SlideShare a Scribd company logo

ARIMA

Stationarity AR process MA process Main steps in ARIMA Forecasting using ARIMA model Goodness of fit

1 of 65
Download to read offline
Data Analysis Course
Time Series Analysis & Forecasting
Venkat Reddy
Contents
• ARIMA
• Stationarity
• AR process
• MA process
• Main steps in ARIMA
• Forecasting using ARIMA model
• Goodness of fit
DataAnalysisCourse
VenkatReddy
2
Drawbacks of the use of traditional
models
• There is no systematic approach for the identification and
selection of an appropriate model, and therefore, the
identification process is mainly trial-and-error
• There is difficulty in verifying the validity of the model
• Most traditional methods were developed from intuitive and
practical considerations rather than from a statistical foundation
DataAnalysisCourse
VenkatReddy
3
ARIMA Models
• Autoregressive Integrated Moving-average
• A “stochastic” modeling approach that can be used to
calculate the probability of a future value lying between two
specified limits
DataAnalysisCourse
VenkatReddy
4
AR & MA Models
• Autoregressive AR process:
• Series current values depend on its own previous values
• AR(p) - Current values depend on its own p-previous values
• P is the order of AR process
• Moving average MA process:
• The current deviation from mean depends on previous deviations
• MA(q) - The current deviation from mean depends on q- previous
deviations
• q is the order of MA process
• Autoregressive Moving average ARMA process
DataAnalysisCourse
VenkatReddy
5
AR Process
DataAnalysisCourse
VenkatReddy
6AR(1) yt = a1* yt-1
AR(2) yt = a1* yt-1 +a2* yt-2
AR(3) yt = a1* yt-1 + a2* yt-2 +a3* yt-2
Ad

Recommended

Arima model
Arima modelArima model
Arima modelJassika
 
Lesson 5 arima
Lesson 5 arimaLesson 5 arima
Lesson 5 arimaankit_ppt
 
Arima model (time series)
Arima model (time series)Arima model (time series)
Arima model (time series)Kumar P
 
Mba 532 2011_part_3_time_series_analysis
Mba 532 2011_part_3_time_series_analysisMba 532 2011_part_3_time_series_analysis
Mba 532 2011_part_3_time_series_analysisChandra Kodituwakku
 
Time Series - Auto Regressive Models
Time Series - Auto Regressive ModelsTime Series - Auto Regressive Models
Time Series - Auto Regressive ModelsBhaskar T
 

More Related Content

What's hot

Time Series
Time SeriesTime Series
Time Seriesyush313
 
Lesson 2 stationary_time_series
Lesson 2 stationary_time_seriesLesson 2 stationary_time_series
Lesson 2 stationary_time_seriesankit_ppt
 
Lesson 4 ar-ma
Lesson 4 ar-maLesson 4 ar-ma
Lesson 4 ar-maankit_ppt
 
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet MahanaArima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet MahanaAmrinder Arora
 
Time Series Analysis - Modeling and Forecasting
Time Series Analysis - Modeling and ForecastingTime Series Analysis - Modeling and Forecasting
Time Series Analysis - Modeling and ForecastingMaruthi Nataraj K
 
Multivariate time series
Multivariate time seriesMultivariate time series
Multivariate time seriesLuigi Piva CQF
 
Time series forecasting with machine learning
Time series forecasting with machine learningTime series forecasting with machine learning
Time series forecasting with machine learningDr Wei Liu
 
Time series forecasting with ARIMA
Time series forecasting with ARIMATime series forecasting with ARIMA
Time series forecasting with ARIMAYury Kashnitsky
 
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...Simplilearn
 
7 classical assumptions of ordinary least squares
7 classical assumptions of ordinary least squares7 classical assumptions of ordinary least squares
7 classical assumptions of ordinary least squaresYugesh Dutt Panday
 
Time Series, Moving Average
Time Series, Moving AverageTime Series, Moving Average
Time Series, Moving AverageSOMASUNDARAM T
 

What's hot (20)

Time Series
Time SeriesTime Series
Time Series
 
AR model
AR modelAR model
AR model
 
Lesson 2 stationary_time_series
Lesson 2 stationary_time_seriesLesson 2 stationary_time_series
Lesson 2 stationary_time_series
 
Lesson 4 ar-ma
Lesson 4 ar-maLesson 4 ar-ma
Lesson 4 ar-ma
 
Time Series Decomposition
Time Series DecompositionTime Series Decomposition
Time Series Decomposition
 
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet MahanaArima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana
Arima Forecasting - Presentation by Sera Cresta, Nora Alosaimi and Puneet Mahana
 
