49 results
3 - Low-Frequency Econometrics
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- By Ulrich K. Müller, Princeton University, Mark W. Watson, Princeton University
- Edited by Bo Honoré, Princeton University, New Jersey, Ariel Pakes, Harvard University, Massachusetts, Monika Piazzesi, Stanford University, California, Larry Samuelson, Yale University, Connecticut
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- Book:
- Advances in Economics and Econometrics
- Published online:
- 27 October 2017
- Print publication:
- 02 November 2017, pp 53-94
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Summary
Many questions in economics involve long-run or “trend” variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of low-frequency trigonometric weighted averages, which in turn can be used to conduct inference about long-run variability and covariability. Because the low-frequency weighted averages have large sample normal distributions, large sample valid inference can often be conducted using familiar small sample normal inference procedures. Moreover, the general approach is applicable for a wide range of persistent stochastic processes that go beyond the familiar I (0) and I (1) models.
INTRODUCTION
This paper discusses inference about trends in economic time series. By “trend” we mean the low-frequency variability evident in a time series after forming moving averages such as low-pass (cf. Baxter and King, 1999) or Hodrick and Prescott (1997) filters. To measure this low-frequency variability we rely on projections of the series onto a small number of trigonometric functions (e.g., discrete Fourier, sine, or cosine transforms). The fact that a small number of projection coefficients capture low-frequency variability reflects the scarcity of low-frequency information in the data, leading to what is effectively a “small-sample” econometric problem. As we show, it is still relatively straightforward to conduct statistical inference using the small sample of low-frequency data summaries.Moreover, these low-frequency methods are appropriate for both weakly and highly persistent processes. Before getting into the details, it is useful to fix ideas by looking at some data.
Figure 1 plots the value of per-capita GDP growth rates (panel A) and price inflation (panel B) for the United States using quarterly data from 1947 through 2014, and where both are expressed in percentage points at an annual rate. The plots show the raw series and two “trends.” The first trend was constructed using a band-pass moving average filter designed to pass cyclical components with periods longer than T/6 ≈ 11 years, and the second is the full-sample projection of the series onto a constant and twelve cosine functions with periods 2T/j for j = 1, …, 12, also designed to capture variability for periods longer than 11 years.
Quantifying ice cliff evolution with multi-temporal point clouds on the debris-covered Khumbu Glacier, Nepal
- C. SCOTT WATSON, DUNCAN J. QUINCEY, MARK W. SMITH, JONATHAN L. CARRIVICK, ANN V. ROWAN, MIKE R. JAMES
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- Journal:
- Journal of Glaciology / Volume 63 / Issue 241 / October 2017
- Published online by Cambridge University Press:
- 07 September 2017, pp. 823-837
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Measurements of glacier ice cliff evolution are sparse, but where they do exist, they indicate that such areas of exposed ice contribute a disproportionate amount of melt to the glacier ablation budget. We used Structure from Motion photogrammetry with Multi-View Stereo to derive 3-D point clouds for nine ice cliffs on Khumbu Glacier, Nepal (in November 2015, May 2016 and October 2016). By differencing these clouds, we could quantify the magnitude, seasonality and spatial variability of ice cliff retreat. Mean retreat rates of 0.30–1.49 cm d−1 were observed during the winter interval (November 2015–May 2016) and 0.74–5.18 cm d−1 were observed during the summer (May 2016–October 2016). Four ice cliffs, which all featured supraglacial ponds, persisted over the full study period. In contrast, ice cliffs without a pond or with a steep back-slope degraded over the same period. The rate of thermo-erosional undercutting was over double that of subaerial retreat. Overall, 3-D topographic differencing allowed an improved process-based understanding of cliff evolution and cliff-pond coupling, which will become increasingly important for monitoring and modelling the evolution of thinning debris-covered glaciers.
