Using Monte Carlo Method to Compare CUSUM and. EWMA Statistics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Using Monte Carlo Method to Compare CUSUM and. EWMA Statistics"

Transcription

1 Using Mone Carlo Mehod o Compare CUSUM and EWMA Saisics Xiaoyu Shen Zhen Zhang Absrac: Since ordinary daases usually conain change poins of variance, CUSUM and EWMA saisics can be used o deec hese change poins. In his projec, we are going o use Mone Carlo Mehod o compare he efficiencies of hese wo saisics according o he average run lengh (ARL). Key words: change poin, CUSUM, EWMA, Mone Carlo Mehod, ARL 1. Inroducion Basic saisical heories old us ha he variance of a daa series is a very useful crierion indicaing he deviaion of he original daa from he mean. However, a series of pracical daa usually may no have he consan variance, such ha deecing he momen when he variance of daa changes has is own significan value. In he qualiy conrol heory, here exis wo qualiy conrol chars based on wo differen saisics, cumulaive sum (CUSUM) and exponenially weighed moving average (EWMA). From hese wo chars, one can easily noice he momen when he properies of daa become abnormal, which may help us o conrol he qualiy of daa. Our opic in his projec will focus on he CUSUM and EWMA saisics. Many saisical papers have revealed ha afer some simple ransformaions, boh CUSUM and EWMA saisics can be used o deec he change poins of variance. 2. Empirical Resuls The expression of cumulaive sum of square is CUSUM: C. 1 2 We can ge he D saisic afer some simple ransformaion of CUSUM. 2 C 1 D C n n n 2 n 1, 1,2, n.

2 Also, we can ge he expression of EWMA. EWMA: W r W r, 2 (1 ) 1 ln( ) 1, 2 2 ( xi ) 1 i 1 1 xi i 1. where i r(1 r) 2 r r 1 2 r i 2 EWMAn ( r) max r(1 r) ln( ) 1 2 i, n r(1 (1 r) ) i 0 2 (1 (1 r) ) is he weigh of he saisic. The mehod which may be found in many boos abou qualiy conrol is no he opic of our projec, so ha i is no included in his paper. Afer giving he expression of CUSUM and EWMA, we need o compare hese wo saisics. To finish his comparison, we inroduce a new crierion, he average run lengh, which may help us o compare he deecing effec of hese wo saisics. The following is he definiion of he average run lengh. Definiion: The average run lengh (ARL) of a sampling inspecion scheme a a given level of qualiy is he average number of samples of n iems aen in he period beween he ime when he process commences o run a he saed level and ha a which he scheme indicaes a change from accepable o rejecable qualiy level is liely o have occurred. In his projec, we can define ARL as he mean of he firs run lengh he change poin ae place afer generaing large numbers of samples. Wih he help of compuers, we could do he simulaion sudy of ARL o compare he deecing effec of CUSUM and EWMA. 3. Pracical Resuls To es he effec of CUSUM saisic, we firs generae wo series of random daa, each of which has 1000 daa. One of hem has no change poins of variance, anoher has wo change poins of variance. I is obvious o noice from he firs pair of plo ha 400 and 700 are he change poins of variance in he second series of daa. We can see from he second pair of graph ha he plo of CUSUM saisic wihou variance change poins is close o a line, while ha wih variance change poins has differen slopes. Afer some simple ransformaion, we ge he D plo (hird pair of plos) which shows he change poins more obviously. The D plo of daa wihou change poins is close o a line (bounded in [-0.015, 0.015]), while he D plo of daa wih change poins grealy exceed ha boundary and has he maximum a poin 700. Even if D plo canno convince us of he fac ha poin 400 is also a change poin, CUSUM saisics and is derivaive D really have good effecs on deecing he change poins of variance.

3 Figure 1: Effec of CUSUM We use he same wo series of daa o es he effec of EWMA saisic. The firs column in Figure 2 is he graphs of daa wihou variance change poins and he second column is hose wih change poins. Alhough differen weigh r may have differen effec of deecing, we can see he change poins of variance obviously from all he plos in he second column. Bu also from hese plos, he values of EWMA saisics seem o be abnormal when he lengh r is close o zero. So i is difficul for EWMA o deec he change poin exising a he beginning of daa.

