Transformations for variance stabilization
|
|
- Heather Nichols
- 5 years ago
- Views:
Transcription
1 FORECASTING USING R Transformations for variance stabilization Rob Hyndman Author, forecast
2 Variance stabilization If the data show increasing variation as the level of the series increases, then a transformation can be useful y 1,...,y n : original observations, w 1,...,w n : transformed observations Mathematical transformations for stabilizing variation Square Root Cube Root Logarithm Inverse w t = y t w t = 3 yt w t =log(y t ) w t = 1/y t Increasing strength
3 Variance stabilization > autoplot(usmelec) + xlab("year") + ylab("") + ggtitle("us monthly net electricity generation")
4 Variance stabilization > autoplot(usmelec^0.5) + xlab("year") + ylab("") + ggtitle("square root electricity generation")
5 Variance stabilization > autoplot(usmelec^ ) + xlab("year") + ylab("") + ggtitle("cube root electricity generation")
6 Variance stabilization > autoplot(log(usmelec)) + xlab("year") + ylab("") + ggtitle("log electricity generation")
7 Variance stabilization > autoplot(-1/usmelec) + xlab("year") + ylab("") + ggtitle("inverse electricity generation")
8 Box-Cox transformations Each of these transformations is close to a member of the family of Box-Cox transformations w t = { log(yt ) λ =0 (y λ t 1)/λ λ 0 λ =1 : No substantive transformation λ = 1 2 : Square root plus linear transformation λ = 1 3 : Cube root plus linear transformation λ =0 : Natural logarithm transformation λ = 1 : Inverse transformation > BoxCox.lambda(usmelec) [1]
9 Back-transformation > usmelec %>% ets(lambda = -0.57) %>% forecast(h = 60) %>% autoplot()
10 FORECASTING USING R Let s practice!
11 FORECASTING USING R ARIMA models
12 ARIMA models Autoregressive (AR) models y t = c + φ 1 y t 1 + φ 2 y t φ p y t p + e t, e t white noise Multiple regression with lagged observations as predictors Moving Average (MA) models y t = c + e t + θ 1 e t 1 + θ 2 e t θ q e t q, e t white noise Multiple regression with lagged errors as predictors Autoregressive Moving Average (ARMA) models y t = c + φ 1 y t φ p y t p + θ 1 e t θ q e t q + e t Multiple regression with lagged observations and lagged errors as predictors ARIMA(p, d, q) models Combine ARMA model with d - lots of differencing
13 US net electricity generation > autoplot(usnetelec) + xlab("year") + ylab("billion kwh") + ggtitle("us net electricity generation")
14 US net electricity generation > fit <- auto.arima(usnetelec) > summary(fit) Series: usnetelec ARIMA(2,1,2) with drift Coefficients: ar1 ar2 ma1 ma2 drift s.e sigma^2 estimated as 2262: log likelihood= AIC=578.7 AICc=580.5 BIC=590.6 Training set error measures: ME RMSE MAE MPE MAPE MASE ACF1 Training set
15 US net electricity generation > fit %>% forecast() %>% autoplot()
16 How does auto.arima() work? Hyndman-Khandakar algorithm: Select number of differences d via unit root tests Select p and q by minimizing AICc Estimate parameters using maximum likelihood estimation Use stepwise search to traverse model space, to save time
17 FORECASTING USING R Let s practice!
18 FORECASTING USING R Seasonal ARIMA models
19 ARIMA models ARIMA (p, d, q) (P, D, Q)m Non-seasonal part of the model Seasonal part of the model d = Number of lag-1 differences p = Number of ordinary AR lags: q = Number of ordinary MA lags: y t 1, y t 2,...,y t p ε t 1, ε t 2,...,ε t q D = Number of seasonal differences P = Number of seasonal AR lags: Q = Number of seasonal MA lags: y t m, y t 2m,...,y t Pm ε t m, ε t 2m..., ε t Qm m = Number of observations per year
20 Example: Monthly retail debit card usage in Iceland > autoplot(debitcards) + xlab("year") + ylab("million ISK") + ggtitle("retail debit card usage in Iceland")
21 Example: Monthly retail debit card usage in Iceland > fit <- auto.arima(debitcards, lambda = 0) > fit Series: debitcards ARIMA(0,1,4)(0,1,1)[12] Box Cox transformation: lambda= 0 Coefficients: ma1 ma2 ma3 ma4 sma s.e sigma^2 estimated as : log likelihood=239.3 AIC= AICc= BIC=-448.6