Time Series Analysis - Modeling and Forecasting
Time Series Analysis - Modeling and ForecastingTime Series Analysis - Modeling and Forecasting
Time Series Analysis - Modeling and Forecasting
 
ARIMA Models - [Lab 3]
ARIMA Models - [Lab 3]ARIMA Models - [Lab 3]
ARIMA Models - [Lab 3]
 
Time series Analysis
Time series AnalysisTime series Analysis
Time series Analysis
 
Time series
Time seriesTime series
Time series
 
time series analysis
time series analysistime series analysis
time series analysis
 
Multivariate time series
Multivariate time seriesMultivariate time series
Multivariate time series
 
Time series forecasting with machine learning
Time series forecasting with machine learningTime series forecasting with machine learning
Time series forecasting with machine learning
 
Time series forecasting with ARIMA
Time series forecasting with ARIMATime series forecasting with ARIMA
Time series forecasting with ARIMA
 
Logistic regression
Logistic regressionLogistic regression
Logistic regression
 
Time series analysis
Time series analysisTime series analysis
Time series analysis
 
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
Time Series Analysis - 2 | Time Series in R | ARIMA Model Forecasting | Data ...
 
Time series Analysis
Time series AnalysisTime series Analysis
Time series Analysis
 
7 classical assumptions of ordinary least squares
7 classical assumptions of ordinary least squares7 classical assumptions of ordinary least squares
7 classical assumptions of ordinary least squares
 
Time Series, Moving Average
Time Series, Moving AverageTime Series, Moving Average
Time Series, Moving Average
 

Similar to ARIMA

6-130914140240-phpapp01.pdf
6-130914140240-phpapp01.pdf6-130914140240-phpapp01.pdf
6-130914140240-phpapp01.pdfssuserdca880
 
ARIMA Model for analysis of time series data.ppt
ARIMA Model for analysis of time series data.pptARIMA Model for analysis of time series data.ppt
ARIMA Model for analysis of time series data.pptREFOTDEBuea
 
Heuristic design of experiments w meta gradient search
Heuristic design of experiments w meta gradient searchHeuristic design of experiments w meta gradient search
Heuristic design of experiments w meta gradient searchGreg Makowski
 
Andres hernandez ai_machine_learning_london_nov2017
Andres hernandez ai_machine_learning_london_nov2017Andres hernandez ai_machine_learning_london_nov2017
Andres hernandez ai_machine_learning_london_nov2017Andres Hernandez
 
Different Models Used In Time Series - InsideAIML
Different Models Used In Time Series - InsideAIMLDifferent Models Used In Time Series - InsideAIML
Different Models Used In Time Series - InsideAIMLVijaySharma802
 
2014-mo444-practical-assignment-04-paulo_faria
2014-mo444-practical-assignment-04-paulo_faria2014-mo444-practical-assignment-04-paulo_faria
2014-mo444-practical-assignment-04-paulo_fariaPaulo Faria
 
forecasting model
forecasting modelforecasting model
forecasting modelFEG
 
Brock Butlett Time Series-Great Lakes
Brock Butlett Time Series-Great Lakes Brock Butlett Time Series-Great Lakes
Brock Butlett Time Series-Great Lakes Brock Butlett
 
House Sale Price Prediction
House Sale Price PredictionHouse Sale Price Prediction
House Sale Price Predictionsriram30691
 
Machine Learning.pdf
Machine Learning.pdfMachine Learning.pdf
Machine Learning.pdfBeyaNasr1
 
Svd filtered temporal usage clustering
Svd filtered temporal usage clusteringSvd filtered temporal usage clustering
Svd filtered temporal usage clusteringLiang Xie, PhD
 
General Tips for participating Kaggle Competitions
General Tips for participating Kaggle CompetitionsGeneral Tips for participating Kaggle Competitions
General Tips for participating Kaggle CompetitionsMark Peng
 
Sparsenet
SparsenetSparsenet
Sparsenetndronen
 
Machine learning and linear regression programming
Machine learning and linear regression programmingMachine learning and linear regression programming
Machine learning and linear regression programmingSoumya Mukherjee
 

Similar to ARIMA (20)

6-130914140240-phpapp01.pdf
6-130914140240-phpapp01.pdf6-130914140240-phpapp01.pdf
6-130914140240-phpapp01.pdf
 
ARIMA Model.ppt
ARIMA Model.pptARIMA Model.ppt
ARIMA Model.ppt
 
ARIMA Model for analysis of time series data.ppt
ARIMA Model for analysis of time series data.pptARIMA Model for analysis of time series data.ppt
ARIMA Model for analysis of time series data.ppt
 