Electrolyte Detection by Ion Beam Analysis, in Continuous Glucose Sensors and in Microliters of Blood using a Homogeneous Thin Solid Film of Blood, HemaDrop™
- Yash Pershad, Ashley A. Mascareno, Makoyi R. Watson, Alex L. Brimhall, Nicole Herbots, Clarizza F. Watson, Abijith Krishnan, Nithin Kannan, Mark W. Mangus, Robert J. Culbertson, B. J. Wilkens, E. J. Culbertson, T. Cappello-Lee, R.A. Neglia
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- Journal:
- MRS Advances / Volume 1 / Issue 29 / 2016
- Published online by Cambridge University Press:
- 21 June 2016, pp. 2133-2139
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- 2016
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Percolation of blood and of interstitial fluids into implantable continuous glucose sensors (CGS) for diabetics presently limits sensor lifetime between 3 and 7 days. Na+ mobile ions in body fluids damage Si-based CGS sensors electronics. The direct detection of Na percolation is investigated by Ion Beam Analysis (IBA) and Proton Induced X-ray Emission (PIXE) in previously used CGS. Based on these results, a new technology called HemaDropTM is then tested to prepare small volume (5-10 µL) of blood for IBA. A species’s detectability by IBA scales with the square of the ratio of element’s atomic number Z to that of the substrate. Because Na has a low atomic number (Z=11), Si signals from sensor substrates can prevent Na detection in Si by 2 mega electron volt (MeV) IBA.
Using 4.7 MeV 23Na (α, α)23Na nuclear resonance (NR) can increase the 23Na scattering cross section and thus its detectability in Si. The NR energy, width, and resonance factor, is calibrated via two well-known alpha (α) particle signals with narrow energy spreads: a 5.486 ± 0.007 MeV 241Am α-source (ΔΕ = 0.12%) and the 3.038 ± 0.003 MeV 16O(α, α)16O NR (ΔΕ = 0.1%). Next, the NR cross section is calibrated via 100 nm NaF thin films on Si(100) by scanning the beam energy. The23Na (α, α) NR energy is found to be 4.696 ± 0.180 MeV, and the NR/RBS cross section 141 ± 7%. This is statistically significant but small compared to the 4.265 MeV 12C NR (1700%) and 3.038 MeV 16O NR (210%), and insufficient to detect small amounts of 23Na in Si. Next, a new method of sample preparation HemaDropTM, is tested for detection of elements in blood, such Fe, Ca, Na, Cl, S, K, C, N, and O, as an alternative to track fluid percolation and Na diffusion in damaged sensors. Detecting more abundant, heavier elements in blood and interstitial fluids can better track fluid percolation and Na+ ions in sensors. Both Na detection and accuracy of measured blood composition by IBA is greatly improved by using HemaDropTM sample preparation to create Homogeneous Thin Solid Films (HTSFs) of blood from 5-10 µL on most substrates. HTSF can be used in vacuo such as 10-8 –10-6 Torr).
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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Contributors
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- By Janice Capel Anderson, S. Wesley Ariarajah, Constantine Belezos, Ian Boxall, Marc Zvi Brettler, Edward Breuer, Daniel Bruno, Mark Chapman, W. T. Dickens, Mark W. Elliott, Eldon Epp, Tassilo Erhardt, Timothy Gorringe, Harriet Harris, Peter C. Hodgson, Leslie Howsam, Werner G. Jeanrond, Scott McLaren, Wayne A. Meeks, Néstor Míguez, Stephen D. Moore, Robert Morgan, Halvor Moxnes, Peter Neuner, Mark Noll, Jorunn Økland, Gaye Ortiz, John Riches, Christopher Rowland, Nicolaas A. Rupke, Edmund J. Rybarczyk, Lamin Sanneh, Constantine Scouteris, R. S. Sugirtharajah, Willard M. Swartley, William R. Telford, David Thompson, Elena Volkova, J. R. Watson, Gerald West, Michael Wheeler, Keith Whitelam
- Edited by John Riches, University of Glasgow
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- The New Cambridge History of the Bible
- Published online:
- 09 June 2015
- Print publication:
- 13 April 2015, pp xi-xii
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The ICV Sign as a Marker of Increased Cerebral Blood Transit Time
- Bijoy K. Menon, Helin Daniel Bai, Jayesh Modi, Andrew M. Demchuk, Mark Hudon, Mayank Goyal, Timothy W. J. Watson
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- Canadian Journal of Neurological Sciences / Volume 40 / Issue 2 / March 2013
- Published online by Cambridge University Press:
- 23 September 2014, pp. 187-191
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Objective/Background:
We describe the internal cerebral vein (ICV) sign, which is a hypo-opacification of the ICV on computed tomogram angiography (CTA) as a new marker of increased cerebral blood transit-time in ipsilateral internal carotid artery occlusions (ICAO).