22 Example: Monthly retail debit card usage in Iceland > fit %>% forecast(h = 36) %>% autoplot() + xlab("year")
23 FORECASTING USING R Let s practice!
Forecasting using R. Rob J Hyndman. 2.4 Non-seasonal ARIMA models. Forecasting using R 1
Forecasting using R Rob J Hyndman 2.4 Non-seasonal ARIMA models Forecasting using R 1 Outline 1 Autoregressive models 2 Moving average models 3 Non-seasonal ARIMA models 4 Partial autocorrelations 5 Estimation
More informationFORECASTING USING R. Dynamic regression. Rob Hyndman Author, forecast
FORECASTING USING R Dynamic regression Rob Hyndman Author, forecast Dynamic regression Regression model with ARIMA errors y t = β 0 + β 1 x 1,t + + β r x r,t + e t y t modeled as function of r explanatory
More informationForecasting using R. Rob J Hyndman. 2.5 Seasonal ARIMA models. Forecasting using R 1
Forecasting using R Rob J Hyndman 2.5 Seasonal ARIMA models Forecasting using R 1 Outline 1 Backshift notation reviewed 2 Seasonal ARIMA models 3 ARIMA vs ETS 4 Lab session 12 Forecasting using R Backshift
More informationSTAT 436 / Lecture 16: Key
STAT 436 / 536 - Lecture 16: Key Modeling Non-Stationary Time Series Many time series models are non-stationary. Recall a time series is stationary if the mean and variance are constant in time and the
More informationForecasting with ARIMA models This version: 14 January 2018
Forecasting with ARIMA models This version: 14 January 2018 Notes for Intermediate Econometrics / Time Series Analysis and Forecasting Anthony Tay Elsewhere we showed that the optimal forecast for a mean
More informationTime Series in R: Forecasting and Visualisation. Forecast evaluation 29 May 2017
Time Series in R: Forecasting and Visualisation Forecast evaluation 29 May 2017 1 Outline 1 Forecasting residuals 2 Evaluating forecast accuracy 3 Forecasting benchmark methods 4 Lab session 7 5 Time series
More informationForecasting using R. Rob J Hyndman. 3.2 Dynamic regression. Forecasting using R 1
Forecasting using R Rob J Hyndman 3.2 Dynamic regression Forecasting using R 1 Outline 1 Regression with ARIMA errors 2 Stochastic and deterministic trends 3 Periodic seasonality 4 Lab session 14 5 Dynamic
More informationForecasting: principles and practice. Rob J Hyndman 3.2 Forecasting with multiple seasonality
Forecasting: principles and practice Rob J Hyndman 3.2 Forecasting with multiple seasonality 1 Outline 1 Time series with complex seasonality 2 STL with multiple seasonal periods 3 Dynamic harmonic regression
More informationHomework 5, Problem 1 Andrii Baryshpolets 6 April 2017
Homework 5, Problem 1 Andrii Baryshpolets 6 April 2017 Total Private Residential Construction Spending library(quandl) Warning: package 'Quandl' was built under R version 3.3.3 Loading required package:
More informationTime-Series analysis for wind speed forecasting
Malaya Journal of Matematik, Vol. S, No. 1, 55-61, 2018 https://doi.org/10.26637/mjm0s01/11 Time-Series analysis for wind speed forecasting Garima Jain1 Abstract In this paper, an enormous amount of study
More information477/577 In-class Exercise 5 : Fitting Wine Sales
477/577 In-class Exercise 5 : Fitting Wine Sales (due Fri 4/06/2017) Name: Use this file as a template for your report. Submit your code and comments together with (selected) output from R console. Your
More informationTIME SERIES ANALYSIS AND FORECASTING USING THE STATISTICAL MODEL ARIMA
CHAPTER 6 TIME SERIES ANALYSIS AND FORECASTING USING THE STATISTICAL MODEL ARIMA 6.1. Introduction A time series is a sequence of observations ordered in time. A basic assumption in the time series analysis
More informationChapter 5: Models for Nonstationary Time Series
Chapter 5: Models for Nonstationary Time Series Recall that any time series that is a stationary process has a constant mean function. So a process that has a mean function that varies over time must be
More informationFirstly, the dataset is cleaned and the years and months are separated to provide better distinction (sample below).
