PITFALLS IN TIME SERIES ANALYSIS. Cliff Hurvich Stern School, NYU
|
|
- Darlene Hampton
- 8 years ago
- Views:
Transcription
1 PITFALLS IN TIME SERIES ANALYSIS Cliff Hurvich Stern School, NYU
2 The t -Test If x 1,..., x n are independent and identically distributed with mean 0, and n is not too small, then t = x 0 s n has a standard normal distribution, where x is the sample mean and s is the sample standard deviation. But if the true mean µ is (say) positive, then t will typically be large, in the right tail of a standard normal distribution. If, for example, the t -statistic is 3, we would have strong evidence that the true population mean is not zero. Indeed, the probability that a standard normal exceed 3 is just So by looking at t -statistics, we can draw conclusions from the data, while controlling the error rates (false positive, false negative). Consider a data set of monthly global temperatures (n = 1632). Is the plot sloping up (global warming), or is it just an illusion?
3 Temperatures, Northern Hemisphere Monthly: , Seasonally Adjusted Degrees C Month
4 - 2 - A simple approach to this: Look at the monthly changes in temperature and test whether these changes have a zero population mean. We get x = Degrees C / Month and t = No evidence of global warming. Another way to approach the problem: Run a simple linear regression of the temperatures on a time variable. The estimated slope is βˆ = Degrees C / Month, and the t -statistic for the slope is t = Now get strong evidence of global warming! There s something strange here, since two apparently reasonable methods give completely different results. What s the problem?
5 - 3 - Regression is also used for prediction. Let s try predicting this month s stock return (y t ) based on three logged financial ratios from the previous month (time t 1). Data for NYSE, December December 1994 (n = 385). The t -statistics for the least-squares coefficients of log dividend yield, log Book-to-Market ratio and log Earnings-to-Price ratio are 3.02, 2.40 and 2.43, respectively. So we have strong evidence of predictability of stock returns based on past financial ratios.
6 - 4 - Now, let s see if current stock price can be predicted from past stock price. Consider the Russell 2000 stock index. The slope in the linear regression of today s price on yesterday s price is βˆ =.994, with a t -statistic of t = 260. So price is highly predictable from past prices.
7 Today's Vs. Yesterday's Russell 2000 Index July 27, Jan 22, n= Russell lagrussell 400
8 - 5 - Of course, to make money, we have to predict returns. The scatterplot indicates that returns are not too predictable. Linear regression of today s returns on yesterday s yields an estimated slope of βˆ = and t =.07. No evidence of predictability of stock returns based on past returns.
9 Today's Vs. Yesterday's Russell 2000 Return July 27, Jan 22, n= RussRet lagrussret 0.05
10 - 6 - Another useful statistical tool is correlation. Consider daily US and UK bond yields (n = 960). The Pearson correlation between the yields is.317, which is highly statistically significant, with a p - value less than Could also try regressing UK yield against US yield. The slope is βˆ =.3709, t = This slope is essentially the same as the correlation in this case. The two yields seem to be significantly linked.
11 - 7 - The problem: None of our conclusions above can be trusted, because the t -statistic does not behave in the usual way in these situations. In time series, we cannot assume that the observations are independent! This will often affect the distribution of the t -statistic, and invalidate the usual inferences. Plan for the rest of the talk: Discuss correlation Describe the autoregressive model for time series Explain why above analyses were flawed Discuss cointegration to measure co-movement of two or more series.
12 - 8 - Correlation Suppose X and Y are two random variables, e.g., Yesterday s Russell and Today s Russell. They have theoretical means µ x and µ y. So µ x = E [X ] and µ y = E [Y ]. Define Variance: Var (X ) = E [(X µ x ) 2 ]. Now define covariance. This describes how X and Y move together, or covary. Cov (X,Y ) = E [(X µ x )(Y µ y )]. Note that Cov (X, X ) = Var (X ). Finally, define correlation: Corr (X,Y ) = Cov (X,Y ). Var (X )Var (Y )
13 - 9 - The Autoregressive Model Let {x t } be a time series, i.e., a sequence of random variables. A very useful model for {x t } is the first-order autoregressive (AR(1)) model. The model is x t = ρx t 1 +ε t, 1<ρ<1 where the {ε t } are independent normal with constant mean (say, zero) and constant variance. Autocorrelation describes the correlations between the series and its time-lagged values. We could plot x t versus x t 1 and estimate the slope. The estimated and true slopes represent the sample and population autocorrelation at lag 1. We could do the same thing for any lag. So we get a sample and population autocorrelation sequence, {ρˆ r } and {ρ r }, for r = 0,1,2,... For the AR (1) model, we have ρ r = ρ r.
