# USE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY

Save this PDF as:

Size: px
Start display at page:

Download "USE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY"

## Transcription

1 Paper PO10 USE OF ARIMA TIME SERIES AND REGRESSORS TO FORECAST THE SALE OF ELECTRICITY Beatrice Ugiliweneza, University of Louisville, Louisville, KY ABSTRACT Objectives: To forecast the sales made by an electric company every month. To show the use of ARIMA and Regression models in forecasting. Method: The data used to forecast were from the total sale of electricity for each end of the month from 1994 to The statistical forecasting method used is the ARIMA time series with the regression model. Results: With a seasonable ARIMA model, a regressor and a dynamic regressor, the model predictions compare with the actual values of sales and hence, the forecast values are reliable. Conclusions: ARIMA time series are useful models to predict the sales of electricity for this company. From this study, we can conclude that ARIMA and Regression models can be used by other businesses for planning. INTRODUCTION Generally, companies focus on the forecasting of sales because they need to plan their expenses and still make a profit. This paper shows how ARIMA time series and Regression models can be used to forecast company sales. A model is used to forecast one year ahead of the total sale of electricity from a sample of ten years available ( ), with the data provided monthly. As a result, the predicted values of the 10 years ( ) compare well enough, with the actual sales values. Thus, the forecast values are reliable. The application can be easily extended to other selling companies. We use these data to demonstrate the use of the SAS Time Series Forecasting System. While the Forecasting System can automate the analysis of data, the investigator needs to interact with the system to find the most effective forecasts. We also show how inflation can be added as a dynamic regressor. METHOD The data were collected on a monthly basis, from the total sales of an electric company for ten years ( ). A sample of 128 data points was obtained. The data were provided by the original investigator. The tool used is the SAS Time Series forecasting system. This system is a SAS point-and-click interface that provides automatic model fitting and forecasting as well as interactive model development. The system provides the best fitting model for each time series. We can use system features to identify series behavior, fit candidate forecasting models, and perform diagnostic checks on the fitted models. To get the SAS Time Series forecasting system, we start with the window shown in Figure

2 Figure 1. Entry Screen for Time Series Forecasting System After inputing the data, the Develop model is chosen. After this, the following window (Figure 2) enables us to construct a model by right-clicking in the white area. Figure 2. Developing the Model Plots and results will be explored with interactive graphical tools. The data were stationary and they had a fixed constant for the mean (the average) and the variance. For this reason, the ARIMA time series model was used. Figure 3 shows that the sale of electricity tends to be seasonal. Hence, the seasonal ARIMA model was used. Page 2 of 11

3 Figure 3: Plot of total sale of electricity Figure 4 shows that the ACF (Autocorrelations function) is spiked at lag 1 and declines toward zero. It also shows that the PACF (Partial autocorrelation function) is spiked at lag 1 and is zero at lag 2. Considering this, the ARIMA (1, 0, 0) s was chosen. Page 3 of 11

4 Figure 4: Plot of autocorrelations The sales of electricity should depend on the total electric usage. For this reason, the total electric usage was chosen as a regressor. Moreover, the results of the sales are affected by the inflation rate, which is a variable, nonconstant regressor. Thus, the inflation rate was added to the model as a dynamic regressor. With this dynamic regressor, a numerator factor with an order 1 is specified, which means that the inflation rate starts at one month. These inflation rate data were found on the historical inflation data website, inflationdata.com. Figure 5 shows the graph of the mean value of the inflation rate per year for ten years, from 1994 to Page 4 of 11

5 Figure5: Plot of the mean value of the inflation rate by year from 1994 to 2004 Briefly, the model used is: Total sale of electricity=inflation rate [N (1))] +Total electric usage +ARIMA (1, 0, 0) 12 This model of ARIMA and the regressors was chosen because it yields a better model than the ARIMA alone. In fact, the following tables show that the mean absolute percent error of the ARIMA + Regressors, which is equal to 5.96, is smaller than the mean absolute percent error of the ARIMA alone, which is Table1: Statistics of fit of the use of the model: Total sale of electricity=inflation rate [N (1))] +Total electric usage + ARIMA (1, 0, 0) 12 Page 5 of 11