ARIMA Model.ppt
ARIMA Model.pptARIMA Model.ppt
ARIMA Model.ppt
 
ARIMA.pptx
ARIMA.pptxARIMA.pptx
ARIMA.pptx
 
Heuristic design of experiments w meta gradient search
Heuristic design of experiments w meta gradient searchHeuristic design of experiments w meta gradient search
Heuristic design of experiments w meta gradient search
 
Andres hernandez ai_machine_learning_london_nov2017
Andres hernandez ai_machine_learning_london_nov2017Andres hernandez ai_machine_learning_london_nov2017
Andres hernandez ai_machine_learning_london_nov2017
 
Different Models Used In Time Series - InsideAIML
Different Models Used In Time Series - InsideAIMLDifferent Models Used In Time Series - InsideAIML
Different Models Used In Time Series - InsideAIML
 
2014-mo444-practical-assignment-04-paulo_faria
2014-mo444-practical-assignment-04-paulo_faria2014-mo444-practical-assignment-04-paulo_faria
2014-mo444-practical-assignment-04-paulo_faria
 
forecasting model
forecasting modelforecasting model
forecasting model
 
Brock Butlett Time Series-Great Lakes
Brock Butlett Time Series-Great Lakes Brock Butlett Time Series-Great Lakes
Brock Butlett Time Series-Great Lakes
 
House Sale Price Prediction
House Sale Price PredictionHouse Sale Price Prediction
House Sale Price Prediction
 
Machine Learning.pdf
Machine Learning.pdfMachine Learning.pdf
Machine Learning.pdf
 
Svd filtered temporal usage clustering
Svd filtered temporal usage clusteringSvd filtered temporal usage clustering
Svd filtered temporal usage clustering
 
General Tips for participating Kaggle Competitions
General Tips for participating Kaggle CompetitionsGeneral Tips for participating Kaggle Competitions
General Tips for participating Kaggle Competitions
 
Sparsenet
SparsenetSparsenet
Sparsenet
 
Machine learning and linear regression programming
Machine learning and linear regression programmingMachine learning and linear regression programming
Machine learning and linear regression programming
 
11 whiteboxtesting
11 whiteboxtesting11 whiteboxtesting
11 whiteboxtesting
 
Six sigma pedagogy
Six sigma pedagogySix sigma pedagogy
Six sigma pedagogy
 
Six sigma
Six sigma Six sigma
Six sigma
 

More from Venkata Reddy Konasani

Machine Learning Deep Learning AI and Data Science
Machine Learning Deep Learning AI and Data Science Machine Learning Deep Learning AI and Data Science
Machine Learning Deep Learning AI and Data Science Venkata Reddy Konasani
 
Model selection and cross validation techniques
Model selection and cross validation techniquesModel selection and cross validation techniques
Model selection and cross validation techniquesVenkata Reddy Konasani
 
Table of Contents - Practical Business Analytics using SAS
Table of Contents - Practical Business Analytics using SAS Table of Contents - Practical Business Analytics using SAS
Table of Contents - Practical Business Analytics using SAS Venkata Reddy Konasani
 
Learning Tableau - Data, Graphs, Filters, Dashboards and Advanced features
Learning Tableau -  Data, Graphs, Filters, Dashboards and Advanced featuresLearning Tableau -  Data, Graphs, Filters, Dashboards and Advanced features
Learning Tableau - Data, Graphs, Filters, Dashboards and Advanced featuresVenkata Reddy Konasani
 
Data exploration validation and sanitization
Data exploration validation and sanitizationData exploration validation and sanitization
Data exploration validation and sanitizationVenkata Reddy Konasani
 

More from Venkata Reddy Konasani (20)

Transformers 101
Transformers 101 Transformers 101
Transformers 101
 
Machine Learning Deep Learning AI and Data Science
Machine Learning Deep Learning AI and Data Science Machine Learning Deep Learning AI and Data Science
Machine Learning Deep Learning AI and Data Science
 
Model selection and cross validation techniques
Model selection and cross validation techniquesModel selection and cross validation techniques
Model selection and cross validation techniques
 
Neural Network Part-2
Neural Network Part-2Neural Network Part-2
Neural Network Part-2
 
GBM theory code and parameters
GBM theory code and parametersGBM theory code and parameters
GBM theory code and parameters
 
Neural Networks made easy
Neural Networks made easyNeural Networks made easy
Neural Networks made easy
 
Decision tree
Decision treeDecision tree
Decision tree
 
Step By Step Guide to Learn R
Step By Step Guide to Learn RStep By Step Guide to Learn R
Step By Step Guide to Learn R
 
Credit Risk Model Building Steps
Credit Risk Model Building StepsCredit Risk Model Building Steps
Credit Risk Model Building Steps
 