14 The AR (1) process is mean reverting: The next value is expected to be closer to the mean (zero) than the current value. The conditional mean of x t +1 is ρx t, and ρ <1. The autocorrelation leads to predictability. As long as ρ 0, the process is predictable. The best predictor of x t +1 is ρx t. However, there is a downside to correlation: It typically invalidates the standard methods of statistical inference. In the global temperatures example, the temperatures show autocorrelation (potentially with a trend added). When you adequately account for the autocorrelation, the t -statistic for global warming based on a regression on time becomes t = This is much less than the value t = 22.2 we got earlier assuming no autocorrelation, but still provides moderately strong evidence of global warming. The autocorrelation also affects the variance of the sample mean, thereby invalidating the corresponding t -statistic.
15 In the example on prediction of stock returns based on financial ratios, it turns out that the financial ratios show strong autocorrelation. If we devise an AR(1) model for the ratios, together with a regression model for the stock returns, there will be a correlation between the errors in the two models. The net result of this is that the least-squares coefficients will be biased (they estimate the wrong thing, on average), and the t -statistics will not be valid. When we correctly account for these problems, the t -statistics on the financial ratios become 1.96, 1.31 and 1.25, as compared to the original (incorrect) values of 3.02, 2.40 and So the evidence for predictability of stock returns based on financial ratios is actually quite marginal, and far weaker than it seemed before.
16 The Random Walk In the AR (1) model, as ρ approaches 1, the mean reversion becomes weaker: We get longer excursions from zero. For an AR (1) model, we have Var (ε t ) Var (x t ) =. 1 ρ 2 As ρ approaches 1, Var (x t ) goes to. When ρ becomes exactly equal to 1, we get the Random Walk, x t =x t 1 +ε t. The random walk is not stationary, and has an infinite variance. In a random walk, the expected waiting time to get back to the current value is infinite. (Extremely long excursions!). In a random walk starting from zero, the path is much more likely to spend almost all of its time above zero than it is to spend about 50% of its time above zero.
17 Stock prices follow a random walk, as long as markets are efficient. If the price change were predictable, investors would quickly figure this out, thereby removing the predictability. In an efficient market, the best forecast of the future price is the current price, and the best forecast of the future return is zero. Since the variance of a random walk is infinite, it makes no sense to talk about the correlation between stock prices (assuming that the prices follow a random walk, or simply assuming that prices have an infinite variance).
18 Two independent random walks Estimated Correlation = xt Index
19 It can be shown that if we take two random walks that are completely independent of each other, there is a very high probability of finding a (spuriously) high correlation coefficient between them. (This may explain the bond yield example). This underscores the futility of looking at correlations between two price series. The t -statistic in the regression of one independent random walk on the other goes to as the sample size increases. So even though there is no relationship between the two series, we are guaranteed to declare (wrongly) that there is a relationship if we use naive regression methods and the sample size is large enough. My two simulated independent random walks seem to move together, but it s just an illusion. The Pearson correlation is.53, and the estimated regression coefficient is.74, with a t -statistic of All of this "structure" is spurious!
20 Unit Root Tests The random walk nature of prices also invalidates the t -statistic in the regression of current price on past price. To try to determine whether our price data came from a random walk, we can test whether the true slope is 1. But the t -statistic for this hypothesis does not have an approximately standard normal distribution, even if we really have a random walk. Fortunately, the distribution of this t -statistic has been determined (Dickey and Fuller), and tables are available. The result is a unit root test. In the unit root test, we test the null hypothesis that the series is a random walk against the alternative hypothesis that it is an AR (1) with ρ<1. Note that under the alternative hypothesis, the series is stationary, and therefore mean reverting, while under the null hypothesis is it nonstationary.
21 Cointegration Suppose we have two nonstationary series {x t } and {y t }, both (approximately) random walks. How do we measure their tendency to move together? Correlation is meaningless here. Both series wander all over the place, since they are nonstationary. Instead of looking at how they wander from a particular point (such as zero), let s look at how they wander from each other. Maybe the "spread" {y t x t } is stationary. Then even though both series wander all over the place separately, they are tied to each other in that the spread between them is mean reverting. So we can make bets on the reversion of this spread. More generally, maybe there is a β such that the linear combination {y t βx t } is stationary. If so, then we say that {x t } and {y t } are cointegrated.