4 Figure 2: Effec of EWMA (r=0.2, 0.6 and 0.9) We now from he previous discussion ha CUSUM and EWMA boh can help o deec he change poin of variance, so i is ime for us o apply Mone Carlo Mehod o he furher research now. According o Mone Carlo simulaion sudy of wo saisics, we find he ARL of CUSUM is always smaller han ha of EWMA, no maer how large he sample size n and weigh r are. If he sample size n is small, he ARL of EWMA decreases when he weigh r increases from 0.2 o 0.9. Bu if he sample size is large, he ARL of EWMA increases when he weigh r increases. n=50 n=100 n=200 CUSUM EWMA (r=0.2) EWMA (r=0.6) EWMA (r=0.9) Table 1: S=100

5 n=50 n=100 n=200 CUSUM EWMA (r=0.2) EWMA (r=0.6) EWMA (r=0.9) Table 2: S=300 n=50 n=100 n=200 CUSUM EWMA (r=0.2) EWMA (r=0.6) EWMA (r=0.9) Table 3: S= Conclusion CUSUM and EWMA can be boh used o deec he change poin of variance. However, afer comparing he ARL of hese wo saisics wih he help of Mone Carlo Mehod, we now ha change poins of variance migh be more easily found by means of CUSUM. In he case of EWMA, when he sample size is small, EWMA wih large weigh has beer effec of change poins deecing. Bu when he sample size is large, EWMA wih small weigh wors beer han ha wih large weigh. In addiion, we noice from he plo ha EWMA saisic canno deec he change poin a he beginning of he daase. The reasons may be he fac ha when he lengh r is small, EWMA will be oo large o reflec he effec of deecing. Also, informaion included in he beginning par of daa may no be adequae for EWMA o deec he overall change poins. Appendix R code for he projec # es he effec of CUSUM a=rnorm(1000);b=a; b[401:700]=rnorm(300,0,0.4);b[701:1000]=rnorm(300,0,1.2); c=a;d=a;e=b;f=b;c[1]=a[1]^2;e[1]=b[1]^2; for(i in 1:999) {c[i+1]=c[i]+a[i+1]^2;e[i+1]=e[i]+b[i+1]^2;} for(j in 1:1000) {d[j]=c[j]/c[1000]-j/1000;f[j]=e[j]/1000-j/1000;}

6 plo(a,ype="l",main="var is consan") plo(b,ype="l",main="var is non-consan") plo(c,ype="l",ylab="c",main="cusum") plo(e,ype="l",ylab="c",main="cusum") plo(d,ype="l",ylab="d",main="d plo",ylim=c(-0.3,0.3)) plo(f,ype="l",ylab="d",main="d plo",ylim=c(-0.3,0.3)) # es he effec of EWMA (r=0.2, 0.6 and 0.9) ewma=funcion(r){ c=a;d=a;e=b;f=b;c[1]=a[1]^2;e[1]=b[1]^2; for(i in 1:999) {c[i+1]=c[i]+a[i+1]^2;e[i+1]=e[i]+b[i+1]^2;} for(j in 1:1000) {d[j]=c[j]/j;f[j]=e[j]/j;} g=a;h=a;h[1]=sqr(2-r)/sqr(r*(1-(1-r)^2))*r*log(d[1]^2); for(i in 2:1000){g[1]=r*(1-r)^(i-1)*log(d[1]^2); for(j in 1:(i-1)) g[j+1]=r*(1-r)^(i-j-1)*log(d[j+1]^2)+g[j]; h[i]=sqr(2-r)/sqr(r*(1-(1-r)^(2*i)))*g[i]} x=b;y=b;y[1]=sqr(2-r)/sqr(r*(1-(1-r)^2))*r*log(f[1]^2); for(i in 2:1000){x[1]=r*(1-r)^(i-1)*log(f[1]^2); for(j in 1:(i-1)) x[j+1]=r*(1-r)^(i-j-1)*log(f[j+1]^2)+x[j]; y[i]=sqr(2-r)/sqr(r*(1-(1-r)^(2*i)))*x[i]} plo(h,ype="l",main="r=0.2") plo(y,ype="l",main="r=0.2") } # calculae he ARL of CUSUM (S=100,300,500, n=50,100,200) arl.cusum = funcion(s,n){ # S=100, n=50 z=rep(0,n) for( in 1:S) {a=rnorm(n); c=a;d=a;c[1]=a[1]^2; for(i in 1:(n-1)) {c[i+1]=c[i]+a[i+1]^2;} for(j in 1:n) {d[j]=c[j]/c[n]-j/n;} z[]=1; for(i in 1:( n-1)) { if (abs(d[i+1])>=abs(d[i])) {z[]=i+1;} else {d[i+1]=d[i]} }} lis(arl=mean(z))