6 Table 2: Statistics of fit of the use of the model: ARIMA (1, 0, 0) 12 RESULTS The working series contains 128 sales collected in ten years ( ) on a monthly basis and among these, a holdout sample of 60 sales on which the model of forecasting is built. These sales have a mean of \$ and a standard deviation of The values of the sales are in thousands of dollars. The Inflation rate is used as a predictor in the model [N (1))] +Total electric usage +ARIMA (1, 0, 0) 12 We use it to give predicted values for the ten years ( ) and forecast values for one year ahead (2005). Figure 3 shows that the company sells more electricity in the period at the end of the year. The best sales of electricity were obtained at the end of Figure 6 shows predicted values obtained with the use of the Inflation rate with the above model, Page 6 of 11

7 Figure 6: Plot of values Figure 6 shows better sales in the period at the end of the year with the best sale at the end of Figure 7 shows that most of the differences between actual values and the predicted values are between -600 and 600 (these values are in thousands of dollars). Except for two values, the absolute value of the errors between the actual and the predicted values is at most 600. The actual values gave a mean of \$ ; so, this error, which is percent of the mean value, is very small. This proves that the Inflation rate [N (1))] +Total electric usage +ARIMA (1, 0, 0) 12 model predicted well. Therefore, the forecasts of this model are reliable. Page 7 of 11

8 Figure 7: Plot of predicted values Figure 8 shows that the forecasts are between 2000 and 4250 (with a 95% confidence interval) with predicted high sales at the end of 2004 and improved sales at the end of The inflation rate [N (1))] +Total electric usage +ARIMA (1, 0, 0) 12 predicts a seasonal sale for 2005 and gives the likelihood interval of values. Page 8 of 11

9 Figure 8: Plot of prediction errors The prediction is given in Figure 9. Page 9 of 11

10 Figure 9: Plot of forecast values ( ) The plot above gives the forecast values for the year The first part of the graph represents the predicted values of the years 1994 to 2004 (these compare with the actual values) and the second part gives the values and the behavior of the forecasts with a 95% confidence interval. Table 3 gives the forecast values of the total sale of electricity for one whole year ahead. These are eleven values on which the electric company can rely on to plan the business for (U95: upper limit of the 95%confidence interval, L95: lower limit of the 95% confidence interval) Table3: Forecast data set from 01 October 2004 to 01 August 2005 */ Page 10 of 11

11 CONCLUSIONS This study demonstrates how ARIMA time series and Regression models are useful to study and forecast sales for a particular company. This paper demonstrates also how the Time Series Forecasting System can be used to construct a model of forecasting. The Inflation rate [N (1))] +Total electric usage +ARIMA (1, 0, 0) 12 predicted the data considerably well and gave reliable forecasts. According to the data presented, this model was best in forecasting the sales, but could not tell why the sales will contain outliers. The SAS Time Series forecasting system helped construct a model, the ARIMA time series and the Regression, which is effective for forecasting and can be applied to other businesses in order to plan their sales. However, it would be interesting to do further research on the factors that influence the sales, such as the growth of the population of consumers, the industrial growth in the region, the immigration, and so on; this would consolidate better this company s planning. CONTACT INFORMATION Your comments and questions are valued and encouraged. Contact the author at: Beatrice Ugiliweneza Department of Mathematics University of Louisville Louisville, KY SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are trademarks of their respective companies. Page 11 of 11

### Promotional Forecast Demonstration

Exhibit 2: Promotional Forecast Demonstration Consider the problem of forecasting for a proposed promotion that will start in December 1997 and continues beyond the forecast horizon. Assume that the promotion

### Using JMP Version 4 for Time Series Analysis Bill Gjertsen, SAS, Cary, NC

Using JMP Version 4 for Time Series Analysis Bill Gjertsen, SAS, Cary, NC Abstract Three examples of time series will be illustrated. One is the classical airline passenger demand data with definite seasonal

### Time 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

### IBM SPSS Forecasting 22

IBM SPSS Forecasting 22 Note Before using this information and the product it supports, read the information in Notices on page 33. Product Information This edition applies to version 22, release 0, modification

### Short Term Load Forecasting Using Time Series Analysis: A Case Study for Karnataka, India

ISO 91:28 Certified Volume 1, Issue 2, November 212 Short Term Load Forecasting Using Time Series Analysis: A Case Study for Karnataka, India Nataraja.C 1, M.B.Gorawar 2, Shilpa.G.N. 3, Shri Harsha.J.