22 A simple approach to cointegration is first to do unit root tests on {x t } and {y t } separately. Next, estimate β by an (ordinary) regression of {y t } on {x t }, and finally do a unit root test on the residuals {y t βˆx t }. If the tests indicate that {x t } and {y t } are nonstationary, but {y t βˆx t } is stationary, then we declare that {x t } and {y t } are cointegrated, with cointegrating parameter βˆ.
Chapter 9: Univariate Time Series Analysis
Chapter 9: Univariate Time Series Analysis In the last chapter we discussed models with only lags of explanatory variables. These can be misleading if: 1. The dependent variable Y t depends on lags of
More informationRob J Hyndman. Forecasting using. 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1
Rob J Hyndman Forecasting using 11. Dynamic regression OTexts.com/fpp/9/1/ Forecasting using R 1 Outline 1 Regression with ARIMA errors 2 Example: Japanese cars 3 Using Fourier terms for seasonality 4
More informationIs the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate?
Is the Forward Exchange Rate a Useful Indicator of the Future Exchange Rate? Emily Polito, Trinity College In the past two decades, there have been many empirical studies both in support of and opposing
More informationThe information content of lagged equity and bond yields
Economics Letters 68 (2000) 179 184 www.elsevier.com/ locate/ econbase The information content of lagged equity and bond yields Richard D.F. Harris *, Rene Sanchez-Valle School of Business and Economics,
More informationChapter 4: Vector Autoregressive Models
Chapter 4: Vector Autoregressive Models 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie IV.1 Vector Autoregressive Models (VAR)...
More informationRelationship among crude oil prices, share prices and exchange rates
Relationship among crude oil prices, share prices and exchange rates Do higher share prices and weaker dollar lead to higher crude oil prices? Akira YANAGISAWA Leader Energy Demand, Supply and Forecast
More informationFinancial Market Efficiency and Its Implications
Financial Market Efficiency: The Efficient Market Hypothesis (EMH) Financial Market Efficiency and Its Implications Financial markets are efficient if current asset prices fully reflect all currently available
More information4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4
4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression
More informationTime Series Analysis
Time Series Analysis Identifying possible ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos
More informationBasic Statistics and Data Analysis for Health Researchers from Foreign Countries
Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association
More information16 : Demand Forecasting
16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam 2 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems You are not responsible for any topics that are not covered in the lecture note
More informationADVANCED FORECASTING MODELS USING SAS SOFTWARE
ADVANCED FORECASTING MODELS USING SAS SOFTWARE Girish Kumar Jha IARI, Pusa, New Delhi 110 012 gjha_eco@iari.res.in 1. Transfer Function Model Univariate ARIMA models are useful for analysis and forecasting
More informationTime Series Analysis of Aviation Data
Time Series Analysis of Aviation Data Dr. Richard Xie February, 2012 What is a Time Series A time series is a sequence of observations in chorological order, such as Daily closing price of stock MSFT in
More informationConcepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance)
Concepts in Investments Risks and Returns (Relevant to PBE Paper II Management Accounting and Finance) Mr. Eric Y.W. Leung, CUHK Business School, The Chinese University of Hong Kong In PBE Paper II, students
More informationTHE PRICE OF GOLD AND STOCK PRICE INDICES FOR
THE PRICE OF GOLD AND STOCK PRICE INDICES FOR THE UNITED STATES by Graham Smith November 2001 Abstract This paper provides empirical evidence on the relationship between the price of gold and stock price
More information" Y. Notation and Equations for Regression Lecture 11/4. Notation:
Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through
More informationLuciano Rispoli Department of Economics, Mathematics and Statistics Birkbeck College (University of London)
Luciano Rispoli Department of Economics, Mathematics and Statistics Birkbeck College (University of London) 1 Forecasting: definition Forecasting is the process of making statements about events whose
More informationThe VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series.