Table of Contents - Practical Business Analytics using SAS
Table of Contents - Practical Business Analytics using SAS Table of Contents - Practical Business Analytics using SAS
Table of Contents - Practical Business Analytics using SAS
 
SAS basics Step by step learning
SAS basics Step by step learningSAS basics Step by step learning
SAS basics Step by step learning
 
Testing of hypothesis case study
Testing of hypothesis case study Testing of hypothesis case study
Testing of hypothesis case study
 
L101 predictive modeling case_study
L101 predictive modeling case_studyL101 predictive modeling case_study
L101 predictive modeling case_study
 
Learning Tableau - Data, Graphs, Filters, Dashboards and Advanced features
Learning Tableau -  Data, Graphs, Filters, Dashboards and Advanced featuresLearning Tableau -  Data, Graphs, Filters, Dashboards and Advanced features
Learning Tableau - Data, Graphs, Filters, Dashboards and Advanced features
 
Machine Learning for Dummies
Machine Learning for DummiesMachine Learning for Dummies
Machine Learning for Dummies
 
Online data sources for analaysis
Online data sources for analaysis Online data sources for analaysis
Online data sources for analaysis
 
A data analyst view of Bigdata
A data analyst view of Bigdata A data analyst view of Bigdata
A data analyst view of Bigdata
 
R- Introduction
R- IntroductionR- Introduction
R- Introduction
 
Cluster Analysis for Dummies
Cluster Analysis for DummiesCluster Analysis for Dummies
Cluster Analysis for Dummies
 
Data exploration validation and sanitization
Data exploration validation and sanitizationData exploration validation and sanitization
Data exploration validation and sanitization
 

Recently uploaded

BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...
BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...
BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...MohonDas
 
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdf
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdfA LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdf
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdfDr.M.Geethavani
 
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...Katherine Villaluna
 
2.22.24 Black Nationalism and the Nation of Islam.pptx
2.22.24 Black Nationalism and the Nation of Islam.pptx2.22.24 Black Nationalism and the Nation of Islam.pptx
2.22.24 Black Nationalism and the Nation of Islam.pptxMaryPotorti1
 
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdfAynouraHamidova
 
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdf
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdfDiploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdf
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdfSUMIT TIWARI
 
New Features in the Odoo 17 Sales Module
New Features in  the Odoo 17 Sales ModuleNew Features in  the Odoo 17 Sales Module
New Features in the Odoo 17 Sales ModuleCeline George
 
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...EduSkills OECD
 
2.20.24 Asian Americans and the Myth of the Model Minority.pptx
2.20.24 Asian Americans and the Myth of the Model Minority.pptx2.20.24 Asian Americans and the Myth of the Model Minority.pptx
2.20.24 Asian Americans and the Myth of the Model Minority.pptxMaryPotorti1
 
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAY
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAYSOCIAL JUSTICE LESSON ON CATCH UP FRIDAY
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAYGloriaRamos83
 
Food Web SlideShare for Ecology Notes Quiz in Canvas
Food Web SlideShare for Ecology Notes Quiz in CanvasFood Web SlideShare for Ecology Notes Quiz in Canvas
Food Web SlideShare for Ecology Notes Quiz in CanvasAlexandraSwartzwelde
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...Nguyen Thanh Tu Collection
 
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdfAynouraHamidova
 
spring_bee_bot_creations_erd primary.pdf
spring_bee_bot_creations_erd primary.pdfspring_bee_bot_creations_erd primary.pdf
spring_bee_bot_creations_erd primary.pdfKonstantina Koutsodimou
 
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...AKSHAYMAGAR17
 
Data Modeling - Entity Relationship Diagrams-1.pdf
Data Modeling - Entity Relationship Diagrams-1.pdfData Modeling - Entity Relationship Diagrams-1.pdf
Data Modeling - Entity Relationship Diagrams-1.pdfChristalin Nelson
 
2.20.24 The March on Washington for Jobs and Freedom.pptx
2.20.24 The March on Washington for Jobs and Freedom.pptx2.20.24 The March on Washington for Jobs and Freedom.pptx
2.20.24 The March on Washington for Jobs and Freedom.pptxMaryPotorti1
 

Recently uploaded (20)

BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...
BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...
BEZA or Bangladesh Economic Zone Authority recruitment exam question solution...
 
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdf
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdfA LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdf
A LABORATORY MANUAL FOR ORGANIC CHEMISTRY.pdf
 
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...
Practical Research 1, Lesson 5: DESIGNING A RESEARCH PROJECT RELATED TO DAILY...
 
