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School: Princeton
Course: Optimization
ORF307-EGR307_S2008 Optimization Alexandre d'Aspremont Optimization of deterministic systems, focusing on linear programming. Model formulations, the simplex method, sensitivity analysis, duality theory, network models, nonlinear programming. Applica
School: Princeton
Course: Time Series Analysis
Structural response to loads When a set of loads is applied to a structure, the structure will transfer the loads to the supports where reactions will develop in order to maintain static equilibrium. At the same time, stresses will develop within the stru
School: Princeton
Course: Time Series Analysis
174 7 LINEAR SYSTEMS AND KALMAN FILTERING: Problems with Solutions Problem ?. The goal of this problem is to quantify the risks and rewards of some hybrid derivatives written on temperature and energy commodities. The data are contained in the data set Te
School: Princeton
Course: Time Series Analysis
+: %DNLV .RQVWDQWLQRV %\ FRPSXWLQJ WKH DYHUDJH RI WKH +'V RYHU WKH ODVW \HDUV IRU WKH PRQWKV -DQXDU\ DQG )HEUXDU\ ZH JHW ! .7PHDQ6 ! .7 >@ 'HFRPSRVLQJ WKH WLPH VHULHV )LJ 3ORW DYHUDJH WHPSHUDWXUHV )LJ 3ORW WUHQG )LJ VHDVRQDO FRPSRQHQW 7KH VHDVRQDO FRPSRQ
School: Princeton
Course: Time Series Analysis
HW7 Bakis Konstantinos Nikolaos 6.13) 6.13.1 Time Series Plot By taking the average CDD over the summers of the last 15 years we get a value for the strike: K [1] 623.0333 Using the Least squares method to do linear regression for the CDD index of the sum
School: Princeton
Course: Time Series Analysis
457 85 758 68 7 8 6 3 123 35 2 7 5 ! 8!8$ 78 5% 7 " #!87 #!57 &8 5 8" 8 7857 5 8 #!7 7 ' 68 8 7 788 5' # 7 ' # 8 77788 !5785 ( $8 7 ! # ! 3 $5! 7)*57 0 13674 24489 2 2 1 32 2 2 2 2 3 2 2 4 2 2 !33 2 2 2" 2 13674 2 2448# 2 2 0 1367
School: Princeton
Course: Time Series Analysis
Structural response to loads When a set of loads is applied to a structure, the structure will transfer the loads to the supports where reactions will develop in order to maintain static equilibrium. At the same time, stresses will develop within the stru
School: Princeton
Course: Time Series Analysis
174 7 LINEAR SYSTEMS AND KALMAN FILTERING: Problems with Solutions Problem ?. The goal of this problem is to quantify the risks and rewards of some hybrid derivatives written on temperature and energy commodities. The data are contained in the data set Te
School: Princeton
Course: Time Series Analysis
7 MULTIVARIATE TIME SERIES, LINEAR SYSTEMS AND KALMAN FILTERING This chapter is devoted to the analysis of the time evolution of random vectors. The rst section presents the generalization to the multivariate case of the univariate time series models stud
School: Princeton
Course: Time Series Analysis
ORF 405 Tuesday October 13, 2009 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order (so are the ques
School: Princeton
Course: Time Series Analysis
Time Series & Filtering Ren Carmona e Bendheim Center for Finance Department of Operations research & Financial Engineering Princeton University Fall 2010 Carmona Time Series & Filtering (Multivariate) Time Series Data 01/04/1993 01/05/1993 01/06/1993 01/
School: Princeton
Course: Time Series Analysis
ORF 405 Thursday October 7, 2010 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order. Manage your tim
School: Princeton
Course: Time Series Analysis