Project: Forecasting Sales Step 1: Plan Your Analysis Answer the following questions to help you plan out your analysis: 1. Does the dataset meet the criteria of a time series dataset? Make sure to explore
More informationForecasting Gold Price. A Comparative Study
Course of Financial Econometrics FIRM Forecasting Gold Price A Comparative Study Alessio Azzutti, University of Florence Abstract: This paper seeks to evaluate the appropriateness of a variety of existing
More informationTime Series Forecasting Methods:
Corso di TRASPORTI E TERRITORIO Time Series Forecasting Methods: EXPONENTIAL SMOOTHING DOCENTI Agostino Nuzzolo (nuzzolo@ing.uniroma2.it) Antonio Comi (comi@ing.uniroma2.it) 1 Classificazione dei metodi
More informationForecasting: principles and practice 1
Forecasting: principles and practice Rob J Hyndman 2.3 Stationarity and differencing Forecasting: principles and practice 1 Outline 1 Stationarity 2 Differencing 3 Unit root tests 4 Lab session 10 5 Backshift
More informationMinitab Project Report - Assignment 6
.. Sunspot data Minitab Project Report - Assignment Time Series Plot of y Time Series Plot of X y X 7 9 7 9 The data have a wavy pattern. However, they do not show any seasonality. There seem to be an
More informationLOAD FORECASTING APPLICATIONS for THE ENERGY SECTOR
LOAD FORECASTING APPLICATIONS for THE ENERGY SECTOR Boris Bizjak, Univerza v Mariboru, FERI 26.2.2016 1 A) Short-term load forecasting at industrial plant Ravne: Load forecasting using linear regression,
More informationCh 5. Models for Nonstationary Time Series. Time Series Analysis
We have studied some deterministic and some stationary trend models. However, many time series data cannot be modeled in either way. Ex. The data set oil.price displays an increasing variation from the
More informationUnivariate ARIMA Models
Univariate ARIMA Models ARIMA Model Building Steps: Identification: Using graphs, statistics, ACFs and PACFs, transformations, etc. to achieve stationary and tentatively identify patterns and model components.
More informationarxiv: v1 [stat.co] 11 Dec 2012
Simulating the Continuation of a Time Series in R December 12, 2012 arxiv:1212.2393v1 [stat.co] 11 Dec 2012 Halis Sak 1 Department of Industrial and Systems Engineering, Yeditepe University, Kayışdağı,
More informationData %>% Power %>% R You ready?
Data %>% Power %>% R You ready? R a powerful open source programming language available in the database as Oracle R Enterprise that lets you do virtually anything Especially (but not only) Statistics Machine
More informationExponentially weighted forecasts
FORECASTING USING R Exponentially weighted forecasts Rob Hyndman Author, forecast Simple exponential smoothing Forecasting Notation: ŷ t+h t = y t+h y 1,...,y t point forecast of Forecast Equation: given
More informationScenario 5: Internet Usage Solution. θ j
Scenario : Internet Usage Solution Some more information would be interesting about the study in order to know if we can generalize possible findings. For example: Does each data point consist of the total
More informationEmpirical Approach to Modelling and Forecasting Inflation in Ghana
Current Research Journal of Economic Theory 4(3): 83-87, 2012 ISSN: 2042-485X Maxwell Scientific Organization, 2012 Submitted: April 13, 2012 Accepted: May 06, 2012 Published: June 30, 2012 Empirical Approach
More informationAutomatic Forecasting
Automatic Forecasting Summary The Automatic Forecasting procedure is designed to forecast future values of time series data. A time series consists of a set of sequential numeric data taken at equally
More informationThe log transformation produces a time series whose variance can be treated as constant over time.
TAT 520 Homework 6 Fall 2017 Note: Problem 5 is mandatory for graduate students and extra credit for undergraduates. 1) The quarterly earnings per share for 1960-1980 are in the object in the TA package.
