Forecasting the Yield Curve of Government Bonds: A Comparative Study

For the past 20 years, researchers have applied the Kalman filter to the modeling and forecasting the term structure of interest rates. Despite its impressive performance in in-sample fitting yield curves, little research has focused on the out-of-sample forecast of yield curves using the Kalman filter. The goal of this thesis is to develop a unified dynamic model based on Diebold and Li (2006) and Nelson and Siegel’s (1987) three-factor model, and estimate this dynamic model using the Kalman filter. We compare both in-sample and out-of-sample performance of our dynamic methods with various other models in the literature. We find that our dynamic model dominates existing models in medium- and long-horizon yield curve predictions. However, the dynamic model should be used with caution when forecasting short maturity yields

Maid of the Mist, Niagara, U.S.A.

The description of the image is "(6) Majestically Grand - the Falls from the 'Maid of the Mist,' Niagara, U.S.A.". The reverse of the image reads "You are on the deck of the small but sturdy little steamer that runs along near the foot of the falls. At this moment you are pretty nearly mid-stream, looking south. The American shore are up over your left shoulder. That tall, dark cliff at the extreme left of what you see is Goat Island. The people up there outlined against the sky look like dolls and no wonder; they are more than 160 feet above your head. Some of them are looking off over the unspeakable grandeurs of the Horseshoe Fall there at the right; some are without doubt looking down at the very boat and remarking that the passengers look like dolls. It is an awesome experience to go so near that never-ceasing downpour of waters from the sky. The air is full of the roar and iridescent spray, and it seems as if the boat must be drawn in under the overwhelming floods never to rise again. Yet, curiously enough, the river right around the boat is not so madly excited as you might expect. It seems more like some great creature, dazed, bewildered, stunned by some incredible experience and not yet quite aware of what has happened. (When it gets down into the Whirlpool Rapids, two miles below here, it is dramatically alive to its situation!) The gigantic curve of the cliffs, reaching in up-stream straight ahead, makes a contour line of over 3000 feet before it comes up against the Canadian banks on the west (right). Geologists say that the Falls ages ago must have been at least seven miles farther down the river (behind you) and have gradually won their way back. Even now the curve of the Horseshoe is worn away from two to four feet in a year. No wonder; 12, 000, 000 cubic feet of water (about 375, 000 tons) sweep over the rocks in one minute, and the same the next minute and the next and the next. See Niagara through the Stereoscope, with special maps locating all the landmarks about the Falls.

Horseshoe Falls from Above, U.S.A.

The description reads "(39) Tireless Niagara - Horseshoe Falls from above - U.S.A.". The reverse states "We are standing on the Canadian side of the river, looking S.E. across the enormous curve of the Horseshoe toward the Dufferin Islands on the Canadian side. 'This is close enough. The time will come undoubtedly when no man can reach this point, when the rocks on which we stand will break and crash into the gulf above which they hang. Table Rock one of the best known points about Niagara in the past, used to extend out over the river from the bank just behind us. It was originally very large but great masses, sometimes a hundred feet in length by fifty in width, have broken off at different periods, the last in 1883, until the whole rock is gone. Off to our left is the centre of the Horseshoe. It is easy to see that in that direction the water is going over in a solid mass, thousands of tons each second, to the river 150 feet below. While the amount of water passing over these rocks varies somewhat according to the height of the river. It has been estimated that the average amount is 12,000,000 cubic feet per minute, that is, about 375,000 tons...Since 1842 the whole contour of these falls has been worn away at the rate of about 2 1/10 ft. per year. In the centre of the Horseshoe where the bulk of the water passes, nearly five feet of rock are worn away each year. The falls have receded 100 feet within the memory of the men now living.' From Niagara Through the Stereoscope, with special 'keyed' maps, published by Underwood & Underwood"

View of Falls from Steel Bridge, Niagara, U.S.A.

The description of the image reads "(4)-8972-General view of Falls from new steel bridge - Maid of the Mist at landing - Niagara, U.S.A." The reverse of the image includes the description, "We are standing on the new steel bridge over Niagara River, 190 feet above the water and looking a little west of south, up the river towards Lake Erie. The high cliff at the extreme left, on the American side, is Prospect Point, where a crowd is gathered at this moment to view the Falls that we see just beyond Prospect Point. That dark, tree-covered mass of rock beyond is Goat Island; and just this side of Goat Island we see a bit of its precipice has been cut off separate from the rest by the powerful current of the waters - the smaller portion is Luna Island, and the Luna Falls go pouring down between the two islands. The face of the precipice curves inward beneath the Luna Falls leaving behind the 160 foot sheet of water the unearthly hollow known as the Cave of the Winds. Beyond Goat Island we see the gigantic curve of the Horseshoe Falls, 3,010 feet long and 158 feet high, reaching around through the clouds of spray to the farther Canadian shore. (The boundary line between British and American territory is in mid-stream.) It has been estimated that every minute 375,000 tons of water pour over these Horseshoe Falls, and they are wearing away the cliffs, moving back up the stream at the rate of 2.4 feet per year. It was probably only about a thousand years ago that they took their plunge just about where we stand now. Down there below us, at the wharf is the Maid of the Mist at the American landing taking on passengers who have come down the steep bank by the inclined railway. Its course takes it through those clouds of spray almost to the very foot of both Falls, - waters falling from 167 feet overhead, and water surging at least as many feet deep under the staunch little vessel. See special 'keyed' maps of Niagara pub. by Underwood and Underwood, also the Niagara Book by Mark Twain, W.D. Howells and others."

Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.