2.22.24 Black Nationalism and the Nation of Islam.pptx
2.22.24 Black Nationalism and the Nation of Islam.pptx2.22.24 Black Nationalism and the Nation of Islam.pptx
2.22.24 Black Nationalism and the Nation of Islam.pptx
 
Capter 5 Climate of Ethiopia and the Horn GeES 1011.pdf
Capter 5 Climate of Ethiopia and the Horn GeES 1011.pdfCapter 5 Climate of Ethiopia and the Horn GeES 1011.pdf
Capter 5 Climate of Ethiopia and the Horn GeES 1011.pdf
 
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 2-2023-Aynura-Hamidova.pdf
 
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdf
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdfDiploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdf
Diploma 2nd yr PHARMACOLOGY chapter 5 part 1.pdf
 
New Features in the Odoo 17 Sales Module
New Features in  the Odoo 17 Sales ModuleNew Features in  the Odoo 17 Sales Module
New Features in the Odoo 17 Sales Module
 
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...
Andreas Schleicher - 20 Feb 2024 - How pop music, podcasts, and Tik Tok are i...
 
2.20.24 Asian Americans and the Myth of the Model Minority.pptx
2.20.24 Asian Americans and the Myth of the Model Minority.pptx2.20.24 Asian Americans and the Myth of the Model Minority.pptx
2.20.24 Asian Americans and the Myth of the Model Minority.pptx
 
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAY
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAYSOCIAL JUSTICE LESSON ON CATCH UP FRIDAY
SOCIAL JUSTICE LESSON ON CATCH UP FRIDAY
 
Food Web SlideShare for Ecology Notes Quiz in Canvas
Food Web SlideShare for Ecology Notes Quiz in CanvasFood Web SlideShare for Ecology Notes Quiz in Canvas
Food Web SlideShare for Ecology Notes Quiz in Canvas
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
BÀI TẬP BỔ TRỢ TIẾNG ANH 11 THEO ĐƠN VỊ BÀI HỌC - CẢ NĂM - CÓ FILE NGHE (GLOB...
 
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf
11 CI SINIF SINAQLARI - 1-2023-Aynura-Hamidova.pdf
 
spring_bee_bot_creations_erd primary.pdf
spring_bee_bot_creations_erd primary.pdfspring_bee_bot_creations_erd primary.pdf
spring_bee_bot_creations_erd primary.pdf
 
DNA damage and repair mechanism
DNA damage and repair mechanism DNA damage and repair mechanism
DNA damage and repair mechanism
 
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...
Ideotype concept and climate resilient crop varieties for future- Wheat, Rice...
 
first section physiology laboratory.pptx
first section physiology laboratory.pptxfirst section physiology laboratory.pptx
first section physiology laboratory.pptx
 
Data Modeling - Entity Relationship Diagrams-1.pdf
Data Modeling - Entity Relationship Diagrams-1.pdfData Modeling - Entity Relationship Diagrams-1.pdf
Data Modeling - Entity Relationship Diagrams-1.pdf
 
2.20.24 The March on Washington for Jobs and Freedom.pptx
2.20.24 The March on Washington for Jobs and Freedom.pptx2.20.24 The March on Washington for Jobs and Freedom.pptx
2.20.24 The March on Washington for Jobs and Freedom.pptx
 