More informationLecture 5: Estimation of time series
Lecture 5, page 1 Lecture 5: Estimation of time series Outline of lesson 5 (chapter 4) (Extended version of the book): a.) Model formulation Explorative analyses Model formulation b.) Model estimation
More informationFE570 Financial Markets and Trading. Stevens Institute of Technology
FE570 Financial Markets and Trading Lecture 5. Linear Time Series Analysis and Its Applications (Ref. Joel Hasbrouck - Empirical Market Microstructure ) Steve Yang Stevens Institute of Technology 9/25/2012
More informationDesign of Time Series Model for Road Accident Fatal Death in Tamilnadu
Volume 109 No. 8 2016, 225-232 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Design of Time Series Model for Road Accident Fatal Death in Tamilnadu
More informationSTA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9)
STA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9) Outline 1 Building ARIMA Models 2 SARIMA 3 Homework 4c Arthur Berg STA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9) 2/ 34 Outline 1 Building ARIMA Models
More informationForecasting: Principles and Practice. Rob J Hyndman. 12. Advanced methods OTexts.com/fpp/9/2/ OTexts.com/fpp/9/3/
Rob J Hyndman Forecasting: Principles and Practice 12. Advanced methods OTexts.com/fpp/9/2/ OTexts.com/fpp/9/3/ Forecasting: Principles and Practice 1 Outline 1 Vector autoregressions 2 Neural network
More informationINTRODUCTION TO TIME SERIES ANALYSIS. The Simple Moving Average Model
INTRODUCTION TO TIME SERIES ANALYSIS The Simple Moving Average Model The Simple Moving Average Model The simple moving average (MA) model: More formally: where t is mean zero white noise (WN). Three parameters:
More informationSTA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9) Outline. Return Rate. US Gross National Product
STA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9) Outline 1 Building ARIMA Models 2 SARIMA 3 Homework 4c Arthur Berg STA 6857 ARIMA and SARIMA Models ( 3.8 and 3.9) 2/ 34 Return Rate Suppose x t is the value
More informationSuan Sunandha Rajabhat University
Forecasting Exchange Rate between Thai Baht and the US Dollar Using Time Series Analysis Kunya Bowornchockchai Suan Sunandha Rajabhat University INTRODUCTION The objective of this research is to forecast
More informationModeling and forecasting global mean temperature time series
Modeling and forecasting global mean temperature time series April 22, 2018 Abstract: An ARIMA time series model was developed to analyze the yearly records of the change in global annual mean surface
More informationPart 1. Multiple Choice (50 questions, 1 point each) Part 2. Problems/Short Answer (10 questions, 5 points each)
GROUND RULES: This exam contains two parts: Part 1. Multiple Choice (50 questions, 1 point each) Part 2. Problems/Short Answer (10 questions, 5 points each) The maximum number of points on this exam is
More informationA Comparison of the Forecast Performance of. Double Seasonal ARIMA and Double Seasonal. ARFIMA Models of Electricity Load Demand
Applied Mathematical Sciences, Vol. 6, 0, no. 35, 6705-67 A Comparison of the Forecast Performance of Double Seasonal ARIMA and Double Seasonal ARFIMA Models of Electricity Load Demand Siti Normah Hassan
More informationTime Series I Time Domain Methods
Astrostatistics Summer School Penn State University University Park, PA 16802 May 21, 2007 Overview Filtering and the Likelihood Function Time series is the study of data consisting of a sequence of DEPENDENT
More informationCase Study: Modelling Industrial Dryer Temperature Arun K. Tangirala 11/19/2016