+: %DNLV .RQVWDQWLQRV %\ FRPSXWLQJ WKH DYHUDJH RI WKH +'V RYHU WKH ODVW \HDUV IRU WKH PRQWKV -DQXDU\ DQG )HEUXDU\ ZH JHW ! .7PHDQ6 ! .7 >@ 'HFRPSRVLQJ WKH WLPH VHULHV )LJ 3ORW DYHUDJH WHPSHUDWXUHV )LJ 3ORW WUHQG )LJ VHDVRQDO FRPSRQHQW 7KH VHDVRQDO FRPSRQ
School: Princeton
Course: Time Series Analysis
HW7 Bakis Konstantinos Nikolaos 6.13) 6.13.1 Time Series Plot By taking the average CDD over the summers of the last 15 years we get a value for the strike: K [1] 623.0333 Using the Least squares method to do linear regression for the CDD index of the sum
School: Princeton
Course: Time Series Analysis
1666 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Find the AR representation of the MA(1) time series Xt = Wt .4Wt1 where cfw_Wt t is a white noise N (0, 2 ). 2. Find the MA representation of the AR(1) time ser
School: Princeton
Course: Time Series Analysis
1626 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Let us assume that cfw_Wt t is a white noise with variance 2 = 1 and let us consider the time series cfw_Xt t dened by: Xt = Wt + (1)t1 Wt1 . Compute the mean f
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Optimization
ORF307-EGR307_S2008 Optimization Alexandre d'Aspremont Optimization of deterministic systems, focusing on linear programming. Model formulations, the simplex method, sensitivity analysis, duality theory, network models, nonlinear programming. Applica
School: Princeton
Course: Time Series Analysis
Structural response to loads When a set of loads is applied to a structure, the structure will transfer the loads to the supports where reactions will develop in order to maintain static equilibrium. At the same time, stresses will develop within the stru
School: Princeton
Course: Time Series Analysis
174 7 LINEAR SYSTEMS AND KALMAN FILTERING: Problems with Solutions Problem ?. The goal of this problem is to quantify the risks and rewards of some hybrid derivatives written on temperature and energy commodities. The data are contained in the data set Te
School: Princeton
Course: Time Series Analysis
+: %DNLV .RQVWDQWLQRV %\ FRPSXWLQJ WKH DYHUDJH RI WKH +'V RYHU WKH ODVW \HDUV IRU WKH PRQWKV -DQXDU\ DQG )HEUXDU\ ZH JHW ! .7PHDQ6 ! .7 >@ 'HFRPSRVLQJ WKH WLPH VHULHV )LJ 3ORW DYHUDJH WHPSHUDWXUHV )LJ 3ORW WUHQG )LJ VHDVRQDO FRPSRQHQW 7KH VHDVRQDO FRPSRQ
School: Princeton
Course: Time Series Analysis
HW7 Bakis Konstantinos Nikolaos 6.13) 6.13.1 Time Series Plot By taking the average CDD over the summers of the last 15 years we get a value for the strike: K [1] 623.0333 Using the Least squares method to do linear regression for the CDD index of the sum
School: Princeton
Course: Time Series Analysis
457 85 758 68 7 8 6 3 123 35 2 7 5 ! 8!8$ 78 5% 7 " #!87 #!57 &8 5 8" 8 7857 5 8 #!7 7 ' 68 8 7 788 5' # 7 ' # 8 77788 !5785 ( $8 7 ! # ! 3 $5! 7)*57 0 13674 24489 2 2 1 32 2 2 2 2 3 2 2 4 2 2 !33 2 2 2" 2 13674 2 2448# 2 2 0 1367
School: Princeton
Course: Time Series Analysis
Bakis Konstantinos-Nikolaos 5.5) HW5 Figure 5.5.1 Polynomial regression of degree 3 for 52 and 50 measurements Figure 5.5.2 Natural spline of degree 3 for 52 and 50 measurements 1 Figure 5.5.3 Smoothing Spline regression of degree 3 for 52 and 50 measurem
School: Princeton
Course: Time Series Analysis
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School: Princeton
Course: Time Series Analysis
Bakis Konstantinos Nikolaos HW3 4.1) 1. Yes the scatter plots give strong evidence of linear dependence between the 2 variables strength and attenuation. 2. ) Intercept X 3.62090564 -0.01471088 The standard deviation of the residuals is: Sd: 0.1420879 3.)