7 } # calculae he ARL of EWMA (S=100,300,500, n=50,100,200, r=0.2, 0.6, 0.9) arl.ewma = funcion(s,n,r){ z=rep(0,s) for( in 1:S) {a=rnorm(n); c=a;d=a;c[1]=a[1]^2; for(i in 1:(n-1)) {c[i+1]=c[i]+a[i+1]^2;} for(j in 1:n) {d[j]=c[j]/j;} g=a;h=a;h[1]=sqr(2-r)/sqr(r*(1-(1-r)^2))*r*log(d[1]^2); for(i in 2:n){g[1]=r*(1-r)^(i-1)*log(d[1]^2); for(j in 1:(i-1)) g[j+1]=r*(1-r)^(i-j-1)*log(d[j+1]^2)+g[j]; h[i]=sqr(2-r)/sqr(r*(1-(1-r)^(2*i)))*g[i]} z[]=round(n/3); for(i in round(n/3):(n-1)) { if (abs(d[i+1])>=abs(d[i])) {z[]=i+1;} else {d[i+1]=d[i]} }} lis(r=r,arl=mean(z)) }

Revisions to Nonfarm Payroll Employment: 1964 to 2011

Revisions to Nonfarm Payroll Employment: 1964 to 2011 Revisions o Nonfarm Payroll Employmen: 1964 o 2011 Tom Sark December 2011 Summary Over recen monhs, he Bureau of Labor Saisics (BLS) has revised upward is iniial esimaes of he monhly change in nonfarm

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

Acceleration Lab Teacher s Guide

Acceleration Lab Teacher s Guide Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution

Entropy: From the Boltzmann equation to the Maxwell Boltzmann distribution Enropy: From he Bolzmann equaion o he Maxwell Bolzmann disribuion A formula o relae enropy o probabiliy Ofen i is a lo more useful o hink abou enropy in erms of he probabiliy wih which differen saes are

More information

A Probability Density Function for Google s stocks

A Probability Density Function for Google s stocks A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?

More information

9. Capacitor and Resistor Circuits

9. Capacitor and Resistor Circuits ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Establishing Prefabricated Wood I-Joist Composite EI

Establishing Prefabricated Wood I-Joist Composite EI July 008 Esablishing Prefabricaed Wood I- Composie EI INTRODUCTION Composie (glued/nailed) floors are common in boh residenial and commercial consrucion, and have been successfully designed by Prefabricaed

More information

INTRODUCTION TO FORECASTING

INTRODUCTION TO FORECASTING INTRODUCTION TO FORECASTING INTRODUCTION: Wha is a forecas? Why do managers need o forecas? A forecas is an esimae of uncerain fuure evens (lierally, o "cas forward" by exrapolaing from pas and curren

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

House Price Index (HPI)

House Price Index (HPI) House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

Rotational Inertia of a Point Mass

Rotational Inertia of a Point Mass Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

Part 1: White Noise and Moving Average Models

Part 1: White Noise and Moving Average Models Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

More information

A Re-examination of the Joint Mortality Functions

A Re-examination of the Joint Mortality Functions Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot College Physics Lab RC Circuits Scott Hildreth Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

More information

GUIDE GOVERNING SMI RISK CONTROL INDICES

GUIDE GOVERNING SMI RISK CONTROL INDICES GUIDE GOVERNING SMI RISK CONTROL IND ICES SIX Swiss Exchange Ld 04/2012 i C O N T E N T S 1. Index srucure... 1 1.1 Concep... 1 1.2 General principles... 1 1.3 Index Commission... 1 1.4 Review of index