Cointegration The VAR models discussed so fare are appropriate for modeling I(0) data, like asset returns or growth rates of macroeconomic time series. Economic theory, however, often implies equilibrium
More informationPart 2: Analysis of Relationship Between Two Variables
Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable
More informationIntroduction to Regression and Data Analysis
Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it
More informationANALYSIS OF EUROPEAN, AMERICAN AND JAPANESE GOVERNMENT BOND YIELDS
Applied Time Series Analysis ANALYSIS OF EUROPEAN, AMERICAN AND JAPANESE GOVERNMENT BOND YIELDS Stationarity, cointegration, Granger causality Aleksandra Falkowska and Piotr Lewicki TABLE OF CONTENTS 1.
More informationDepartment of Economics
Department of Economics Working Paper Do Stock Market Risk Premium Respond to Consumer Confidence? By Abdur Chowdhury Working Paper 2011 06 College of Business Administration Do Stock Market Risk Premium
More informationJetBlue Airways Stock Price Analysis and Prediction
JetBlue Airways Stock Price Analysis and Prediction Team Member: Lulu Liu, Jiaojiao Liu DSO530 Final Project JETBLUE AIRWAYS STOCK PRICE ANALYSIS AND PREDICTION 1 Motivation Started in February 2000, JetBlue
More informationDynamic Relationship between Interest Rate and Stock Price: Empirical Evidence from Colombo Stock Exchange
International Journal of Business and Social Science Vol. 6, No. 4; April 2015 Dynamic Relationship between Interest Rate and Stock Price: Empirical Evidence from Colombo Stock Exchange AAMD Amarasinghe
More informationIs the Basis of the Stock Index Futures Markets Nonlinear?
University of Wollongong Research Online Applied Statistics Education and Research Collaboration (ASEARC) - Conference Papers Faculty of Engineering and Information Sciences 2011 Is the Basis of the Stock
More informationChapter 5: Bivariate Cointegration Analysis
Chapter 5: Bivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie V. Bivariate Cointegration Analysis...
More informationExamining the Relationship between ETFS and Their Underlying Assets in Indian Capital Market
2012 2nd International Conference on Computer and Software Modeling (ICCSM 2012) IPCSIT vol. 54 (2012) (2012) IACSIT Press, Singapore DOI: 10.7763/IPCSIT.2012.V54.20 Examining the Relationship between
More information**BEGINNING OF EXAMINATION** The annual number of claims for an insured has probability function: , 0 < q < 1.
**BEGINNING OF EXAMINATION** 1. You are given: (i) The annual number of claims for an insured has probability function: 3 p x q q x x ( ) = ( 1 ) 3 x, x = 0,1,, 3 (ii) The prior density is π ( q) = q,
More informationRegression Analysis: A Complete Example
Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty
More informationTime Series - ARIMA Models. Instructor: G. William Schwert
APS 425 Fall 25 Time Series : ARIMA Models Instructor: G. William Schwert 585-275-247 schwert@schwert.ssb.rochester.edu Topics Typical time series plot Pattern recognition in auto and partial autocorrelations
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationCOMP6053 lecture: Time series analysis, autocorrelation. jn2@ecs.soton.ac.uk
COMP6053 lecture: Time series analysis, autocorrelation jn2@ecs.soton.ac.uk Time series analysis The basic idea of time series analysis is simple: given an observed sequence, how can we build a model that
More informationDynamics of Real Investment and Stock Prices in Listed Companies of Tehran Stock Exchange
Dynamics of Real Investment and Stock Prices in Listed Companies of Tehran Stock Exchange Farzad Karimi Assistant Professor Department of Management Mobarakeh Branch, Islamic Azad University, Mobarakeh,
More informationTHE EFFECTS OF BANKING CREDIT ON THE HOUSE PRICE
THE EFFECTS OF BANKING CREDIT ON THE HOUSE PRICE * Adibeh Savari 1, Yaser Borvayeh 2 1 MA Student, Department of Economics, Science and Research Branch, Islamic Azad University, Khuzestan, Iran 2 MA Student,
More informationReview for Exam 2. Instructions: Please read carefully
Review for Exam Instructions: Please read carefully The exam will have 1 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation questions.
