Estimating the Positive and Negative Jumps of Asset Returns Via Kalman Filtering. The Case of Nasdaq Index

The daily asset (log) return is considered to consist of two parts, the positive and negative jump. These jumps are determined by the arrival of positive and negative news in the market, are not observable and their differences define the asset returns. In order to estimate the jumps, the basic discrete time-homogeneous linear Kalman filter is applied, in which all the noises are assumed to be normally distributed. Then, under the assumption that the estimated jumps have to be non-negative, the method of their pdfs’ truncation, according to the non-negativity constraints, is used, and it is accompanied by appropriate scaling. The fitting of the model is justified by examining the fitting of the estimated returns to the empirical ones. For that purpose, the daily Nasdaq returns during the three year period 2006-2008 are used.     

Pyrrolizidine Alkaloids from Onosma leptantha

Three new pyrrolizidine alkaloids, leptanthine ( 2 ), its corresponding N‐oxide 1 , and N‐oxide of 3′‐O‐acetylechihumiline ( 3 ), were isolated from the aerial parts of Onosma leptantha, together with two known alkaloids of the same type, echihumiline ( 5 ) and echihumiline N‐oxide ( 4 ). Their structures and configurations were determined by chemical and spectroscopic methods, especially 1D and 2D NMR analyses, including long‐range ¹H,¹⁵N correlations at natural abundance.     

Determination of Cisplatin and Carboplatin Anticancer Drugs by Non-suppressed Ion Chromatography with an Inductively Coupled Plasma Atomic Emission Detector

Two non-suppressed ion chromatographic (IC) methods, one with an anion and one with a cation separation column, were investigated for first time to determine cisplatin and carboplatin anticancer drugs using inductively coupled plasma–atomic emission spectrometry as a detector. The Shodex IC YK-421 (4.6?×?125?mm²) column was considered as the preferred separation column. The mobile phase in this case consisted of tartaric acid and boric acid. The flow rate was 1?mL/min and the injection volume was 20 μL. Separation was carried out in about 2?min with column temperature at 30°C after optimization. With cationic separation, the cisplatin elutes first, as opposed to the anionic one, where it elutes second. In addition, with both columns, a second peak for cisplatin appears which is attributed to a hydrolysis product of the drug. For the cation chromatographic method, the repeatability ranged from 3.1 to 5.9%, whereas the inter-day precision was 13.3 and 16.3% for cisplatin and carboplatin, respectively. The detection limits were 0.1?mg/?L Pt for both compounds. The proposed method was applied to the analysis of human urine with satisfactory recoveries indicating that there are no matrix effects.     

On the Number of Appearances of a Word in a Sequence of I.I.D. Trials

Let X ₁,...,X _n be a sequence of i.i.d. random variables taking values in an alphabet =₁,...,_q,q 2, with probabilities P(X _a=_i)=p _i,a=1,...,n,i=1,...,q. We consider a fixed h-letter word W=w₁...w_h which is produced under the above scheme. We define by R(W) the number of appearances of W as Renewal (which is equal with the maximum number of non-overlapping appearances) and by N(W) the number of total appearances of W (overlapping ones) in the sequence X _{a 1} a1n under the i.i.d. hypothesis. We derive a bound on the total variation distance between the distribution (R(W)) of the r.v. R(W) and that of a Poisson with parameter E(R(W)). We use the Stein-Chen method and related results from Barbour et al. (1992), as well as, combinatorial results from Schbath (1995b) concerning the periodic structure of the word W. Analogous results are obtained for the total variation distance between the distribution of the r.v. N(W) and that of an appropriate Compound Poisson r.v. Related limit theorems are obtained and via numerical computations our bounds are presented in tables.     

Evaluation of matrix solid‐phase dispersion extraction for the determination of polycyclic aromatic hydrocarbons in household dust with the aid of experimental design and response surface methodology

A simple, fast, and inexpensive procedure for sample preparation based on matrix solid‐phase dispersion was developed for the determination of Environmental Protection Agency 16 priority polycyclic aromatic hydrocarbons in indoor dust samples. Parameters that affect the extraction efficiency such as type of dispersant, elution solvent, and solvent volume were evaluated and optimized with the aid of experimental design and response surface methodology. Analysis was performed by HPLC coupled with UV‐Vis diode array detector (UV‐DAD). For verification, a GC coupled with a mass spectrometer in SIM mode was also applied. Recoveries obtained were from 53 to 120% for all target analytes with detection limits ranging from 0.2 to 10 ng/g and 0.2 to 2 ng/g for LC‐UV‐DAD and GC‐MS, respectively. The optimized method was used for the analysis of 11 household dust samples collected from private houses.     

Compound Poisson Approximation for Multiple Runs in a Markov Chain

We consider a sequence X ₁, ..., X _n of r.v.'s generated by a stationary Markov chain with state space A = {0, 1, ..., r}, r 1. We study the overlapping appearances of runs of k _i consecutive i's, for all i = 1, ..., r, in the sequence X ₁,..., X _n. We prove that the number of overlapping appearances of the above multiple runs can be approximated by a Compound Poisson r.v. with compounding distribution a mixture of geometric distributions. As an application of the previous result, we introduce a specific Multiple-failure mode reliability system with Markov dependent components, and provide lower and upper bounds for the reliability of the system.