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Vector Autoregressions (VARs): Operational Perspectives

Vector Autoregressions (VARs): Operational Perspectives Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

More information

Stability. Coefficients may change over time. Evolution of the economy Policy changes

Stability. Coefficients may change over time. Evolution of the economy Policy changes Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,

More information

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE

COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE COMPUTATION OF CENTILES AND Z-SCORES FOR HEIGHT-FOR-AGE, WEIGHT-FOR-AGE AND BMI-FOR-AGE The mehod used o consruc he 2007 WHO references relied on GAMLSS wih he Box-Cox power exponenial disribuion (Rigby

More information

Modelling and Forecasting Volatility of Gold Price with Other Precious Metals Prices by Univariate GARCH Models

Modelling and Forecasting Volatility of Gold Price with Other Precious Metals Prices by Univariate GARCH Models Deparmen of Saisics Maser's Thesis Modelling and Forecasing Volailiy of Gold Price wih Oher Precious Meals Prices by Univariae GARCH Models Yuchen Du 1 Supervisor: Lars Forsberg 1 Yuchen.Du.84@suden.uu.se

More information

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen

A Note on the Impact of Options on Stock Return Volatility. Nicolas P.B. Bollen A Noe on he Impac of Opions on Sock Reurn Volailiy Nicolas P.B. Bollen ABSTRACT This paper measures he impac of opion inroducions on he reurn variance of underlying socks. Pas research generally finds

More information

A Further Examination of Insurance Pricing and Underwriting Cycles

A Further Examination of Insurance Pricing and Underwriting Cycles A Furher Examinaion of Insurance ricing and Underwriing Cycles AFIR Conference, Sepember 2005, Zurich, Swizerland Chris K. Madsen, GE Insurance Soluions, Copenhagen, Denmark Svend Haasrup, GE Insurance

More information

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

More information

Mortality Variance of the Present Value (PV) of Future Annuity Payments

Mortality Variance of the Present Value (PV) of Future Annuity Payments Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR

DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Invesmen Managemen and Financial Innovaions, Volume 4, Issue 3, 7 33 DOES TRADING VOLUME INFLUENCE GARCH EFFECTS? SOME EVIDENCE FROM THE GREEK MARKET WITH SPECIAL REFERENCE TO BANKING SECTOR Ahanasios

More information

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faster Cryptanalytic Time-Memory Trade-Off Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

ARCH 2013.1 Proceedings

ARCH 2013.1 Proceedings Aricle from: ARCH 213.1 Proceedings Augus 1-4, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference

More information

MOTION ALONG A STRAIGHT LINE

MOTION ALONG A STRAIGHT LINE Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,

More information

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software Informaion Theoreic Evaluaion of Change Predicion Models for Large-Scale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer

More information

Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr

Chapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i

More information

Dopamine, dobutamine, digitalis, and diuretics during intraaortic balloon support

Dopamine, dobutamine, digitalis, and diuretics during intraaortic balloon support Dopamine, dobuamine, digialis, and diureics during inraaoric balloon suppor Sephen Slogoff, M.D. n his presenaion, should like o discuss some conceps of drug herapy for inraaoric balloon paiens. Figure

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009 ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

More information

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? *

Does Option Trading Have a Pervasive Impact on Underlying Stock Prices? * Does Opion Trading Have a Pervasive Impac on Underlying Soc Prices? * Neil D. Pearson Universiy of Illinois a Urbana-Champaign Allen M. Poeshman Universiy of Illinois a Urbana-Champaign Joshua Whie Universiy

More information

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES

INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchange-raded ineres rae fuures and heir opions are described. The fuure opions include hose paying

More information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

Diane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC

Diane K. Michelson, SAS Institute Inc, Cary, NC Annie Dudley Zangi, SAS Institute Inc, Cary, NC ABSTRACT Paper DK-02 SPC Daa Visualizaion of Seasonal and Financial Daa Using JMP Diane K. Michelson, SAS Insiue Inc, Cary, NC Annie Dudley Zangi, SAS Insiue Inc, Cary, NC JMP Sofware offers many ypes