ARIMA

  • 1. Data Analysis Course Time Series Analysis & Forecasting Venkat Reddy
  • 2. Contents • ARIMA • Stationarity • AR process • MA process • Main steps in ARIMA • Forecasting using ARIMA model • Goodness of fit DataAnalysisCourse VenkatReddy 2
  • 3. Drawbacks of the use of traditional models • There is no systematic approach for the identification and selection of an appropriate model, and therefore, the identification process is mainly trial-and-error • There is difficulty in verifying the validity of the model • Most traditional methods were developed from intuitive and practical considerations rather than from a statistical foundation DataAnalysisCourse VenkatReddy 3
  • 4. ARIMA Models • Autoregressive Integrated Moving-average • A “stochastic” modeling approach that can be used to calculate the probability of a future value lying between two specified limits DataAnalysisCourse VenkatReddy 4
  • 5. AR & MA Models • Autoregressive AR process: • Series current values depend on its own previous values • AR(p) - Current values depend on its own p-previous values • P is the order of AR process • Moving average MA process: • The current deviation from mean depends on previous deviations • MA(q) - The current deviation from mean depends on q- previous deviations • q is the order of MA process • Autoregressive Moving average ARMA process DataAnalysisCourse VenkatReddy 5
  • 6. AR Process DataAnalysisCourse VenkatReddy 6AR(1) yt = a1* yt-1 AR(2) yt = a1* yt-1 +a2* yt-2 AR(3) yt = a1* yt-1 + a2* yt-2 +a3* yt-2
  • 7. MA Process DataAnalysisCourse VenkatReddy 7 MA(1) εt = b1*εt-1 MA(2) εt = b1*εt-1 + b2*εt-2 MA(3) εt = b1*εt-1 + b2*εt-2+ b3*εt-3
  • 8. ARIMA Models • Autoregressive (AR) process: • Series current values depend on its own previous values • Moving average (MA) process: • The current deviation from mean depends on previous deviations • Autoregressive Moving average (ARMA) process • Autoregressive Integrated Moving average (ARIMA)process. • ARIMA is also known as Box-Jenkins approach. It is popular because of its generality; • It can handle any series, with or without seasonal elements, and it has well- documented computer programs DataAnalysisCourse VenkatReddy 8
  • 9. ARIMA Model → AR filter → Integration filter → MA filter → εt (long term) (stochastic trend) (short term) (white noise error) ARIMA (2,0,1) yt = a1yt-1 + a2yt-2 + b1εt-1 ARIMA (3,0,1) yt = a1yt-1 + a2yt-2 + a3yt-3 + b1εt-1 ARIMA (1,1,0) Δyt = a1 Δyt-1 + εt , where Δyt = yt - yt-1 ARIMA (2,1,0) Δyt = a1 Δyt-1 + a2Δ yt-2 + εt where Δyt = yt - yt-1 To build a time series model issuing ARIMA, we need to study the time series and identify p,d,q DataAnalysisCourse VenkatReddy 9
  • 10. ARIMA equations • ARIMA(1,0,0) • yt = a1yt-1 + εt • ARIMA(2,0,0) • yt = a1yt-1 + a2yt-2 + εt • ARIMA (2,1,1) • Δyt = a1 Δyt-1 + a2Δ yt-2 + b1εt-1 where Δyt = yt - yt-1 DataAnalysisCourse VenkatReddy 10
  • 11. Overall Time series Analysis & Forecasting Process • Prepare the data for model building- Make it stationary • Identify the model type • Estimate the parameters • Forecast the future values DataAnalysisCourse VenkatReddy 11
  • 12. ARIMA (p,d,q) modeling To build a time series model issuing ARIMA, we need to study the time series and identify p,d,q • Ensuring Stationarity • Determine the appropriate values of d • Identification: • Determine the appropriate values of p & q using the ACF, PACF, and unit root tests • p is the AR order, d is the integration order, q is the MA order • Estimation : • Estimate an ARIMA model using values of p, d, & q you think are appropriate. • Diagnostic checking: • Check residuals of estimated ARIMA model(s) to see if they are white noise; pick best model with well behaved residuals. • Forecasting: • Produce out of sample forecasts or set aside last few data points for in-sample forecasting. DataAnalysisCourse VenkatReddy 12
  • 13. The Box-Jenkins Approach DataAnalysisCourse VenkatReddy 13 1.Differencing the series to achieve stationary 2.Identify the model 3.Estimate the parameters of the model Diagnostic checking. Is the model adequate? No Yes4. Use Model for forecasting
  • 15. Some non stationary series DataAnalysisCourse VenkatReddy 15 1 2 3 4
  • 16. Stationarity • In order to model a time series with the Box-Jenkins approach, the series has to be stationary • In practical terms, the series is stationary if tends to wonder more or less uniformly about some fixed level • In statistical terms, a stationary process is assumed to be in a particular state of statistical equilibrium, i.e., p(xt) is the same for all t • In particular, if zt is a stationary process, then the first difference zt = zt - zt-1and higher differences d zt are stationary DataAnalysisCourse VenkatReddy 16
