discovery Miles 3 570
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.