### Time 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

### MGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal

MGT 267 PROJECT Forecasting the United States Retail Sales of the Pharmacies and Drug Stores Done by: Shunwei Wang & Mohammad Zainal Dec. 2002 The retail sale (Million) ABSTRACT The present study aims

### 4. 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

### Forecasting areas and production of rice in India using ARIMA model

International Journal of Farm Sciences 4(1) :99-106, 2014 Forecasting areas and production of rice in India using ARIMA model K PRABAKARAN and C SIVAPRAGASAM* Agricultural College and Research Institute,

### TIME 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

### Search Marketing Cannibalization. Analytical Techniques to measure PPC and Organic interaction

Search Marketing Cannibalization Analytical Techniques to measure PPC and Organic interaction 2 Search Overview How People Use Search Engines Navigational Research Health/Medical Directions News Shopping

### A Multiplicative Seasonal Box-Jenkins Model to Nigerian Stock Prices

A Multiplicative Seasonal Box-Jenkins Model to Nigerian Stock Prices Ette Harrison Etuk Department of Mathematics/Computer Science, Rivers State University of Science and Technology, Nigeria Email: ettetuk@yahoo.com

### Luciano 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

### Studying Achievement

Journal of Business and Economics, ISSN 2155-7950, USA November 2014, Volume 5, No. 11, pp. 2052-2056 DOI: 10.15341/jbe(2155-7950)/11.05.2014/009 Academic Star Publishing Company, 2014 http://www.academicstar.us

### Modeling and Forecasting of Gold Prices on Financial Markets

Modeling and Forecasting of Gold Prices on Financial Markets Rebecca Davis Department of Mathematical Sciences Pentecost University College Accra-Ghana. Vincent Kofi Dedu Department of Mathematics Kwame

### I. Introduction. II. Background. KEY WORDS: Time series forecasting, Structural Models, CPS

Predicting the National Unemployment Rate that the "Old" CPS Would Have Produced Richard Tiller and Michael Welch, Bureau of Labor Statistics Richard Tiller, Bureau of Labor Statistics, Room 4985, 2 Mass.

### 16 : 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

### Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model

Tropical Agricultural Research Vol. 24 (): 2-3 (22) Forecasting of Paddy Production in Sri Lanka: A Time Series Analysis using ARIMA Model V. Sivapathasundaram * and C. Bogahawatte Postgraduate Institute

### TIME SERIES ANALYSIS

TIME SERIES ANALYSIS Ramasubramanian V. I.A.S.R.I., Library Avenue, New Delhi- 110 012 ram_stat@yahoo.co.in 1. Introduction A Time Series (TS) is a sequence of observations ordered in time. Mostly these

### The SAS Time Series Forecasting System

The SAS Time Series Forecasting System An Overview for Public Health Researchers Charles DiMaggio, PhD College of Physicians and Surgeons Departments of Anesthesiology and Epidemiology Columbia University

### COMP6053 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

### Rob 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

### Time Series Graphs. Model ACF PACF. White Noise All zeros All zeros. AR(p) Exponential Decay P significant lags before dropping to zero

Time Series Graphs Model ACF PACF White Noise All zeros All zeros AR(p) Exponential Decay P significant lags before dropping to zero MA(q) q significant lags before dropping to zero Exponential Decay ARMA(p,q)

### Joseph Twagilimana, University of Louisville, Louisville, KY

ST14 Comparing Time series, Generalized Linear Models and Artificial Neural Network Models for Transactional Data analysis Joseph Twagilimana, University of Louisville, Louisville, KY ABSTRACT The aim

### JetBlue 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

### Some useful concepts in univariate time series analysis

Some useful concepts in univariate time series analysis Autoregressive moving average models Autocorrelation functions Model Estimation Diagnostic measure Model selection Forecasting Assumptions: 1. Non-seasonal