Methods:A retrospective analysis of 153 patients with acute unilateral M1 middle cerebral artery (MCA) occlusions ± ICAOs was performed. The degree of contrast opacification of the ICV on the ipsilesional side was compared to that of the unaffected side.
Results:Of 153 patients in our study, 135 had M1 MCA occlusions ± intra-cranial ICAO (M1±iICAO) and 18 had isolated extracranial ICAO (eICAO). In the patients with proximal M1±iICAO, 57/65 (87.1%) showed the ICV sign. Of the 8 patients without the ICV sign in this group, 6 had prominent lenticulostriate arteries arising from the non-occluded M1 segment, 1 had a recurrent artery of Huebner, and 1 had filling of distal ICA/M1 segment through prominent Circle of Willis collaterals. For the 70 patients with isolated distal M1±iICAO, 7/70 (10%) showed the ICV sign, with all 7 showing occluded lenticulostriate arteries. Of the patients with eICAO, 8/18 showed the ICV sign, all 8 with the ICV sign had poor Circle of Willis collaterals.
Conclusions:The ICV sign correlates well with presence of proximal M1±iICAO in patients with either occluded lenticulostriate arteries or poor Circle of Willis collaterals. In patients with eICAO, the sign correlates with reduced Circle of Willis collaterals and may be a marker of increased ipsilateral cerebral blood transit time.
Contributors
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- By Lola Adewale, Nargis Ahmad, James Bennett, Stephanie Bew, Michael Broadhead, Peter Bromley, Alison S. Carr, David Chisholm, David de Beer, Bruce Emerson, Philippa Evans, Lisa Flewin, Michael W. Frost, Simon R. Haynes, Jane Herod, Alet Jacobs, Ian James, Ian A. Jenkins, Adrian R. Lloyd-Thomas, Daniel Lutman, Angus McEwan, Su Mallory, Vaithianadan Mani, George H. Meakin, Anthony Moriarty, Neil Morton, Reema Nandi, Naveen Raj, Steve Roberts, Steven Scuplak, Judith A. Short, Jonathan Smith, Ben Stanhope, Peter A. Stoddart, Mike R. J. Sury, Dan Taylor, Karl C. Thies, Mark Thomas, Isabeau Walker, Agnes Watson, Kathy A. Wilkinson, Glyn Williams, Sally Wilmshurst
- Edited by Ian James, Isabeau Walker
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- Core Topics in Paediatric Anaesthesia
- Published online:
- 05 August 2013
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- 04 July 2013, pp viii-x
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Testing for Cointegration When Some of the Cointegrating Vectors are Prespecified
- Michael T.K. Horvath, Mark W. Watson
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- Econometric Theory / Volume 11 / Issue 5 / October 1995
- Published online by Cambridge University Press:
- 11 February 2009, pp. 984-1014
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Many economic models imply that ratios, simple differences, or “spreads” of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's, and —1's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of the cointegrating vectors are prespecified under the null or under the alternative hypotheses. These tests are constructed in a vector error correction model and are motivated as Wald tests from a Gaussian version of the model. When all of the cointegrating vectors are prespecified under the alternative, the tests correspond to the standard Wald tests for the inclusion of error correction terms in the VAR. Modifications of this basic test are developed when a subset of the cointegrating vectors contain unknown parameters. The asymptotic null distributions of the statistics are derived, critical values are determined, and the local power properties of the test are studied. Finally, the test is applied to data on foreign exchange future and spot prices to test the stability of the forward–spot premium.
3 - Macroeconomic Forecasting Using Many Predictors
- Edited by Mathias Dewatripont, Université Libre de Bruxelles, Lars Peter Hansen, University of Chicago, Stephen J. Turnovsky, University of Washington
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- Advances in Economics and Econometrics
- Published online:
- 06 January 2010
- Print publication:
- 20 January 2003, pp 87-114
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Summary
INTRODUCTION
The past twenty-five years have seen enormous intellectual effort and progress on the development of small-scale macroeconometric models. Indeed, standing in the year 2000, it is not too much of an overstatement to say that the statistical analysis of small macroeconometric models in a stationary environment is largely a completed research topic. In particular, we have complete theories of estimation, inference, and identification in stationary vector autoregressions (VARs). We have accumulated a vast amount of experience using these models for empirical analysis. Identified VARs have become the workhorse models for estimating the dynamic effects of policy changes and for answering questions about the sources of business cycle variability. Both univariate autoregressions and VARs are now standard benchmarks used to evaluate economic forecasts. Although work remains to be done, great progress has been made on the complications associated with nonstationarity, both in the form of the extreme persistence often found in macroeconomic time series and in detecting and modeling instability in economic relations. Threshold autoregressions and Markov switching models successfully capture much of the nonlinearity in macroeconomic relations, at least for countries such as the United States.