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

Forecasting, Ordering and Stock- Holding for Erratic Demand

Forecasting, Ordering and Stock- Holding for Erratic Demand ISF 2002 23 rd o 26 h June 2002 Forecasing, Ordering and Sock- Holding for Erraic Demand Andrew Eaves Lancaser Universiy / Andalus Soluions Limied Inroducion Erraic and slow-moving demand Demand classificaion

More information

RC Circuit and Time Constant

RC Circuit and Time Constant ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisor-capacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he

More information

WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS

WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS WATER MIST FIRE PROTECTION RELIABILITY ANALYSIS Shuzhen Xu Research Risk and Reliabiliy Area FM Global Norwood, Massachuses 262, USA David Fuller Engineering Sandards FM Global Norwood, Massachuses 262,

More information

The Kinetics of the Stock Markets

The Kinetics of the Stock Markets Asia Pacific Managemen Review (00) 7(1), 1-4 The Kineics of he Sock Markes Hsinan Hsu * and Bin-Juin Lin ** (received July 001; revision received Ocober 001;acceped November 001) This paper applies he

More information

SKF Documented Solutions

SKF Documented Solutions SKF Documened Soluions Real world savings and we can prove i! How much can SKF save you? Le s do he numbers. The SKF Documened Soluions Program SKF is probably no he firs of your supplier parners o alk

More information

Trends in TCP/IP Retransmissions and Resets

Trends in TCP/IP Retransmissions and Resets Trends in TCP/IP Reransmissions and Reses Absrac Concordia Chen, Mrunal Mangrulkar, Naomi Ramos, and Mahaswea Sarkar {cychen, mkulkarn, msarkar,naramos}@cs.ucsd.edu As he Inerne grows larger, measuring

More information

Machine Learning in Pairs Trading Strategies

Machine Learning in Pairs Trading Strategies Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1 - TRANSIENTS EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67 - FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1 - RANIEN Uni conen 2 Undersand he ransien behaviour of resisor-capacior (R) and resisor-inducor (RL) D circuis

More information

Inductance and Transient Circuits

Inductance and Transient Circuits Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n). FW 662 Densiy-dependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Long-erm

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

Testing the linearity of a time series. Some Monte Carlo and Empirical Tests

Testing the linearity of a time series. Some Monte Carlo and Empirical Tests Tesing he lineariy of a ime series. Some Mone Carlo and Empirical Tess By Efsraios Tserkezos (Corresponding auhor). Mahemaical Modelling in new Technologies and Economy Posgraduae Programme. Applied Mahemaics

More information

A Mathematical Description of MOSFET Behavior

A Mathematical Description of MOSFET Behavior 10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical

More information

Section 5.1 The Unit Circle

Section 5.1 The Unit Circle Secion 5.1 The Uni Circle The Uni Circle EXAMPLE: Show ha he poin, ) is on he uni circle. Soluion: We need o show ha his poin saisfies he equaion of he uni circle, ha is, x +y 1. Since ) ) + 9 + 9 1 P

More information

Idealistic characteristics of Islamic Azad University masters - Islamshahr Branch from Students Perspective

Idealistic characteristics of Islamic Azad University masters - Islamshahr Branch from Students Perspective Available online a www.pelagiaresearchlibrary.com European Journal Experimenal Biology, 202, 2 (5):88789 ISSN: 2248 925 CODEN (USA): EJEBAU Idealisic characerisics Islamic Azad Universiy masers Islamshahr

More information

Hotel Room Demand Forecasting via Observed Reservation Information

Hotel Room Demand Forecasting via Observed Reservation Information Proceedings of he Asia Pacific Indusrial Engineering & Managemen Sysems Conference 0 V. Kachivichyanuul, H.T. Luong, and R. Piaaso Eds. Hoel Room Demand Forecasing via Observed Reservaion Informaion aragain

More information

The Application of Multi Shifts and Break Windows in Employees Scheduling

The Application of Multi Shifts and Break Windows in Employees Scheduling The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

More information

Capital budgeting techniques

Capital budgeting techniques Capial budgeing echniques A reading prepared by Pamela Peerson Drake O U T L I N E 1. Inroducion 2. Evaluaion echniques 3. Comparing echniques 4. Capial budgeing in pracice 5. Summary 1. Inroducion The