More informationSimple Linear Regression Inference
Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation
More informationChapter 7: Simple linear regression Learning Objectives
Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -
More informationSales forecasting # 2
Sales forecasting # 2 Arthur Charpentier arthur.charpentier@univ-rennes1.fr 1 Agenda Qualitative and quantitative methods, a very general introduction Series decomposition Short versus long term forecasting
More informationUnivariate and Multivariate Methods PEARSON. Addison Wesley
Time Series Analysis Univariate and Multivariate Methods SECOND EDITION William W. S. Wei Department of Statistics The Fox School of Business and Management Temple University PEARSON Addison Wesley Boston
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationChicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011
Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this
More informationTest3. Pessimistic Most Likely Optimistic Total Revenues 30 50 65 Total Costs -25-20 -15
Test3 1. The market value of Charcoal Corporation's common stock is $20 million, and the market value of its riskfree debt is $5 million. The beta of the company's common stock is 1.25, and the market
More informationMTH 140 Statistics Videos
MTH 140 Statistics Videos Chapter 1 Picturing Distributions with Graphs Individuals and Variables Categorical Variables: Pie Charts and Bar Graphs Categorical Variables: Pie Charts and Bar Graphs Quantitative
More informationGRADO EN ECONOMÍA. Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate?
FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES GRADO EN ECONOMÍA Is the Forward Rate a True Unbiased Predictor of the Future Spot Exchange Rate? Autor: Elena Renedo Sánchez Tutor: Juan Ángel Jiménez Martín
More informationChapter 13 Introduction to Linear Regression and Correlation Analysis
Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing
More informationA Trading Strategy Based on the Lead-Lag Relationship of Spot and Futures Prices of the S&P 500
A Trading Strategy Based on the Lead-Lag Relationship of Spot and Futures Prices of the S&P 500 FE8827 Quantitative Trading Strategies 2010/11 Mini-Term 5 Nanyang Technological University Submitted By:
More informationThe importance of graphing the data: Anscombe s regression examples
The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective
More informationI. Basic concepts: Buoyancy and Elasticity II. Estimating Tax Elasticity III. From Mechanical Projection to Forecast
Elements of Revenue Forecasting II: the Elasticity Approach and Projections of Revenue Components Fiscal Analysis and Forecasting Workshop Bangkok, Thailand June 16 27, 2014 Joshua Greene Consultant IMF-TAOLAM
More informationTIME SERIES ANALYSIS
TIME SERIES ANALYSIS L.M. BHAR AND V.K.SHARMA Indian Agricultural Statistics Research Institute Library Avenue, New Delhi-0 02 lmb@iasri.res.in. Introduction Time series (TS) data refers to observations
More informationPerforming Unit Root Tests in EViews. Unit Root Testing
Página 1 de 12 Unit Root Testing The theory behind ARMA estimation is based on stationary time series. A series is said to be (weakly or covariance) stationary if the mean and autocovariances of the series
More informationImpulse Response Functions
Impulse Response Functions Wouter J. Den Haan University of Amsterdam April 28, 2011 General definition IRFs The IRF gives the j th -period response when the system is shocked by a one-standard-deviation
More informationForecasting in supply chains
1 Forecasting in supply chains Role of demand forecasting Effective transportation system or supply chain design is predicated on the availability of accurate inputs to the modeling process. One of the
More informationCorrelational Research
Correlational Research Chapter Fifteen Correlational Research Chapter Fifteen Bring folder of readings The Nature of Correlational Research Correlational Research is also known as Associational Research.
More informationWeek TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480
1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500
More informationHomework 11. Part 1. Name: Score: / null
Name: Score: / Homework 11 Part 1 null 1 For which of the following correlations would the data points be clustered most closely around a straight line? A. r = 0.50 B. r = -0.80 C. r = 0.10 D. There is
More informationChapter 6: Multivariate Cointegration Analysis
Chapter 6: Multivariate Cointegration Analysis 1 Contents: Lehrstuhl für Department Empirische of Wirtschaftsforschung Empirical Research and und Econometrics Ökonometrie VI. Multivariate Cointegration
More informationFinancial Risk Management Exam Sample Questions/Answers
Financial Risk Management Exam Sample Questions/Answers Prepared by Daniel HERLEMONT 1 2 3 4 5 6 Chapter 3 Fundamentals of Statistics FRM-99, Question 4 Random walk assumes that returns from one time period
More informationARE STOCK PRICES PREDICTABLE? by Peter Tryfos York University
ARE STOCK PRICES PREDICTABLE? by Peter Tryfos York University For some years now, the question of whether the history of a stock's price is relevant, useful or pro table in forecasting the future price
More informationGetting Correct Results from PROC REG
Getting Correct Results from PROC REG Nathaniel Derby, Statis Pro Data Analytics, Seattle, WA ABSTRACT PROC REG, SAS s implementation of linear regression, is often used to fit a line without checking
More informationStock market booms and real economic activity: Is this time different?