Case Study: Modelling Industrial Dryer Temperature Arun K. Tangirala 11/19/2016 Background This is a case study concerning time-series modelling of the temperature of an industrial dryer. Data set contains
More informationAR(p) + I(d) + MA(q) = ARIMA(p, d, q)
AR(p) + I(d) + MA(q) = ARIMA(p, d, q) Outline 1 4.1: Nonstationarity in the Mean 2 ARIMA Arthur Berg AR(p) + I(d)+ MA(q) = ARIMA(p, d, q) 2/ 19 Deterministic Trend Models Polynomial Trend Consider the
More informationSolar irradiance forecasting for Chulalongkorn University location using time series models
Senior Project Proposal 2102490 Year 2016 Solar irradiance forecasting for Chulalongkorn University location using time series models Vichaya Layanun ID 5630550721 Advisor: Assist. Prof. Jitkomut Songsiri
More informationFORECASTING SUGARCANE PRODUCTION IN INDIA WITH ARIMA MODEL
FORECASTING SUGARCANE PRODUCTION IN INDIA WITH ARIMA MODEL B. N. MANDAL Abstract: Yearly sugarcane production data for the period of - to - of India were analyzed by time-series methods. Autocorrelation
More informationA Procedure for Identification of Appropriate State Space and ARIMA Models Based on Time-Series Cross-Validation
algorithms Article A Procedure for Identification of Appropriate State Space and ARIMA Models Based on Time-Series Cross-Validation Patrícia Ramos 1,2, * and José Manuel Oliveira 1,3 1 INESC Technology
More informationChapter 9: Forecasting
Chapter 9: Forecasting One of the critical goals of time series analysis is to forecast (predict) the values of the time series at times in the future. When forecasting, we ideally should evaluate the
More informationJournal of Statistical Software
JSS Journal of Statistical Software July 2008, Volume 27, Issue 3. doi: 10.18637/jss.v000.i00 Automatic Time Series Forecasting: the forecast Package for R Rob J Hyndman Monash University Yeasmin Khandakar
More informationMODELING INFLATION RATES IN NIGERIA: BOX-JENKINS APPROACH. I. U. Moffat and A. E. David Department of Mathematics & Statistics, University of Uyo, Uyo
Vol.4, No.2, pp.2-27, April 216 MODELING INFLATION RATES IN NIGERIA: BOX-JENKINS APPROACH I. U. Moffat and A. E. David Department of Mathematics & Statistics, University of Uyo, Uyo ABSTRACT: This study
More informationHomework 4. 1 Data analysis problems
Homework 4 1 Data analysis problems This week we will be analyzing a number of data sets. We are going to build ARIMA models using the steps outlined in class. It is also a good idea to read section 3.8
More informationForecasting using R. Rob J Hyndman. 2.3 Stationarity and differencing. Forecasting using R 1
Forecasting using R Rob J Hyndman 2.3 Stationarity and differencing Forecasting using R 1 Outline 1 Stationarity 2 Differencing 3 Unit root tests 4 Lab session 10 5 Backshift notation Forecasting using
More informationUnivariate Time Series Analysis; ARIMA Models
Econometrics 2 Fall 24 Univariate Time Series Analysis; ARIMA Models Heino Bohn Nielsen of4 Outline of the Lecture () Introduction to univariate time series analysis. (2) Stationarity. (3) Characterizing
More informationAvailable online at ScienceDirect. Procedia Computer Science 72 (2015 )
Available online at www.sciencedirect.com ScienceDirect Procedia Computer Science 72 (2015 ) 630 637 The Third Information Systems International Conference Performance Comparisons Between Arima and Arimax
More informationSpectral Analysis. Al Nosedal University of Toronto. Winter Al Nosedal University of Toronto Spectral Analysis Winter / 71
Spectral Analysis Al Nosedal University of Toronto Winter 2016 Al Nosedal University of Toronto Spectral Analysis Winter 2016 1 / 71 essentially, all models are wrong, but some are useful George E. P.
More informationStat 565. (S)Arima & Forecasting. Charlotte Wickham. stat565.cwick.co.nz. Feb