School: Princeton
Course: Time Series Analysis
50 3 MULTIVARIATE DATA EXPLORATION: Problems with Solutions Problem . This problem is based on the data contained in the data set UTILITIES included in the library Rsafd. It is a matrix with two columns, each row corresponding to a given day. The rst colu
School: Princeton
Course: Time Series Analysis
12 1 EXPLORATORY DATA ANALYSIS: Problems with Solutions Problem 1.3 Solution: Plot 1. YY has two tails. Both tails are heavier than the tails of the Gaussian distribution. Plot 2. ZZ has two tails. The upper tail is Gaussian. However, the lower tail is he
School: Princeton
Course: Time Series Analysis
HW1 Bakis Konstantinos-Nikolaos Problem 1.3 For the upper left plot obtained using the qqnorm function, the fact that the rightmost and leftmost points are above and below the line indicates that the right and left tails of the distribution are fatter tha
School: Princeton
Course: Time Series Analysis
1666 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Find the AR representation of the MA(1) time series Xt = Wt .4Wt1 where cfw_Wt t is a white noise N (0, 2 ). 2. Find the MA representation of the AR(1) time ser
School: Princeton
Course: Time Series Analysis
1626 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Let us assume that cfw_Wt t is a white noise with variance 2 = 1 and let us consider the time series cfw_Xt t dened by: Xt = Wt + (1)t1 Wt1 . Compute the mean f
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Time Series Analysis
106 4 PARAMETRIC REGRESSION: Problems with Solutions Problem ?. The purpose of this problem is to perform a rst analysis of the data set BASKETBALL contained in the ascii le basketball.asc, very much in the spirit of the previous problem. 1. a. Use least
School: Princeton
Course: Time Series Analysis
98 4 PARAMETRIC REGRESSION: Problems with Solutions Problem ?. The purpose of this problem is to analyze the data contained in the data set STRENGTH. The rst column gives the fracture strength (as a percentage of ultimate tensile strength) and the second
School: Princeton
Course: Time Series Analysis
HW2 Bakis Konstantinos-Nikolaos Problem 3.1 In order to fit the GPD to X and Y the function shape.plot was implemented in order to find the cut-off points for separating the tail from the bulk of the distribution. The cut-off point should be large enough
School: Princeton
Course: Time Series Analysis
Condence and Prediction Intervals for a Simple Least Squares Linear Regression In this note, we are in the regression set up, working with n observations (x1 , y1 ), (x2 , y2 ), , (xn , yn ). Least squares regression is based on the assumption that the ob
School: Princeton
Course: Time Series Analysis
7 MULTIVARIATE TIME SERIES, LINEAR SYSTEMS AND KALMAN FILTERING This chapter is devoted to the analysis of the time evolution of random vectors. The rst section presents the generalization to the multivariate case of the univariate time series models stud
School: Princeton
Course: Time Series Analysis
7 MULTIVARIATE TIME SERIES, LINEAR SYSTEMS AND KALMAN FILTERING This chapter is devoted to the analysis of the time evolution of random vectors. The rst section presents the generalization to the multivariate case of the univariate time series models stud
School: Princeton
Course: Time Series Analysis
6 TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT Time series are ubiquitous in everyday manipulations of nancial data. They are especially well suited to the nature of nancial markets, and models and methods have been developed to capture time dependencies
School: Princeton
Course: Time Series Analysis
4 PARAMETRIC REGRESSION This chapter provides an introduction to several types of regression analysis: simple and multiple linear, as well as simple polynomial and nonlinear. In all cases we identify the regression function in a parametric family, hence t
School: Princeton