International Review of Economics and Finance 9 (2000) 387 415 Stock market booms and real economic activity: Is this time different? Mathias Binswanger* Institute for Economics and the Environment, University
More informationTime Series Analysis
Time Series Analysis Forecasting with ARIMA models Andrés M. Alonso Carolina García-Martos Universidad Carlos III de Madrid Universidad Politécnica de Madrid June July, 2012 Alonso and García-Martos (UC3M-UPM)
More informationHow To Model A Series With Sas
Chapter 7 Chapter Table of Contents OVERVIEW...193 GETTING STARTED...194 TheThreeStagesofARIMAModeling...194 IdentificationStage...194 Estimation and Diagnostic Checking Stage...... 200 Forecasting Stage...205
More informationDepartment of Economics and Related Studies Financial Market Microstructure. Topic 1 : Overview and Fixed Cost Models of Spreads
Session 2008-2009 Department of Economics and Related Studies Financial Market Microstructure Topic 1 : Overview and Fixed Cost Models of Spreads 1 Introduction 1.1 Some background Most of what is taught
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationNon-Stationary Time Series andunitroottests
Econometrics 2 Fall 2005 Non-Stationary Time Series andunitroottests Heino Bohn Nielsen 1of25 Introduction Many economic time series are trending. Important to distinguish between two important cases:
More informationBusiness Cycles and Natural Gas Prices
Department of Economics Discussion Paper 2004-19 Business Cycles and Natural Gas Prices Apostolos Serletis Department of Economics University of Calgary Canada and Asghar Shahmoradi Department of Economics
More informationFORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits
Technical Paper Series Congressional Budget Office Washington, DC FORECASTING DEPOSIT GROWTH: Forecasting BIF and SAIF Assessable and Insured Deposits Albert D. Metz Microeconomic and Financial Studies
More information2013 MBA Jump Start Program. Statistics Module Part 3
2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just
More informationUsing Duration Times Spread to Forecast Credit Risk
Using Duration Times Spread to Forecast Credit Risk European Bond Commission / VBA Patrick Houweling, PhD Head of Quantitative Credits Research Robeco Asset Management Quantitative Strategies Forecasting
More informationAnswer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade
Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements
More informationBooth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay. Solutions to Midterm
Booth School of Business, University of Chicago Business 41202, Spring Quarter 2015, Mr. Ruey S. Tsay Solutions to Midterm Problem A: (30 pts) Answer briefly the following questions. Each question has
More informationAgenda. Managing Uncertainty in the Supply Chain. The Economic Order Quantity. Classic inventory theory
Agenda Managing Uncertainty in the Supply Chain TIØ485 Produkjons- og nettverksøkonomi Lecture 3 Classic Inventory models Economic Order Quantity (aka Economic Lot Size) The (s,s) Inventory Policy Managing
More informationSAMPLE MID-TERM QUESTIONS
SAMPLE MID-TERM QUESTIONS William L. Silber HOW TO PREPARE FOR THE MID- TERM: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below,
More informationAdvanced Forecasting Techniques and Models: ARIMA
Advanced Forecasting Techniques and Models: ARIMA Short Examples Series using Risk Simulator For more information please visit: www.realoptionsvaluation.com or contact us at: admin@realoptionsvaluation.com
More informationPearson's Correlation Tests
Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation
More informationLecture 1: Asset Allocation
Lecture 1: Asset Allocation Investments FIN460-Papanikolaou Asset Allocation I 1/ 62 Overview 1. Introduction 2. Investor s Risk Tolerance 3. Allocating Capital Between a Risky and riskless asset 4. Allocating
More informationPricing Corn Calendar Spread Options. Juheon Seok and B. Wade Brorsen
Pricing Corn Calendar Spread Options by Juheon Seok and B. Wade Brorsen Suggested citation format: Seok, J., and B. W. Brorsen. 215. Pricing Corn Calendar Spread Options. Proceedings of the NCCC-134 Conference
More informationTesting for Cointegrating Relationships with Near-Integrated Data
Political Analysis, 8:1 Testing for Cointegrating Relationships with Near-Integrated Data Suzanna De Boef Pennsylvania State University and Harvard University Jim Granato Michigan State University Testing
More informationOutline: Demand Forecasting
Outline: Demand Forecasting Given the limited background from the surveys and that Chapter 7 in the book is complex, we will cover less material. The role of forecasting in the chain Characteristics of