### Durbin-Watson Significance Tables

Durbin-Watson Significance Tables Appendix A The Durbin-Watson test statistic tests the null hypothesis that the residuals from an ordinary least-squares regression are not autocorrelated against the alternative

### IBM SPSS Forecasting 21

IBM SPSS Forecasting 21 Note: Before using this information and the product it supports, read the general information under Notices on p. 107. This edition applies to IBM SPSS Statistics 21 and to all

Chapter 7 Chapter Table of Contents OVERVIEW...193 GETTING STARTED...194 TheThreeStagesofARIMAModeling...194 IdentificationStage...194 Estimation and Diagnostic Checking Stage...... 200 Forecasting Stage...205

### White Paper. Desktop Forecasting for Small and Midsize Businesses

White Paper Desktop Forecasting for Small and Midsize Businesses Contents Introduction... 1 Why Forecasting Is Important... 1 Looking Inside SAS Forecasting for Desktop... 1 Introduction... 1 Overview

### Chapter 25 Specifying Forecasting Models

Chapter 25 Specifying Forecasting Models Chapter Table of Contents SERIES DIAGNOSTICS...1281 MODELS TO FIT WINDOW...1283 AUTOMATIC MODEL SELECTION...1285 SMOOTHING MODEL SPECIFICATION WINDOW...1287 ARIMA

### Study & Development of Short Term Load Forecasting Models Using Stochastic Time Series Analysis

International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 9, Issue 11 (February 2014), PP. 31-36 Study & Development of Short Term Load Forecasting

### Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA

Forecasting Geographic Data Michael Leonard and Renee Samy, SAS Institute Inc. Cary, NC, USA Abstract Virtually all businesses collect and use data that are associated with geographic locations, whether

### Energy Load Mining Using Univariate Time Series Analysis

Energy Load Mining Using Univariate Time Series Analysis By: Taghreed Alghamdi & Ali Almadan 03/02/2015 Caruth Hall 0184 Energy Forecasting Energy Saving Energy consumption Introduction: Energy consumption.

### APPLICATION OF BOX-JENKINS METHOD AND ARTIFICIAL NEURAL NETWORK PROCEDURE FOR TIME SERIES FORECASTING OF PRICES

STATISTICS IN TRANSITION new series, Spring 2015 83 STATISTICS IN TRANSITION new series, Spring 2015 Vol. 16, No. 1, pp. 83 96 APPLICATION OF BOX-JENKINS METHOD AND ARTIFICIAL NEURAL NETWORK PROCEDURE

### Univariate 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

### Multiple Regression in SPSS STAT 314

Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan

### Paper DM09. Yankees and Red Sox: A Time Series Analysis of Win Percentage Correlations between Professional Baseball Teams

Paper DM09 Yankees and Red Sox: A Time Series Analysis of Win Percentage Correlations between Professional Baseball Teams Grant Johnson, University of Louisville, Louisville, KY ABSTRACT Objective. The

### Eviews Tutorial. File New Workfile. Start observation End observation Annual

APS 425 Professor G. William Schwert Advanced Managerial Data Analysis CS3-110L, 585-275-2470 Fax: 585-461-5475 email: schwert@schwert.ssb.rochester.edu Eviews Tutorial 1. Creating a Workfile: First you

### (More Practice With Trend Forecasts)

Stats for Strategy HOMEWORK 11 (Topic 11 Part 2) (revised Jan. 2016) DIRECTIONS/SUGGESTIONS You may conveniently write answers to Problems A and B within these directions. Some exercises include special

### Technical note on seasonal adjustment for Wholesale price index (Fruits and vegetables)

Technical note on seasonal adjustment for Wholesale price index (Fruits and vegetables) February 4, 2013 Contents 1 WPI (Fruits and vegetables) 2 1.1 Additive versus multiplicative seasonality.....................