Course: Time Series Analysis
3 MULTIVARIATE DATA EXPLORATION This chapter provides a rst excursion away from the simple problems of univariate samples and univariate distribution estimation. We consider samples of observations of several variables. We extend some of the exploratory d
School: Princeton
Course: Time Series Analysis
ORF 405 Tuesday October 13, 2009 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order (so are the ques
School: Princeton
Course: Time Series Analysis
Time Series & Filtering Ren Carmona e Bendheim Center for Finance Department of Operations research & Financial Engineering Princeton University Fall 2010 Carmona Time Series & Filtering (Multivariate) Time Series Data 01/04/1993 01/05/1993 01/06/1993 01/
School: Princeton
Course: Time Series Analysis
Regression Rene Carmona Bendheim Center for Finance Department of Operations research & Financial Engineering Princeton University Fall 2010 Carmona Regression Multivariate Data: UTIL.index > head(UTIL.index) ENRON.index DUKE.index UTILITY.index 01/04/199
School: Princeton
Course: Time Series Analysis
Exploratory Data Analysis, Heavy Tail Distributions, Dependence and Monte Carlo Simulations Rene Carmona Bendheim Center for Finance Department of Operations research & Financial Engineering Princeton University Fall 2010 Carmona Exploratory Data Analysis
School: Princeton
Course: Time Series Analysis
ORF 405 Thursday October 7, 2010 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order. Manage your tim
School: Princeton
Course: Probability And Stochastic Systems
ORF 309 Solutions to Homework 6 Fall 2012 Due on Nov. 14, 2012 Exercise 5.4 For each i cfw_A, B, C , dene Ti := the time it takes for the clerk to serve customer i. In order for A to still be in the post oce after the other two have left, B must nish befo
School: Princeton
Course: Probability And Stochastic Systems
ECO 312, Econometrics, Fall 2012. Assignment 6 Due Wednesday, November 21. Problem 1 SW10.2 Problem 2 Consider a fixed effects panel data model: Yit = i + Xit + uit. Suppose there are only two time periods: T=2. In class, we discussed two estimation stra
School: Princeton
Course: Probability And Stochastic Systems
Regression with Panel Data (SW Ch. 10) A panel dataset contains observations on multiple entities (individuals), where each entity is observed at two or more points in time. Examples: Data on 420 California school districts in 1999 and again in 2000, for
School: Princeton
Course: -
BallPicking Aboxcontains2red,3blueand4blackballs.Threeballsaredrawnfromtheboxatrandom. Whatistheprobabilitythat(i)thethreeballsareofdifferentcolours?(ii)twoballsareofthe samecolourandthethirdofdifferentcolour?(iii)alltheballsareofthesamecolour? Here, P(X>
School: Princeton
Schedule of eCommerce Projects Orf 401 eCommerce Spring 2006 Monday May 15, 2006 006 Friend Center (basement) ime Name (link to Presentations) Title(link to Paper) Presentation CrashAtMyPlace.com (CAMP.com) Beta of Site 05 HomelyHotels *Curtis
School: Princeton
Course: Optimization
set NUTR ordered; set FOOD ordered; param cost {FOOD} >= 0; param f_min {FOOD} >= 0, default 0; param f_max {j in FOOD} >= f_min[j], default 2; param n_min {NUTR} >= 0, default 0; param n_max {i in NUTR} >= n_min[i], default Infinity; param amt {NUTR
School: Princeton
Course: Fundamentals Of Engineering Statistics
2009 Princeton University Christian Rolon Mike McPherson Christian Villaran [FACTORS IN REAL GDP PER CAPITA AND PERCENTAGE GROWTH] This report is a statistical analysis of four factors (trade share, average years in school, number of assassinations,
School: Princeton
Course: Optimization
ORF307: Assignment 2 Due Thursday March 9 1. Solve exercise 2.7 in the textbook and plot the sequence of points produced by the simplex method. 2. Solve exercise 2.9 in the textbook. 3. Solve exercise 2.10 in the textbook. Can you solve the followin
School: Princeton