Stat 565 (S)Arima & Forecasting Feb 2 2016 Charlotte Wickham stat565.cwick.co.nz Today A note from HW #3 Pick up with ARIMA processes Introduction to forecasting HW #3 The sample autocorrelation coefficients
More informationSTAT Financial Time Series
STAT 6104 - Financial Time Series Chapter 4 - Estimation in the time Domain Chun Yip Yau (CUHK) STAT 6104:Financial Time Series 1 / 46 Agenda 1 Introduction 2 Moment Estimates 3 Autoregressive Models (AR
More information03 Time series with trend and seasonality components. Andrius Buteikis,
03 Time series with trend and seasonality components Andrius Buteikis, andrius.buteikis@mif.vu.lt http://web.vu.lt/mif/a.buteikis/ Time series with deterministic components Up until now we assumed our
More informationPart 1. Multiple Choice (40 questions, 1 point each) Part 2. Problems/Short Answer (10 questions, 6 points each)
GROUND RULES: This exam contains two parts: Part 1. Multiple Choice (40 questions, 1 point each) Part 2. Problems/Short Answer (10 questions, 6 points each) The maximum number of points on this exam is
More informationAutoregressive Integrated Moving Average Model to Predict Graduate Unemployment in Indonesia
DOI 10.1515/ptse-2017-0005 PTSE 12 (1): 43-50 Autoregressive Integrated Moving Average Model to Predict Graduate Unemployment in Indonesia Umi MAHMUDAH u_mudah@yahoo.com (State Islamic University of Pekalongan,
More informationBasics: Definitions and Notation. Stationarity. A More Formal Definition
Basics: Definitions and Notation A Univariate is a sequence of measurements of the same variable collected over (usually regular intervals of) time. Usual assumption in many time series techniques is that
More informationFORECASTING YIELD PER HECTARE OF RICE IN ANDHRA PRADESH
International Journal of Mathematics and Computer Applications Research (IJMCAR) ISSN 49-6955 Vol. 3, Issue 1, Mar 013, 9-14 TJPRC Pvt. Ltd. FORECASTING YIELD PER HECTARE OF RICE IN ANDHRA PRADESH R. RAMAKRISHNA
More informationAdvanced Econometrics
Advanced Econometrics Marco Sunder Nov 04 2010 Marco Sunder Advanced Econometrics 1/ 25 Contents 1 2 3 Marco Sunder Advanced Econometrics 2/ 25 Music Marco Sunder Advanced Econometrics 3/ 25 Music Marco
More informationAnalysis. Components of a Time Series
Module 8: Time Series Analysis 8.2 Components of a Time Series, Detection of Change Points and Trends, Time Series Models Components of a Time Series There can be several things happening simultaneously
More informationDynamic Time Series Regression: A Panacea for Spurious Correlations
International Journal of Scientific and Research Publications, Volume 6, Issue 10, October 2016 337 Dynamic Time Series Regression: A Panacea for Spurious Correlations Emmanuel Alphonsus Akpan *, Imoh
More information4. MA(2) +drift: y t = µ + ɛ t + θ 1 ɛ t 1 + θ 2 ɛ t 2. Mean: where θ(l) = 1 + θ 1 L + θ 2 L 2. Therefore,
61 4. MA(2) +drift: y t = µ + ɛ t + θ 1 ɛ t 1 + θ 2 ɛ t 2 Mean: y t = µ + θ(l)ɛ t, where θ(l) = 1 + θ 1 L + θ 2 L 2. Therefore, E(y t ) = µ + θ(l)e(ɛ t ) = µ 62 Example: MA(q) Model: y t = ɛ t + θ 1 ɛ
More informationTime Series Outlier Detection
Time Series Outlier Detection Tingyi Zhu July 28, 2016 Tingyi Zhu Time Series Outlier Detection July 28, 2016 1 / 42 Outline Time Series Basics Outliers Detection in Single Time Series Outlier Series Detection
More informationForecasting Area, Production and Yield of Cotton in India using ARIMA Model
Forecasting Area, Production and Yield of Cotton in India using ARIMA Model M. K. Debnath 1, Kartic Bera 2 *, P. Mishra 1 1 Department of Agricultural Statistics, Bidhan Chanda Krishi Vishwavidyalaya,
More informationEstimation and application of best ARIMA model for forecasting the uranium price.