### Graphical Tools for Exploring and Analyzing Data From ARIMA Time Series Models

Graphical Tools for Exploring and Analyzing Data From ARIMA Time Series Models William Q. Meeker Department of Statistics Iowa State University Ames, IA 50011 January 13, 2001 Abstract S-plus is a highly

### Time 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),

### Time Series Analysis: Basic Forecasting.

Time Series Analysis: Basic Forecasting. As published in Benchmarks RSS Matters, April 2015 http://web3.unt.edu/benchmarks/issues/2015/04/rss-matters Jon Starkweather, PhD 1 Jon Starkweather, PhD jonathan.starkweather@unt.edu

### Time 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

### Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0.

Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged

### Analysis of Financial Time Series with EViews

Analysis of Financial Time Series with EViews Enrico Foscolo Contents 1 Asset Returns 2 1.1 Empirical Properties of Returns................. 2 2 Heteroskedasticity and Autocorrelation 4 2.1 Testing for

### Traffic Safety Facts. Research Note. Time Series Analysis and Forecast of Crash Fatalities during Six Holiday Periods Cejun Liu* and Chou-Lin Chen

Traffic Safety Facts Research Note March 2004 DOT HS 809 718 Time Series Analysis and Forecast of Crash Fatalities during Six Holiday Periods Cejun Liu* and Chou-Lin Chen Summary This research note uses

### Practical Time Series Analysis Using SAS

Practical Time Series Analysis Using SAS Anders Milhøj Contents Preface... vii Part 1: Time Series as a Subject for Analysis... 1 Chapter 1 Time Series Data... 3 1.1 Time Series Questions... 3 1.2 Types

### Implied Volatility Skews in the Foreign Exchange Market. Empirical Evidence from JPY and GBP: 1997-2002

Implied Volatility Skews in the Foreign Exchange Market Empirical Evidence from JPY and GBP: 1997-2002 The Leonard N. Stern School of Business Glucksman Institute for Research in Securities Markets Faculty

### Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

### Extended control charts

Extended control charts The control chart types listed below are recommended as alternative and additional tools to the Shewhart control charts. When compared with classical charts, they have some advantages

### Software Review: ITSM 2000 Professional Version 6.0.

Lee, J. & Strazicich, M.C. (2002). Software Review: ITSM 2000 Professional Version 6.0. International Journal of Forecasting, 18(3): 455-459 (June 2002). Published by Elsevier (ISSN: 0169-2070). http://0-

### Automating FP&A Analytics Using SAP Visual Intelligence and Predictive Analysis

September 9 11, 2013 Anaheim, California Automating FP&A Analytics Using SAP Visual Intelligence and Predictive Analysis Varun Kumar Learning Points Create management insight tool using SAP Visual Intelligence

### , then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (

Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we

### Time 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)

### 430 Statistics and Financial Mathematics for Business

Prescription: 430 Statistics and Financial Mathematics for Business Elective prescription Level 4 Credit 20 Version 2 Aim Students will be able to summarise, analyse, interpret and present data, make predictions

### White Paper. Thirsting for Insight? Quench It With 5 Data Management for Analytics Best Practices.

White Paper Thirsting for Insight? Quench It With 5 Data Management for Analytics Best Practices. Contents Data Management: Why It s So Essential... 1 The Basics of Data Preparation... 1 1: Simplify Access

### Forecasting Share Prices of Axis and ICICI Banks by Econometric Modeling

Forecasting Share Prices of Axis and ICICI Banks by Econometric Modeling Monika Saxena Assistant Professor Indus Business Academy Knowledge Park 3, Plot No 44 Greater Noida India Abstract The objective

### Confidence Intervals for One Standard Deviation Using Standard Deviation

Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from

### Time Series Analysis of Stock Prices Using the Box- Jenkins Approach

Georgia Southern University Digital Commons@Georgia Southern Electronic Theses & Dissertations Jack N. Averitt College of Graduate Studies (COGS) Time Series Analysis of Stock Prices Using the Box- Jenkins

### THE UNIVERSITY OF CHICAGO, Booth School of Business Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay. Solutions to Homework Assignment #2

THE UNIVERSITY OF CHICAGO, Booth School of Business Business 41202, Spring Quarter 2014, Mr. Ruey S. Tsay Solutions to Homework Assignment #2 Assignment: 1. Consumer Sentiment of the University of Michigan.