Despite this enormous progress, it is also not too much of an overstatement to say that these small-scale macroeconometric models have had little effect on practical macroeconomic forecasting and policymaking. There are several reasons for this, but the most obvious is the inherent defect of small models: they include only a small number of variables. Practical forecasters and policymakers find it useful to extract information from many more series than are typically included in a VAR.
TEM of Sub-Micrometer Particles using the FIB Lift-Out Technique
- Janice K. Lomness, Brian W. Kempshall, Lucille A. Giannuzzi, Mark B. Watson
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- Journal:
- Microscopy and Microanalysis / Volume 7 / Issue S2 / August 2001
- Published online by Cambridge University Press:
- 02 July 2020, pp. 950-951
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- August 2001
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The ability to acquire TEM specimens from micrometer sized particles using an innovative FIB LO technique has been previously demonstrated [1-3]. This technique allowed for the preparation of a TEM LO specimen from regions which were smaller than the conventional dimensions of the LO specimen (∼5 μm × 20 μm). This paper shows how the LO technique previously developed for the preparation of micrometer sized particles [3] may be extended and utilized for the preparation of submicrometer sized particles for TEM analysis.
In this study, TiO2 particles on the order of 200 nm in width were investigated. A small portion of the TiO2 particles was dusted onto double stick carbon tape adhered to a sample stud and then sputtered coated with Au-Pd to protect the outer surface from FIB imaging. The sample stud containing the TiO2 particles was placed in an FEI 200TEM FIB workstation. Figure 1 is a FIB image of the Ti02 particles of interest. Gaps around these particles were deposited with Pt using the FIB assisted CVD process as shown in Figure 2. in this procedure, the Pt acts as a “weld” to hold the particles together, and to allow for a larger region to be milled (e.g., >10 μm) for subsequent specimen preparation.
PART FOUR - METHODOLOGY
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Texas A & M University, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
- Published online:
- 06 July 2010
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- 23 July 2001, pp 271-272
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Introduction
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Texas A & M University, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
- Published online:
- 06 July 2010
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- 23 July 2001, pp 1-27
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Summary
At the beginning of the twentieth century, there was very little fundamental theory of time series analysis and surely very few economic time series data. Autoregressive models and moving average models were introduced more or less simultaneously and independently by the British statistician Yule (1921, 1926, 1927) and the Russian statistician Slutsky (1927). The mathematical foundations of stationary stochastic processes were developed by Wold (1938), Kolmogorov (1933, 1941a, 1941b), Khintchine (1934), and Mann and Wald (1943). Thus, modern time series analysis is a mere eight decades old. Clive W. J. Granger has been working in the field for nearly half of its young life. His ideas and insights have had a fundamental impact on statistics, econometrics, and dynamic economic theory.
Granger summarized his research activity in a recent ET Interview (Phillips 1997), which appears as the first reprint in this volume, by saying, “I plant a lot of seeds, a few of them come up, and most of them do not.” Many of the seeds that he planted now stand tall and majestic like the Torrey Pines along the California coastline just north of the University of California, San Diego, campus in La Jolla, where he has been an economics faculty member since 1974. Phillips notes in the ET Interview that “It is now virtually impossible to do empirical work in time series econometrics without using some of his [Granger's] methods or being influenced by some of his ideas.”
18 - Long Memory Relationships and the Aggregation of Dynamic Models
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
- Published online:
- 06 July 2010
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- 23 July 2001, pp 338-348
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Summary
By aggregating simple, possibly dependent, dynamic micro-relationships, it is shown that the aggregate series may have univariate long-memory models and obey integrated, or infinite length transfer function relationships. A long-memory time series model is one having spectrum or order ω−2d for small frequencies ω, d > 0. These models have infinite variance for d ≧ ½ but finite variance for d > ½. For d = 1 the series that need to be differenced to achieve stationarity occur, but this case is not found to occur from aggregation. It is suggested that if series obeying such models occur in practice, from aggregation, then present techniques being used for analysis are not appropriate.