Course: Optimization
ORF 307 Homework 6 Solutions Exercise 1. We solve this problem by optimizing on the expected value of the asset to be priced. The constraints are that the discounted expected value of the known payoffs is equal to the prices of the assets for which w
School: Princeton
Course: Optimization
ORF 307 Homework 5 Solutions Exercise 1. The adjacency matrix A (including the extra link) is: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 1 1 1 0 0 0 0 0 0 0 0 0 0
School: Princeton
Course: Optimization
ORF 307 Homework 4 Solutions Exercise 1. The Lagrangian of this problem is: L(x, 1 , 2 , ) = cT x + T Ax - T x + T (Dx - f ) 1 2 with 1 , 2 0 The Lagrange dual function is: g(1 , 2 , ) = infx = infx T D (c D L(x, 1 , 2 , ) T Dc x = infx + T Ax -
School: Princeton
Course: Optimization
ORF 307 Homework 3 Solutions Exercise 1. 3.1 The initial dictionary for the perturbed problem is: 0 w1 = w2 = w3 = 1 2 1+ 3 +10x1 -.5x1 -.5x1 -x1 -57x2 +5.5x2 +1.5x2 -9x3 +2.5x3 +.5x3 -24x4 -9x4 -x4 We pivot x1 into the basis and w2 out of the
School: Princeton
Course: Optimization
ORF 307 Homework 1 Solutions Exercise 1. 2.1 Initialization: Write down the initial dictionary 0 5 3 +6x1 -2x1 -x1 +8x2 -x2 -3x2 +5x3 -x3 -x3 +9x4 -3x4 -2x4 w1 = w2 = 5 The largest positive coefficient in the objective is 9 for x4 . We then calcula
School: Princeton
Course: Fundamentals Of Engineering Statistics
1. I would expect that the pct.bf of one Nevada man would be independent of any others I would assume that this group of Nevada men is less than 10% of the entire population I would assume that the Nevada men were chosen at random for each study. Fr
School: Princeton
Course: Fundamentals Of Engineering Statistics
18.2 a. I would expect that this histogram would be unimodal and symmetric centered around .1 or 10%. b. no, this could not be approximated by a normal model because it fails the success/failure condition there are not 10 expected negative outcomes c
School: Princeton
Course: Fundamentals Of Engineering Statistics
1. a. there is a positive linear association between col05 and col06, from the best fit line, it looks like about a 1 to 1 ratio. COL06 60 40 80 100 120 60 80 COL05 100 120 b. 1. there are no obvious outliers 2. Straight enough? This plot l
School: Princeton
Course: Fundamentals Of Engineering Statistics
6 a. x=c(rep(0,96),rep(1,4) xx=sample(x,100000,rep=T) newx=matrix(xx,1000,100) y=rowSums(newx) hist(y) Histogram of y Frequency 0 0 50 100 150 200 2 4 y 6 8 10 This histogram is unimodal skewed to the right with the right tail being longe
School: Princeton
Course: Fundamentals Of Engineering Statistics
10. a. 1.08 z= 23.84-20/3.56 = 1.08 b. 10 because z = 34-23.84/3.56 = 2.85 vs z = 10-23.84/3.56 = 3.89 12. a. 23.84-20 = new mean = 3.84, the s would be unchanged at 3.56 b. mean = 38.35, new s = 5.73 14. Mean = 28*10 + 100 = $380 Max = 33*10 + 100 =
School: Princeton
Course: Fundamentals Of Engineering Statistics
3.30 a. colPercents(ex3.30) 1 2 3 1 23.7 21.1 21.4 2 60.5 60.6 49.6 3 15.8 18.3 29.0 Total 100.0 100.0 100.0 Count 76.0 71.0 131.0 > rowPercents(ex3.30) 1 2 3 Total Count 1 29.5 24.6 45.9 100.0 61 2 29.9 27.9 42.2 100.0 154 3 19.0 20.6 60.3 99.9 63 >
School: Princeton
Course: Time Series Analysis
Structural response to loads When a set of loads is applied to a structure, the structure will transfer the loads to the supports where reactions will develop in order to maintain static equilibrium. At the same time, stresses will develop within the stru
School: Princeton
Course: Time Series Analysis
174 7 LINEAR SYSTEMS AND KALMAN FILTERING: Problems with Solutions Problem ?. The goal of this problem is to quantify the risks and rewards of some hybrid derivatives written on temperature and energy commodities. The data are contained in the data set Te
School: Princeton
Course: Time Series Analysis