Estimation and application of best ARIMA model for forecasting the uranium price. Medeu Amangeldi May 13, 2018 Capstone Project Superviser: Dongming Wei Second reader: Zhenisbek Assylbekov Abstract This
More informationEconometría 2: Análisis de series de Tiempo
Econometría 2: Análisis de series de Tiempo Karoll GOMEZ kgomezp@unal.edu.co http://karollgomez.wordpress.com Segundo semestre 2016 III. Stationary models 1 Purely random process 2 Random walk (non-stationary)
More informationTime Series Modeling. Shouvik Mani April 5, /688: Practical Data Science Carnegie Mellon University
Time Series Modeling Shouvik Mani April 5, 2018 15-388/688: Practical Data Science Carnegie Mellon University Goals After this lecture, you will be able to: Explain key properties of time series data Describe,
More informationA Data-Driven Model for Software Reliability Prediction
A Data-Driven Model for Software Reliability Prediction Author: Jung-Hua Lo IEEE International Conference on Granular Computing (2012) Young Taek Kim KAIST SE Lab. 9/4/2013 Contents Introduction Background
More informationA time series is called strictly stationary if the joint distribution of every collection (Y t
5 Time series A time series is a set of observations recorded over time. You can think for example at the GDP of a country over the years (or quarters) or the hourly measurements of temperature over a
More informationCh 9. FORECASTING. Time Series Analysis
In this chapter, we assume the model is known exactly, and consider the calculation of forecasts and their properties for both deterministic trend models and ARIMA models. 9.1 Minimum Mean Square Error
More informationCh 6. Model Specification. Time Series Analysis
We start to build ARIMA(p,d,q) models. The subjects include: 1 how to determine p, d, q for a given series (Chapter 6); 2 how to estimate the parameters (φ s and θ s) of a specific ARIMA(p,d,q) model (Chapter
More informationLab: Box-Jenkins Methodology - US Wholesale Price Indicator
Lab: Box-Jenkins Methodology - US Wholesale Price Indicator In this lab we explore the Box-Jenkins methodology by applying it to a time-series data set comprising quarterly observations of the US Wholesale
More informationAutomatic seasonal auto regressive moving average models and unit root test detection
ISSN 1750-9653, England, UK International Journal of Management Science and Engineering Management Vol. 3 (2008) No. 4, pp. 266-274 Automatic seasonal auto regressive moving average models and unit root
More informationForecasting U.S.A Imports from China, Singapore, Indonesia, and Thailand.
Forecasting U.S.A Imports from China, Singapore, Indonesia, and Thailand. An Empirical Project Chittawan Chanagul UK 40186 (Econometric Forecasting): Prof. Robert M. Kunst Introduction Times Series Data
More informationLecture 19 Box-Jenkins Seasonal Models
Lecture 19 Box-Jenkins Seasonal Models If the time series is nonstationary with respect to its variance, then we can stabilize the variance of the time series by using a pre-differencing transformation.
More informationOutlier detection in ARIMA and seasonal ARIMA models by. Bayesian Information Type Criteria
Outlier detection in ARIMA and seasonal ARIMA models by Bayesian Information Type Criteria Pedro Galeano and Daniel Peña Departamento de Estadística Universidad Carlos III de Madrid 1 Introduction The
More informationPrashant Pant 1, Achal Garg 2 1,2 Engineer, Keppel Offshore and Marine Engineering India Pvt. Ltd, Mumbai. IJRASET 2013: All Rights are Reserved 356
Forecasting Of Short Term Wind Power Using ARIMA Method Prashant Pant 1, Achal Garg 2 1,2 Engineer, Keppel Offshore and Marine Engineering India Pvt. Ltd, Mumbai Abstract- Wind power, i.e., electrical
More informationUniversity of Oxford. Statistical Methods Autocorrelation. Identification and Estimation
University of Oxford Statistical Methods Autocorrelation Identification and Estimation Dr. Órlaith Burke Michaelmas Term, 2011 Department of Statistics, 1 South Parks Road, Oxford OX1 3TG Contents 1 Model
More informationUsing Analysis of Time Series to Forecast numbers of The Patients with Malignant Tumors in Anbar Provinc
Using Analysis of Time Series to Forecast numbers of The Patients with Malignant Tumors in Anbar Provinc /. ) ( ) / (Box & Jenkins).(.(2010-2006) ARIMA(2,1,0). Abstract: The aim of this research is to
More informationClassic Time Series Analysis
Classic Time Series Analysis Concepts and Definitions Let Y be a random number with PDF f Y t ~f,t Define t =E[Y t ] m(t) is known as the trend Define the autocovariance t, s =COV [Y t,y s ] =E[ Y t t
More informationMCMC analysis of classical time series algorithms.
