Returns series

By default, Maple returns series solutions accurate to the order of t. The order can be increased as ... 

The data that can go into computing factor returns will of course depend on what the factors are. It can include bond and index level data as well as currency exchange rates. Assume that we have the factor return series. To construct covariances, we could postulate that the underlying random processes are time stationary and compute covariances using equally weighted factor returns. We actually know that mar-... 

Factor return series often have different lengths, some series starting earlier than others. Return series can also have holes. As a result, what works well for two factors is here useless. That is, filling the factor covariance matrix row i and column j using the usual formula produces a non-positive definite matrix. A statistical approach known as the EM algorithm is the conventional workaround. Details on the algorithm can be found in Dempster, Laird, and Rubin, and for the purpose of this discussion, we only need to know that there exists a tool that can use incomplete series to produce an optimal estimate of the true covariance matrix. 

With a model that has on the order of 180 factors, we need to solve for over 16,000 covariances. Factor returns series include, in many cases, less than 30 to 40 periods. With such a small sample size compared to the number of factors, we have a severely underdetermined problem and are virtually assured that the covariance forecasts will show a large degree of spurious linear dependence among the factors. One consequence is that it becomes possible to create portfolios with artificially low risk forecasts. The structure of these portfolios would be pecu-... 

Unfortunately, we cannot stop there and use equation (23.11). The benefit of using global factors is that they help compute cross-market terms and constitute the skeleton of the matrix. The drawback is a loss of resolution at the local level. A solution to this problem is to replace local blocks by a local covariance matrix computed using the full set of original local factors. Off-diagonal blocks need to be adjusted in the process to insure that the final matrix is positive definite. A more detailed discussion of how the local covariance blocks are replaced can be found in Stefek. Local covariance blocks can be computed individually for each market, but also for emerging markets spread factors and currency factors. As a result, shorter half-life can be used for return series that are typically more volatile, such as currency and emerging market returns. 

The reaction is initiated with nickel carbonyl. The feeds are adjusted to give the bulk of the carbonyl from carbon monoxide. The reaction takes place continuously in an agitated reactor with a Hquid recirculation loop. The reaction is mn at about atmospheric pressure and at about 40°C with an acetylene carbon monoxide mole ratio of 1.1 1 in the presence of 20% excess alcohol. The reactor effluent is washed with nickel chloride brine to remove excess alcohol and nickel salts and the brine—alcohol mixture is stripped to recover alcohol for recycle. The stripped brine is again used as extractant, but with a bleed stream returned to the nickel carbonyl conversion unit. The neutralized cmde monomer is purified by a series of continuous, low pressure distillations. 

Statistical Process Control. A properly miming production process is characterized by the random variation of the process parameters for a series of lots or measurements. The SPG approach is a statistical technique used to monitor variation in a process. If the variation is not random, action is taken to locate and eliminate the cause of the lack of randomness, returning the process or measurement to a state of statistical control, ie, of exhibiting only random variation. 

The first reactor in series in the Arco, lEP, and Phillips processes is adiabatic (vessel filled with catalyst). The exothermic heat of reaction is removed in a pump-around loop where a portion of the reactor contents are taken from the reactor, pumped through an external exchanger, cooled, and returned to the reactor. 

Almost 40 years later the Lummus Co. patented an integrated process involving the addition of chlorine along with the sodium chloride and sodium hydroxide from the cathode side of an electrolytic cell to a tertiary alcohol such as tertiary butanol to produce the tertiary alkyl hypochlorite. The hypochlorite phase separates, and the aqueous brine solution is returned to the electrolytic cells. The alkyl hypochlorite reacts with an olefin in the presence of water to produce a chlorohydrin and the tertiary alcohol, which is returned to the chlorinator. With propylene, a selectivity to the chlorohydrin of better than 96% is reported (52). A series of other patents covering this technology appeared during the 1980s (53—56). 

Bucket Elevators. In a bucket elevator, a series of buckets attached to an endless belt or chain are filled with material and lifted vertically to a head pulley or sprocket, where the material is dumped. The buckets are then returned back down to a tail pulley or sprocket at the bottom. Bucket elevators are not self-feeding. They must be fed at a controlled rate to avoid overfilling the buckets and damagiag the machinery. In the usual arrangement of a bucket elevator, the chain or belt path is vertical or steeply inclined ia a single plane. Special chain supported bucket systems that can travel ia two and three planes have been developed. 

Most FCC unit regenerators employ 6-16 sets of primary and secondary cyclones in series, depending on unit size. These cyclones are designed to recover catalyst particles that are larger than 20 p. The recovered catalyst particles are returned to the regenerator via the diplegs. The flue gas exits the cyclones through a plenum chamber. 

Instead of using conventional refrigeration and condensers to convert incoming gas into LNG, the system was designed to feed 2,340 Nm / day (86,800 scfd) into each of two expanders. Both are connected in parallel, with compressors attached at the back end. The compressors are connected in series to boost a single stream of returning gas. 

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