More information

Purchasing Power Parity (PPP), Sweden before and after EURO times

Purchasing Power Parity (PPP), Sweden before and after EURO times School of Economics and Managemen Purchasing Power Pariy (PPP), Sweden before and afer EURO imes - Uni Roo Tes - Coinegraion Tes Masers hesis in Saisics - Spring 2008 Auhors: Mansoor, Rashid Smora, Ami

More information

Distributing Human Resources among Software Development Projects 1

Distributing Human Resources among Software Development Projects 1 Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

More information

Does Capital Punishment Have a Deterrence Effect on the Murder Rate? Issues and Evidence

Does Capital Punishment Have a Deterrence Effect on the Murder Rate? Issues and Evidence Does Capal Punishmen Have a Deerrence Effec on he Murder Rae? Issues and Evidence Seven S. Cuellar, Ph.D.* Deparmen of Economics Sonoma Sae Universy 181 Eas Coai Avenue Rohner Park, CA 998 () -5 Seve.Cuellar@Sonoma.edu

More information

Real-time Particle Filters

Real-time Particle Filters Real-ime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING?

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING? Chaper 10: THE BASICS OF CAPITAL BUDGETING Should we build his plan? Topic Overview Projec Types Capial Budgeing Decision Crieria Payback Period Discouned Payback Period Ne Presen Value () Inernal Rae

More information

Chapter 4: Exponential and Logarithmic Functions

Chapter 4: Exponential and Logarithmic Functions Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

More information

Modeling Stock Price Dynamics with Fuzzy Opinion Networks

Modeling Stock Price Dynamics with Fuzzy Opinion Networks Modeling Sock Price Dynamics wih Fuzzy Opinion Neworks Li-Xin Wang Deparmen of Auomaion Science and Technology Xian Jiaoong Universiy, Xian, P.R. China Email: lxwang@mail.xju.edu.cn Key words: Sock price

More information

Circuit Types. () i( t) ( )

Circuit Types. () i( t) ( ) Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All

More information

Return Calculation of U.S. Treasury Constant Maturity Indices

Return Calculation of U.S. Treasury Constant Maturity Indices Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion

More information

THE DETERMINATION OF PORT FACILITIES MANAGEMENT FEE WITH GUARANTEED VOLUME USING OPTIONS PRICING MODEL

THE DETERMINATION OF PORT FACILITIES MANAGEMENT FEE WITH GUARANTEED VOLUME USING OPTIONS PRICING MODEL 54 Journal of Marine Science and echnology, Vol. 13, No. 1, pp. 54-60 (2005) HE DEERMINAION OF POR FACILIIES MANAGEMEN FEE WIH GUARANEED VOLUME USING OPIONS PRICING MODEL Kee-Kuo Chen Key words: build-and-lease

More information

Automatic measurement and detection of GSM interferences

Automatic measurement and detection of GSM interferences Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde

More information

Chapter 2: Principles of steady-state converter analysis

Chapter 2: Principles of steady-state converter analysis Chaper 2 Principles of Seady-Sae Converer Analysis 2.1. Inroducion 2.2. Inducor vol-second balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer

More information

Chapter 2 Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

The Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines*

The Relationship between Stock Return Volatility and. Trading Volume: The case of The Philippines* The Relaionship beween Sock Reurn Volailiy and Trading Volume: The case of The Philippines* Manabu Asai Faculy of Economics Soka Universiy Angelo Unie Economics Deparmen De La Salle Universiy Manila May

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal

II.1. Debt reduction and fiscal multipliers. dbt da dpbal da dg. bal Quarerly Repor on he Euro Area 3/202 II.. Deb reducion and fiscal mulipliers The deerioraion of public finances in he firs years of he crisis has led mos Member Saes o adop sizeable consolidaion packages.

More information

Fourier Series & The Fourier Transform

Fourier Series & The Fourier Transform Fourier Series & The Fourier Transform Wha is he Fourier Transform? Fourier Cosine Series for even funcions and Sine Series for odd funcions The coninuous limi: he Fourier ransform (and is inverse) The

More information

Permutations and Combinations

Permutations and Combinations Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

More information

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

More information