### SPC Data Visualization of Seasonal and Financial Data Using JMP WHITE PAPER

SPC Data Visualization of Seasonal and Financial Data Using JMP WHITE PAPER SAS White Paper Table of Contents Abstract.... 1 Background.... 1 Example 1: Telescope Company Monitors Revenue.... 3 Example

### 8. Time Series and Prediction

8. Time Series and Prediction Definition: A time series is given by a sequence of the values of a variable observed at sequential points in time. e.g. daily maximum temperature, end of day share prices,

### Lecture 18 Linear Regression

Lecture 18 Statistics Unit Andrew Nunekpeku / Charles Jackson Fall 2011 Outline 1 1 Situation - used to model quantitative dependent variable using linear function of quantitative predictor(s). Situation

### Prediction of Stock Price usingautoregressiveintegrated Moving AverageFilter Arima P,D,Q

Global Journal of Science Frontier Research Mathematics and Decision Sciences Volume 13 Issue 8 Version 1.0 Year Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals

### The average hotel manager recognizes the criticality of forecasting. However, most

Introduction The average hotel manager recognizes the criticality of forecasting. However, most managers are either frustrated by complex models researchers constructed or appalled by the amount of time

### Section A. Index. Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1. Page 1 of 11. EduPristine CMA - Part I

Index Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting techniques... 1 EduPristine CMA - Part I Page 1 of 11 Section A. Planning, Budgeting and Forecasting Section A.2 Forecasting

J. Stuart Hunter Princeton University Copyright 2007, SAS Institute Inc. All rights reserved. JMP INNOVATOR S SUMMIT Time Series Approaches to Quality Prediction for Production and the Arts of Charts Traverse

### Monitoring the SARS Epidemic in China: A Time Series Analysis

Journal of Data Science 3(2005), 279-293 Monitoring the SARS Epidemic in China: A Time Series Analysis Dejian Lai The University of Texas and Jiangxi University of Finance and Economics Abstract: In this

### Using SAS to Create Sales Expectations for Everyday and Seasonal Products Ellebracht, Netherton, Gentry, Hallmark Cards, Inc.

Paper SA-06-2012 Using SAS to Create Sales Expectations for Everyday and Seasonal Products Ellebracht, Netherton, Gentry, Hallmark Cards, Inc., Kansas City, MO Abstract In order to provide a macro-level

### EMPIRICAL INVESTIGATION AND MODELING OF THE RELATIONSHIP BETWEEN GAS PRICE AND CRUDE OIL AND ELECTRICITY PRICES

Page 119 EMPIRICAL INVESTIGATION AND MODELING OF THE RELATIONSHIP BETWEEN GAS PRICE AND CRUDE OIL AND ELECTRICITY PRICES Morsheda Hassan, Wiley College Raja Nassar, Louisiana Tech University ABSTRACT Crude

### Time Series Analysis

Time Series Analysis hm@imm.dtu.dk Informatics and Mathematical Modelling Technical University of Denmark DK-2800 Kgs. Lyngby 1 Outline of the lecture Identification of univariate time series models, cont.:

### JOHANNES TSHEPISO TSOKU NONOFO PHOKONTSI DANIEL METSILENG FORECASTING SOUTH AFRICAN GOLD SALES: THE BOX-JENKINS METHODOLOGY

DOI: 0.20472/IAC.205.08.3 JOHANNES TSHEPISO TSOKU North West University, South Africa NONOFO PHOKONTSI North West University, South Africa DANIEL METSILENG Department of Health, South Africa FORECASTING

### Credit Risk Analysis Using Logistic Regression Modeling

Credit Risk Analysis Using Logistic Regression Modeling Introduction A loan officer at a bank wants to be able to identify characteristics that are indicative of people who are likely to default on loans,

### Estimating and Forecasting Network Traffic Performance based on Statistical Patterns Observed in SNMP data.

Estimating and Forecasting Network Traffic Performance based on Statistical Patterns Observed in SNMP data. K. Hu 1,2, A. Sim 1, Demetris Antoniades 3, Constantine Dovrolis 3 1 Lawrence Berkeley National

### 9th Russian Summer School in Information Retrieval Big Data Analytics with R

9th Russian Summer School in Information Retrieval Big Data Analytics with R Introduction to Time Series with R A. Karakitsiou A. Migdalas Industrial Logistics, ETS Institute Luleå University of Technology