  • 17. Testing Stationarity • Dickey-Fuller test • P value has to be less than 0.05 or 5% • If p value is greater than 0.05 or 5%, you accept the null hypothesis, you conclude that the time series has a unit root. • In that case, you should first difference the series before proceeding with analysis. • What DF test ? • Imagine a series where a fraction of the current value is depending on a fraction of previous value of the series. • DF builds a regression line between fraction of the current value Δyt and fraction of previous value δyt-1 • The usual t-statistic is not valid, thus D-F developed appropriate critical values. If P value of DF test is <5% then the series is stationary DataAnalysisCourse VenkatReddy 17
  • 18. Demo: Testing Stationarity • Sales_1 data DataAnalysisCourse VenkatReddy 18 Stochastic trend: Inexplicable changes in direction
  • 19. Demo: Testing Stationarity DataAnalysisCourse VenkatReddy 19 Augmented Dickey-Fuller Unit Root Tests Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F Zero Mean 0 0.3251 0.7547 0.74 0.8695 1 0.3768 0.7678 1.26 0.9435 2 0.3262 0.7539 1.05 0.9180 Single Mean 0 -6.9175 0.2432 -1.77 0.3858 2.05 0.5618 1 -3.5970 0.5662 -1.06 0.7163 1.52 0.6913 2 -3.7030 0.5522 -0.88 0.7783 1.02 0.8116 Trend 0 -11.8936 0.2428 -2.50 0.3250 3.16 0.5624 1 -7.1620 0.6017 -1.60 0.7658 1.34 0.9063 2 -9.0903 0.4290 -1.53 0.7920 1.35 0.9041
  • 20. Achieving Stationarity • Differencing : Transformation of the series to a new time series where the values are the differences between consecutive values • Procedure may be applied consecutively more than once, giving rise to the "first differences", "second differences", etc. • Regular differencing (RD) (1st order) xt = xt – xt-1 (2nd order) 2xt = ( xt - xt-1 )=xt – 2xt-1 + xt-2 • It is unlikely that more than two regular differencing would ever be needed • Sometimes regular differencing by itself is not sufficient and prior transformation is also needed DataAnalysisCourse VenkatReddy 20
  • 22. Demo: Achieving Stationarity DataAnalysisCourse VenkatReddy 22 data lagsales_1; set sales_1; sales1=sales-lag1(sales); run; Augmented Dickey-Fuller Unit Root Tests Type Lags Rho Pr < Rho Tau Pr < Tau F Pr > F Zero Mean 0 -37.7155 <.0001 -7.46 <.0001 1 -32.4406 <.0001 -3.93 0.0003 2 -19.3900 0.0006 -2.38 0.0191 Single Mean 0 -38.9718 <.0001 -7.71 0.0002 29.70 0.0010 1 -37.3049 <.0001 -4.10 0.0036 8.43 0.0010 2 -25.6253 0.0002 -2.63 0.0992 3.50 0.2081 Trend 0 -39.0703 <.0001 -7.58 0.0001 28.72 0.0010 1 -37.9046 <.0001 -4.08 0.0180 8.35 0.0163 2 -25.7179 0.0023 -2.59 0.2875 3.37 0.5234
  • 24. Achieving Stationarity-Othermethods • Is the trend stochastic or deterministic? • If stochastic (inexplicable changes in direction): use differencing • If deterministic(plausible physical explanation for a trend or seasonal cycle) : use regression • Check if there is variance that changes with time • YES : make variance constant with log or square root transformation • Remove the trend in mean with: • 1st/2nd order differencing • Smoothing and differencing (seasonality) • If there is seasonality in the data: • Moving average and differencing • Smoothing DataAnalysisCourse VenkatReddy 24
  • 26. Identification of orders p and q • Identification starts with d • ARIMA(p,d,q) • What is Integration here? • First we need to make the time series stationary • We need to learn about ACF & PACF to identify p,q • Once we are working with a stationary time series, we can examine the ACF and PACF to help identify the proper number of lagged y (AR) terms and ε (MA) terms. DataAnalysisCourse VenkatReddy 26
  • 27. Autocorrelation Function (ACF) • Autocorrelation is a correlation coefficient. However, instead of correlation between two different variables, the correlation is between two values of the same variable at times Xi and Xi+k. • Correlation with lag-1, lag2, lag3 etc., • The ACF represents the degree of persistence over respective lags of a variable. ρk = γk / γ0 = covariance at lag k/ variance ρk = E[(yt – μ)(yt-k – μ)]2 E[(yt – μ)2] ACF (0) = 1, ACF (k) = ACF (-k) DataAnalysisCourse VenkatReddy 27
  • 28. ACF Graph DataAnalysisCourse VenkatReddy 28 -0.50 0.000.501.00 0 10 20 30 40 Lag Bartlett's formula for MA(q) 95% confidence bands