More informationAN EMPIRICAL INVESTIGATION OF THE RELATIONSHIP AMONG P/E RATIO, STOCK RETURN AND DIVIDEND YIELS FOR ISTANBUL STOCK EXCHANGE
AN EMPIRICAL INVESTIGATION OF THE RELATIONSHIP AMONG P/E RATIO, STOCK RETURN AND DIVIDEND YIELS FOR ISTANBUL STOCK EXCHANGE Funda H. SEZGIN Mimar Sinan Fine Arts University, Faculty of Science and Letters
More informationThere are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month
More informationDiscussion of The Returns to Currency Speculation
Discussion of The Returns to Currency Speculation John H. Cochrane January 5, 2007 UIP Uk interest rate = 5%, US interest rate = 2%. Invest in UK? 1. Naive: Yes, Make 3% more 2. Traditional: No, Pound
More informationForecasting in STATA: Tools and Tricks
Forecasting in STATA: Tools and Tricks Introduction This manual is intended to be a reference guide for time series forecasting in STATA. It will be updated periodically during the semester, and will be
More informationTime Series Analysis
JUNE 2012 Time Series Analysis CONTENT A time series is a chronological sequence of observations on a particular variable. Usually the observations are taken at regular intervals (days, months, years),
More informationShould we Really Care about Building Business. Cycle Coincident Indexes!
Should we Really Care about Building Business Cycle Coincident Indexes! Alain Hecq University of Maastricht The Netherlands August 2, 2004 Abstract Quite often, the goal of the game when developing new
More informationbusiness statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
More informationTIME SERIES ANALYSIS & FORECASTING
CHAPTER 19 TIME SERIES ANALYSIS & FORECASTING Basic Concepts 1. Time Series Analysis BASIC CONCEPTS AND FORMULA The term Time Series means a set of observations concurring any activity against different
More informationExample: Boats and Manatees
Figure 9-6 Example: Boats and Manatees Slide 1 Given the sample data in Table 9-1, find the value of the linear correlation coefficient r, then refer to Table A-6 to determine whether there is a significant
More informationModule 5: Statistical Analysis
Module 5: Statistical Analysis To answer more complex questions using your data, or in statistical terms, to test your hypothesis, you need to use more advanced statistical tests. This module reviews the
More informationChapter 1. Vector autoregressions. 1.1 VARs and the identi cation problem
Chapter Vector autoregressions We begin by taking a look at the data of macroeconomics. A way to summarize the dynamics of macroeconomic data is to make use of vector autoregressions. VAR models have become
More informationInternational Statistical Institute, 56th Session, 2007: Phil Everson
Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction
More informationCorrelation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables 2
Lesson 4 Part 1 Relationships between two numerical variables 1 Correlation Coefficient The correlation coefficient is a summary statistic that describes the linear relationship between two numerical variables
More informationCapital Market Inflation theory: An empirical approach
Capital Market Inflation theory: An empirical approach Mimoza Shabani, SOAS, University of London 1.0 INTRODUCTION A good economic model is said to make sharp and clear predictions that are consistent
More informationEconometrics I: Econometric Methods
Econometrics I: Econometric Methods Jürgen Meinecke Research School of Economics, Australian National University 24 May, 2016 Housekeeping Assignment 2 is now history The ps tute this week will go through
More informationContents. List of Figures. List of Tables. List of Examples. Preface to Volume IV
Contents List of Figures List of Tables List of Examples Foreword Preface to Volume IV xiii xvi xxi xxv xxix IV.1 Value at Risk and Other Risk Metrics 1 IV.1.1 Introduction 1 IV.1.2 An Overview of Market
More informationA Review of Cross Sectional Regression for Financial Data You should already know this material from previous study
A Review of Cross Sectional Regression for Financial Data You should already know this material from previous study But I will offer a review, with a focus on issues which arise in finance 1 TYPES OF FINANCIAL
More informationI.e., the return per dollar from investing in the shares from time 0 to time 1,
XVII. SECURITY PRICING AND SECURITY ANALYSIS IN AN EFFICIENT MARKET Consider the following somewhat simplified description of a typical analyst-investor's actions in making an investment decision. First,
More information