### Univariate Time Series Analysis; ARIMA Models

Econometrics 2 Spring 25 Univariate Time Series Analysis; ARIMA Models Heino Bohn Nielsen of4 Outline of the Lecture () Introduction to univariate time series analysis. (2) Stationarity. (3) Characterizing

### Modeling the effect of inflation

Lecture notes on forecasting Robert Nau Fuqua School of Business Duke University http://people.duke.edu/~rnau/forecasting.htm Forecasting with adjustments for inflation and seasonality Deflation with price

### Calculating Interval Forecasts

Calculating Chapter 7 (Chatfield) Monika Turyna & Thomas Hrdina Department of Economics, University of Vienna Summer Term 2009 Terminology An interval forecast consists of an upper and a lower limit between

### Monitoring Trends in Network Flow for Situational Awareness

Monitoring Trends in Network Flow for Situational Awareness SEI CERT NetSA 2011 Carnegie Mellon University NO WARRANTY THIS MATERIAL OF CARNEGIE MELLON UNIVERSITY AND ITS SOFTWARE ENGINEERING INSTITUTE

### VAR modeling with applications in Marketing

PhD Course VAR modeling with applications in Marketing November 20-22, 2014 Esplanade 36, 20354 Hamburg, 5th Floor, Room 5007 Course instructor: Professor Koen Pauwels Course Value: 2 SWS or 4 LPs Course

### Multiple Regression Analysis in Minitab 1

Multiple Regression Analysis in Minitab 1 Suppose we are interested in how the exercise and body mass index affect the blood pressure. A random sample of 10 males 50 years of age is selected and their

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Advanced time-series analysis Lisa Tompson Research Associate UCL Jill Dando Institute of Crime Science l.tompson@ucl.ac.uk Overview Fundamental principles

### Regression 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

### Time Series Analysis and Forecasting

Time Series Analysis and Forecasting Math 667 Al Nosedal Department of Mathematics Indiana University of Pennsylvania Time Series Analysis and Forecasting p. 1/11 Introduction Many decision-making applications

### Demand Forecasting and Production Planning for Highly Seasonal Demand Situations: Case Study of a Pressure Container Factory

ScienceAsia 27 (2) : 27-278 Demand Forecasting and Production Planning for Highly Seasonal Demand Situations: Case Study of a Pressure Container Factory Pisal Yenradee a,*, Anulark Pinnoi b and Amnaj Charoenthavornying

### 2015 Workshops for Professors

SAS Education Grow with us Offered by the SAS Global Academic Program Supporting teaching, learning and research in higher education 2015 Workshops for Professors 1 Workshops for Professors As the market

### Forecasting Using Eviews 2.0: An Overview

Forecasting Using Eviews 2.0: An Overview Some Preliminaries In what follows it will be useful to distinguish between ex post and ex ante forecasting. In terms of time series modeling, both predict values

### Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

### Introducing Oracle Crystal Ball Predictor: a new approach to forecasting in MS Excel Environment

Introducing Oracle Crystal Ball Predictor: a new approach to forecasting in MS Excel Environment Samik Raychaudhuri, Ph. D. Principal Member of Technical Staff ISF 2010 Oracle Crystal

### Monte Carlo Simulation (General Simulation Models)

Monte Carlo Simulation (General Simulation Models) STATGRAPHICS Rev. 9/16/2013 Summary... 1 Example #1... 1 Example #2... 8 Summary Monte Carlo simulation is used to estimate the distribution of variables

### Journal of Business Valuation and Economic Loss Analysis

Journal of Business Valuation and Economic Loss Analysis Volume 4, Issue 2 2009 Article 3 HURRICANE KATRINA AND ECONOMIC LOSS Petroleum-Refining Industry Business Interruption Losses due to Hurricane Katrina

### Elements of statistics (MATH0487-1)

Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -

### Forecasting methods applied to engineering management

Forecasting methods applied to engineering management Áron Szász-Gábor Abstract. This paper presents arguments for the usefulness of a simple forecasting application package for sustaining operational