7 MULTIVARIATE TIME SERIES, LINEAR SYSTEMS AND KALMAN FILTERING This chapter is devoted to the analysis of the time evolution of random vectors. The rst section presents the generalization to the multivariate case of the univariate time series models stud
School: Princeton
Course: Time Series Analysis
ORF 405 Tuesday October 13, 2009 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order (so are the ques
School: Princeton
Course: Time Series Analysis
Time Series & Filtering Ren Carmona e Bendheim Center for Finance Department of Operations research & Financial Engineering Princeton University Fall 2010 Carmona Time Series & Filtering (Multivariate) Time Series Data 01/04/1993 01/05/1993 01/06/1993 01/
School: Princeton
Course: Time Series Analysis
ORF 405 Thursday October 7, 2010 FIRST MIDTERM: SOLUTIONS Remember that No unjustied answer will be given credit, even if the answer is correct!. The ve problems are independent of each other, so they can be worked out in any given order. Manage your tim
School: Princeton
Schedule of eCommerce Projects Orf 401 eCommerce Spring 2006 Monday May 15, 2006 006 Friend Center (basement) ime Name (link to Presentations) Title(link to Paper) Presentation CrashAtMyPlace.com (CAMP.com) Beta of Site 05 HomelyHotels *Curtis
School: Princeton
Course: Fundamentals Of Engineering Statistics
2009 Princeton University Christian Rolon Mike McPherson Christian Villaran [FACTORS IN REAL GDP PER CAPITA AND PERCENTAGE GROWTH] This report is a statistical analysis of four factors (trade share, average years in school, number of assassinations,
School: Princeton
Course: Time Series Analysis
+: %DNLV .RQVWDQWLQRV %\ FRPSXWLQJ WKH DYHUDJH RI WKH +'V RYHU WKH ODVW \HDUV IRU WKH PRQWKV -DQXDU\ DQG )HEUXDU\ ZH JHW ! .7PHDQ6 ! .7 >@ 'HFRPSRVLQJ WKH WLPH VHULHV )LJ 3ORW DYHUDJH WHPSHUDWXUHV )LJ 3ORW WUHQG )LJ VHDVRQDO FRPSRQHQW 7KH VHDVRQDO FRPSRQ
School: Princeton
Course: Time Series Analysis
HW7 Bakis Konstantinos Nikolaos 6.13) 6.13.1 Time Series Plot By taking the average CDD over the summers of the last 15 years we get a value for the strike: K [1] 623.0333 Using the Least squares method to do linear regression for the CDD index of the sum
School: Princeton
Course: Time Series Analysis
1666 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Find the AR representation of the MA(1) time series Xt = Wt .4Wt1 where cfw_Wt t is a white noise N (0, 2 ). 2. Find the MA representation of the AR(1) time ser
School: Princeton
Course: Time Series Analysis
1626 FIRST TIME SERIES MODELS: AR, MA, ARMA, & ALL THAT: Problems with Solutions Problem ?. 1. Let us assume that cfw_Wt t is a white noise with variance 2 = 1 and let us consider the time series cfw_Xt t dened by: Xt = Wt + (1)t1 Wt1 . Compute the mean f
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Time Series Analysis
LOCAL & NONPARAMETRIC REGRESSION: Problems with Solutions 127 Problem . Given two functions f and g their convolution f g is the function dened by the formula: + [f g ](x) = f (y )g (x y ) dy 1. Use a simple substitution to check that f g = g f . 2. Prove
School: Princeton
Course: Time Series Analysis
106 4 PARAMETRIC REGRESSION: Problems with Solutions Problem ?. The purpose of this problem is to perform a rst analysis of the data set BASKETBALL contained in the ascii le basketball.asc, very much in the spirit of the previous problem. 1. a. Use least
School: Princeton
Course: Time Series Analysis
98 4 PARAMETRIC REGRESSION: Problems with Solutions Problem ?. The purpose of this problem is to analyze the data contained in the data set STRENGTH. The rst column gives the fracture strength (as a percentage of ultimate tensile strength) and the second
School: Princeton
Course: Probability And Stochastic Systems
ORF 309 Solutions to Homework 6 Fall 2012 Due on Nov. 14, 2012 Exercise 5.4 For each i cfw_A, B, C , dene Ti := the time it takes for the clerk to serve customer i. In order for A to still be in the post oce after the other two have left, B must nish befo