  • 29. Partial Autocorrelation Function (PACF) • The exclusive correlation coefficient • Partial regression coefficient - The lag k partial autocorrelation is the partial regression coefficient, θkk in the kth order auto regression • In general, the "partial" correlation between two variables is the amount of correlation between them which is not explained by their mutual correlations with a specified set of other variables. • For example, if we are regressing a variable Y on other variables X1, X2, and X3, the partial correlation between Y and X3 is the amount of correlation between Y and X3 that is not explained by their common correlations with X1 and X2. • yt = θk1yt-1 + θk2yt-2 + …+ θkkyt-k + εt • Partial correlation measures the degree of association between two random variables, with the effect of a set of controlling random variables removed. DataAnalysisCourse VenkatReddy 29
  • 30. PACF Graph DataAnalysisCourse VenkatReddy 30 -0.50 0.000.501.00 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqrt(n)]
  • 31. Identificationof AR Processes& its order -p • For AR models, the ACF will dampen exponentially • The PACF will identify the order of the AR model: • The AR(1) model (yt = a1yt-1 + εt) would have one significant spike at lag 1 on the PACF. • The AR(3) model (yt = a1yt-1+a2yt-2+a3yt-3+εt) would have significant spikes on the PACF at lags 1, 2, & 3. DataAnalysisCourse VenkatReddy 31
  • 37. AR(3) model DataAnalysisCourse VenkatReddy 37 yt = 0.3yt-1 + 0.3yt-2 + 0.1yt-3 +εt
  • 39. Identificationof MA Processes& its order - q • Recall that a MA(q) can be represented as an AR(∞), thus we expect the opposite patterns for MA processes. • The PACF will dampen exponentially. • The ACF will be used to identify the order of the MA process. • MA(1) (yt = εt + b1 εt-1) has one significant spike in the ACF at lag 1. • MA (3) (yt = εt + b1 εt-1 + b2 εt-2 + b3 εt-3) has three significant spikes in the ACF at lags 1, 2, & 3. DataAnalysisCourse VenkatReddy 39
  • 52. Demo1: Identification of the model • ACF is dampening, PCF graph cuts off. - Perfect example of an AR process DataAnalysisCourse VenkatReddy 52 proc arima data= chem_readings plots=all; identify var=reading scan esacf center ; run;
  • 53. Demo: Identification of the model PACF cuts off after lag 2 1. d = 0, p =2, q= 0 DataAnalysisCourse VenkatReddy 53 SAS ARMA(p+d,q) Tentative Order Selection Tests SCAN ESACF p+d q p+d q 2 0 2 3 1 5 4 4 5 3 yt = a1yt-1 + a2yt-2 + εt
  • 54. LAB: Identification of model • Download web views data • Use sgplot to create a trend chart • What does ACF & PACF graphs say? • Identify the model using below table • Write the model equation DataAnalysisCourse VenkatReddy 54
  • 56. Parameter Estimate • We already know the model equation. AR(1,0,0) or AR(2,1,0) or ARIMA(2,1,1) • We need to estimate the coefficients using Least squares. Minimizing the sum of squares of deviations DataAnalysisCourse VenkatReddy 56
  • 57. Demo1: Parameter Estimation • Chemical reading data DataAnalysisCourse VenkatReddy 57 proc arima data=chem_readings; identify var=reading scan esacf center; estimate p=2 q=0 noint method=ml; run; yt = 0. 424yt-1 + 0.2532yt-2 + εt Maximum Likelihood Estimation Parameter Estimate Standard Error t Value Approx Pr > |t| Lag AR1,1 0.42444 0.06928 6.13 <.0001 1 AR1,2 0.25315 0.06928 3.65 0.0003 2
  • 58. Lab: Parameter Estimation • Estimate the parameters for webview data DataAnalysisCourse VenkatReddy 58
  • 60. Forecasting • Now the model is ready • We simply need to use this model for forecasting DataAnalysisCourse VenkatReddy 60 proc arima data=chem_readings; identify var=reading scan esacf center; estimate p=2 q=0 noint method=ml; forecast lead=4 ; run; Forecasts for variable Reading Obs Forecast Std Error 95% Confidence Limits 198 17.2405 0.3178 16.6178 17.8633 199 17.2235 0.3452 16.5469 17.9000 200 17.1759 0.3716 16.4475 17.9043 201 17.1514 0.3830 16.4007 17.9020
  • 61. LAB: Forecasting using ARIMA • Forecast the number of sunspots for next three hours DataAnalysisCourse VenkatReddy 61
  • 62. Validation: How good is my model? • Does our model really give an adequate description of the data • Two criteria to check the goodness of fit • Akaike information criterion (AIC) • Schwartz Bayesiancriterion (SBC)/Bayesian information criterion (BIC). • These two measures are useful in comparing two models. • The smaller the AIC & SBC the better the model DataAnalysisCourse VenkatReddy 62
  • 63. Goodness of fit • Remember… Residual analysis and Mean deviation, Mean Absolute Deviation and Root Mean Square errors? • Four common techniques are the: • Mean absolute deviation, • Mean absolute percent error • Mean square error, • Root mean square error. DataAnalysisCourse VenkatReddy 63 n i ii n1 YˆY =MAD n i ii n1 2 YˆY =MSE MSERMSE n i i ii n 1 Y YˆY100 =MAPE
  • 64. Lab: Overall Steps on sunspot example • Import the time series data • Prepare the data for model building- Make it stationary • Identify the model type • Estimate the parameters • Forecast the future values DataAnalysisCourse VenkatReddy 64