MCMC analysis of classical time series algorithms. mbalawata@yahoo.com Lappeenranta University of Technology Lappeenranta, 19.03.2009 Outline Introduction 1 Introduction 2 3 Series generation Box-Jenkins
More informationTime Series and Forecasting Using R
Time Series and Forecasting Using R Lab Sessions 25 May 2016 Before doing any exercises in R, load the fpp package using library(fpp) and the ggplot2 package using library(ggplot2). Lab Session: Time series
More informationChapter 3, Part V: More on Model Identification; Examples
Chapter 3, Part V: More on Model Identification; Examples Automatic Model Identification Through AIC As mentioned earlier, there is a clear need for automatic, objective methods of identifying the best
More informationSeasonal Autoregressive Integrated Moving Average Model for Precipitation Time Series
Journal of Mathematics and Statistics 8 (4): 500-505, 2012 ISSN 1549-3644 2012 doi:10.3844/jmssp.2012.500.505 Published Online 8 (4) 2012 (http://www.thescipub.com/jmss.toc) Seasonal Autoregressive Integrated
More informationLesson 13: Box-Jenkins Modeling Strategy for building ARMA models
Lesson 13: Box-Jenkins Modeling Strategy for building ARMA models Facoltà di Economia Università dell Aquila umberto.triacca@gmail.com Introduction In this lesson we present a method to construct an ARMA(p,
More informationTime Series Analysis -- An Introduction -- AMS 586
Time Series Analysis -- An Introduction -- AMS 586 1 Objectives of time series analysis Data description Data interpretation Modeling Control Prediction & Forecasting 2 Time-Series Data Numerical data
More informationREVIEW OF SHORT-TERM TRAFFIC FLOW PREDICTION TECHNIQUES
INTRODUCTION In recent years the traditional objective of improving road network efficiency is being supplemented by greater emphasis on safety, incident detection management, driver information, better
More informationFORECASTING THE INVENTORY LEVEL OF MAGNETIC CARDS IN TOLLING SYSTEM
FORECASTING THE INVENTORY LEVEL OF MAGNETIC CARDS IN TOLLING SYSTEM Bratislav Lazić a, Nebojša Bojović b, Gordana Radivojević b*, Gorana Šormaz a a University of Belgrade, Mihajlo Pupin Institute, Serbia
More informationStat 153 Time Series. Problem Set 4
Stat Time Series Problem Set Problem I generated 000 observations from the MA() model with parameter 0.7 using the following R function and then fitted the ARMA(, ) model to the data. order = c(, 0, )),
More informationCircle a single answer for each multiple choice question. Your choice should be made clearly.
TEST #1 STA 4853 March 4, 215 Name: Please read the following directions. DO NOT TURN THE PAGE UNTIL INSTRUCTED TO DO SO Directions This exam is closed book and closed notes. There are 31 questions. Circle
More informationThe intelligent forecasting model of time series
Automation, Control and Intelligent Systems 2013; 1(4): 90-98 Published online August 10, 2013 (http://www.sciencepublishinggroup.com/j/acis) doi: 10.11648/j.acis.20130104.12 The intelligent forecasting
More informationLecture 6: Forecasting of time series
Lecture 6, page 1 Lecture 6: Forecasting of time series Outline of lesson 6 (chapter 5) Forecasting Very complicated and untidy in the book A lot of theory developed (in which we will not dwell). Only
More informationExamination paper for TMA4285 Time Series Models
Department of Mathematical Sciences Examination paper for TMA4285 Series Models Academic contact during examination: Professor Jarle Tufto Phone: 99 70 55 19 Examination date: December 8, 2016 Examination
More informationFunctional time series
Rob J Hyndman Functional time series with applications in demography 4. Connections, extensions and applications Outline 1 Yield curves 2 Electricity prices 3 Dynamic updating with partially observed functions
More information2. An Introduction to Moving Average Models and ARMA Models
. An Introduction to Moving Average Models and ARMA Models.1 White Noise. The MA(1) model.3 The MA(q) model..4 Estimation and forecasting of MA models..5 ARMA(p,q) models. The Moving Average (MA) models
More informationFORECASTING OF COTTON PRODUCTION IN INDIA USING ARIMA MODEL
FORECASTING OF COTTON PRODUCTION IN INDIA USING ARIMA MODEL S.Poyyamozhi 1, Dr. A. Kachi Mohideen 2. 1 Assistant Professor and Head, Department of Statistics, Government Arts College (Autonomous), Kumbakonam
More informationPackage TSPred. April 5, 2017
Type Package Package TSPred April 5, 2017 Title Functions for Benchmarking Time Series Prediction Version 3.0.2 Date 2017-04-05 Author Rebecca Pontes Salles [aut, cre, cph] (CEFET/RJ), Eduardo Ogasawara
More informationSeasonal Models and Seasonal Adjustment
LECTURE 10 Seasonal Models and Seasonal Adjustment So far, we have relied upon the method of trigonometrical regression for building models which can be used for forecasting seasonal economic time series.
More information