School: Princeton
Course: Probability And Stochastic Systems
ECO 312, Econometrics, Fall 2012. Assignment 6 Due Wednesday, November 21. Problem 1 SW10.2 Problem 2 Consider a fixed effects panel data model: Yit = i + Xit + uit. Suppose there are only two time periods: T=2. In class, we discussed two estimation stra
School: Princeton
Course: Optimization
ORF307: Assignment 2 Due Thursday March 9 1. Solve exercise 2.7 in the textbook and plot the sequence of points produced by the simplex method. 2. Solve exercise 2.9 in the textbook. 3. Solve exercise 2.10 in the textbook. Can you solve the followin
School: Princeton
Course: Optimization
ORF 307 Homework 6 Solutions Exercise 1. We solve this problem by optimizing on the expected value of the asset to be priced. The constraints are that the discounted expected value of the known payoffs is equal to the prices of the assets for which w
School: Princeton
Course: Optimization
ORF 307 Homework 5 Solutions Exercise 1. The adjacency matrix A (including the extra link) is: 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 1 1 1 0 0 0 0 0 0 0 0 0 0
School: Princeton
Course: Optimization
ORF 307 Homework 4 Solutions Exercise 1. The Lagrangian of this problem is: L(x, 1 , 2 , ) = cT x + T Ax - T x + T (Dx - f ) 1 2 with 1 , 2 0 The Lagrange dual function is: g(1 , 2 , ) = infx = infx T D (c D L(x, 1 , 2 , ) T Dc x = infx + T Ax -
School: Princeton
Course: Optimization
ORF 307 Homework 3 Solutions Exercise 1. 3.1 The initial dictionary for the perturbed problem is: 0 w1 = w2 = w3 = 1 2 1+ 3 +10x1 -.5x1 -.5x1 -x1 -57x2 +5.5x2 +1.5x2 -9x3 +2.5x3 +.5x3 -24x4 -9x4 -x4 We pivot x1 into the basis and w2 out of the
School: Princeton
Course: Optimization
ORF 307 Homework 1 Solutions Exercise 1. 2.1 Initialization: Write down the initial dictionary 0 5 3 +6x1 -2x1 -x1 +8x2 -x2 -3x2 +5x3 -x3 -x3 +9x4 -3x4 -2x4 w1 = w2 = 5 The largest positive coefficient in the objective is 9 for x4 . We then calcula
School: Princeton
Course: Fundamentals Of Engineering Statistics
1. I would expect that the pct.bf of one Nevada man would be independent of any others I would assume that this group of Nevada men is less than 10% of the entire population I would assume that the Nevada men were chosen at random for each study. Fr
School: Princeton
Course: Fundamentals Of Engineering Statistics
18.2 a. I would expect that this histogram would be unimodal and symmetric centered around .1 or 10%. b. no, this could not be approximated by a normal model because it fails the success/failure condition there are not 10 expected negative outcomes c
School: Princeton
Course: Fundamentals Of Engineering Statistics
1. a. there is a positive linear association between col05 and col06, from the best fit line, it looks like about a 1 to 1 ratio. COL06 60 40 80 100 120 60 80 COL05 100 120 b. 1. there are no obvious outliers 2. Straight enough? This plot l
School: Princeton
Course: Fundamentals Of Engineering Statistics
6 a. x=c(rep(0,96),rep(1,4) xx=sample(x,100000,rep=T) newx=matrix(xx,1000,100) y=rowSums(newx) hist(y) Histogram of y Frequency 0 0 50 100 150 200 2 4 y 6 8 10 This histogram is unimodal skewed to the right with the right tail being longe
School: Princeton
Course: Fundamentals Of Engineering Statistics
10. a. 1.08 z= 23.84-20/3.56 = 1.08 b. 10 because z = 34-23.84/3.56 = 2.85 vs z = 10-23.84/3.56 = 3.89 12. a. 23.84-20 = new mean = 3.84, the s would be unchanged at 3.56 b. mean = 38.35, new s = 5.73 14. Mean = 28*10 + 100 = $380 Max = 33*10 + 100 =
School: Princeton
Course: Fundamentals Of Engineering Statistics
3.30 a. colPercents(ex3.30) 1 2 3 1 23.7 21.1 21.4 2 60.5 60.6 49.6 3 15.8 18.3 29.0 Total 100.0 100.0 100.0 Count 76.0 71.0 131.0 > rowPercents(ex3.30) 1 2 3 Total Count 1 29.5 24.6 45.9 100.0 61 2 29.9 27.9 42.2 100.0 154 3 19.0 20.6 60.3 99.9 63 >