INTRODUCTION
In this paper it is shown that aggregation of dynamic equations, that is equations involving lagged dependent variables, can lead to a class of model that has fundamentally different properties to those in current use in econometrics. If these models are found to arise in practice, then they should prove useful in improving long-run forecasts in economics and also in finding stronger distributed lag relationships between economic variables.
The following definitions are required for later sections:
Suppose that xt is a zero-mean time series generated from a zero-mean, variance σ2 white noise series εt by use of the linear filter a(B), where B is the backward operator, so that
and that a(B) may be written
where a′(z) has no poles or roots at z = 0.
Index
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
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- 06 July 2010
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- 23 July 2001, pp 373-378
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Frontmatter
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
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- 06 July 2010
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- 23 July 2001, pp i-viii
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18 - Prediction with a Generalized Cost of Error Function
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Texas A & M University, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
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- 06 July 2010
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- 23 July 2001, pp 366-374
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Summary
Classical prediction theory limits itself to quadratic cost functions, and hence least-square predictors. However, the cost functions that arise in practice in economics and management situations are not likely to be quadratic in form, and frequently will be non-symmetric. It is the object of this paper to throw light on prediction in such situations and to suggest some practical implications. It is suggested that a useful, although suboptimal, manner of taking into account generalized cost functions is to add a constant bias term to the predictor. Two theorems are proved showing that under fairly general conditions the bias term can be taken to be zero when one uses a symmetric cost function. If the cost function is a non-symmetric linear function, an expression for the bias can be simply obtained.
INTRODUCTION
Suppose that one predicts some stochastic process and that it is subsequently found that an error of size x has been made. With such an error one can usually determine the cost of having made the error and the amount of this cost will usually increase as the magnitude of the error increases. Let g(x) represent the cost of error function. In both the classical theory of statistical prediction and in practice, this function is usually taken to be of the form g(x) = cx2, so that least-squares predictors are considered. However, in the fields of economics and management an assumption that the cost of error function is proportional to x2 is not particularly realistic.
Index
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Texas A & M University, Mark W. Watson, Princeton University, New Jersey
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- Book:
- Essays in Econometrics
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- 06 July 2010
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- 23 July 2001, pp 517-523
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PART THREE - LONG MEMORY
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
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- 06 July 2010
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- 23 July 2001, pp 319-320
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1 - Investigating Causal Relations by Econometric Models and Cross-Spectral Methods
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Essays in Econometrics
- Published online:
- 06 July 2010
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- 23 July 2001, pp 31-47
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Summary
There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.
The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later.
9 - Developments in the Study of Cointegrated Economic Variables
- Clive W. J. Granger
- Edited by Eric Ghysels, University of North Carolina, Chapel Hill, Norman R. Swanson, Rutgers University, New Jersey, Mark W. Watson, Princeton University, New Jersey
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- Book:
- Essays in Econometrics
- Published online:
- 06 July 2010
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- 23 July 2001, pp 173-188
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Summary
INTRODUCTION
At the least sophisticated level of economic theory lies the belief that certain pairs of economic variables should not diverge from each other by too great an extent, at least in the long run. Thus, such variables may drift apart in the short run or according to seasonal factors, but if they continue to be too far apart in the long-run, then economic forces, such as a market mechanism or government intervention, will begin to bring them together again. Examples of such variables are interest rates on assets of different maturities, prices of a commodity in different parts of the country, income and expenditure by local government and the value of sales and production costs of an industry. Other possible examples would be prices and wages, imports and exports, market prices of substitute commodities, money supply and prices and spot and future prices of a commodity. In some cases an economic theory involving equilibrium concepts might suggest close relations in the long-run, possibly with the addition of yet further variables. However, in each case the correctness of the beliefs about long-term relatedness is an empirical question. The idea underlying cointegration allows specification of models that capture part of such beliefs, at least for a particular type of variable that is frequently found to occur in macroeconomics. Since a concept such as the long-run is a dynamic one, the natural area for these ideas is that of time-series theory and analysis.