Univariate Time Series Analysis .Univariate Time Series Analysis Univariate Time Series Analysis

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  • Univariate Time Series Analysis

    Univariate Time Series Analysis

    Klaus Wohlrabe1 and Stefan Mittnik

    1 Ifo Institute for Economic Research, wohlrabe@ifo.de

    SS 2016

    1 / 442

  • Univariate Time Series Analysis

    1 Organizational Details and Outline

    2 An (unconventional) introductionTime series CharacteristicsNecessity of (economic) forecastsComponents of time series dataSome simple filtersTrend extractionCyclical ComponentSeasonal ComponentIrregular ComponentSimple Linear Models

    3 A more formal introduction

    4 (Univariate) Linear ModelsNotation and TerminologyStationarity of ARMA ProcessesIdentification Tools

    2 / 442

  • Univariate Time Series Analysis

    5 Modeling ARIMA Processes: The Box-Jenkins ApproachEstimation of Identification FunctionsIdentificationEstimation

    Yule-Walker EstimationLeast Squares EstimatorsMaximum Likelihood Estimator (MLE)

    Model specificationDiagnostic Checking

    6 PredictionSome TheoryExamplesForecasting in PracticeA second Case StudyForecasting with many predictors

    7 Trends and Unit Roots3 / 442

  • Univariate Time Series Analysis

    Stationarity vs. NonstationarityTesting for Unit Roots: Dickey-Fuller-TestTesting for Unit Roots: KPSS

    8 Models for financial time seriesARCHGARCHGARCH: Extensions

    4 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Table of content I1 Organizational Details and Outline

    2 An (unconventional) introductionTime series CharacteristicsNecessity of (economic) forecastsComponents of time series dataSome simple filtersTrend extractionCyclical ComponentSeasonal ComponentIrregular ComponentSimple Linear Models

    3 A more formal introduction

    4 (Univariate) Linear ModelsNotation and Terminology

    5 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Table of content IIStationarity of ARMA ProcessesIdentification Tools

    5 Modeling ARIMA Processes: The Box-Jenkins ApproachEstimation of Identification FunctionsIdentificationEstimation

    Yule-Walker EstimationLeast Squares EstimatorsMaximum Likelihood Estimator (MLE)

    Model specificationDiagnostic Checking

    6 PredictionSome TheoryExamplesForecasting in Practice

    6 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Table of content IIIA second Case StudyForecasting with many predictors

    7 Trends and Unit RootsStationarity vs. NonstationarityTesting for Unit Roots: Dickey-Fuller-TestTesting for Unit Roots: KPSS

    8 Models for financial time seriesARCHGARCHGARCH: Extensions

    7 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Introduction

    Time series analysis:Focus: Univariate Time Series and Multivariate TimeSeries Analysis.A lot of theory and many empirical applications with realdataOrganization:

    12.04. - 24.05.: Univariate Time Series Analysis, sixlectures (Klaus Wohlrabe)31.05. - End of Semester: Multivariate Time SeriesAnalysis (Stefan Mittnik)15.04. - 27.05. mondays and fridays: Tutorials (Univariate):Malte Kurz, Elisabeth Heller

    Lectures and Tutorials are complementary!

    8 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Introduction

    Time series analysis:Focus: Univariate Time Series and Multivariate TimeSeries Analysis.A lot of theory and many empirical applications with realdataOrganization:

    12.04. - 24.05.: Univariate Time Series Analysis, sixlectures (Klaus Wohlrabe)31.05. - End of Semester: Multivariate Time SeriesAnalysis (Stefan Mittnik)15.04. - 27.05. mondays and fridays: Tutorials (Univariate):Malte Kurz, Elisabeth Heller

    Lectures and Tutorials are complementary!

    8 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Introduction

    Time series analysis:Focus: Univariate Time Series and Multivariate TimeSeries Analysis.A lot of theory and many empirical applications with realdataOrganization:

    12.04. - 24.05.: Univariate Time Series Analysis, sixlectures (Klaus Wohlrabe)31.05. - End of Semester: Multivariate Time SeriesAnalysis (Stefan Mittnik)15.04. - 27.05. mondays and fridays: Tutorials (Univariate):Malte Kurz, Elisabeth Heller

    Lectures and Tutorials are complementary!

    8 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Introduction

    Time series analysis:Focus: Univariate Time Series and Multivariate TimeSeries Analysis.A lot of theory and many empirical applications with realdataOrganization:

    12.04. - 24.05.: Univariate Time Series Analysis, sixlectures (Klaus Wohlrabe)31.05. - End of Semester: Multivariate Time SeriesAnalysis (Stefan Mittnik)15.04. - 27.05. mondays and fridays: Tutorials (Univariate):Malte Kurz, Elisabeth Heller

    Lectures and Tutorials are complementary!

    8 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Tutorials and Script

    Script is available at: moodle website (see course website)Password: armaxgarchxScript is available at the day before the lecture (noon)All datasets and programme codesTutorial: Mixture between theory and R - Examples

    9 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Literature

    Shumway and Stoffer (2010): Time Series Analysis andIts Applications: With R ExamplesBox, Jenkins, Reinsel (2008): Time Series Analysis:Forecasting and ControlLtkepohl (2005): Applied Time Series Econometrics.Hamilton (1994): Time Series Analysis.Ltkepohl (2006): New Introduction to Multiple Time SeriesAnalysisChatham (2003): The Analysis of Time Series: AnIntroductionNeusser (2010): Zeitreihenanalyse in denWirtschaftswissenschaften

    10 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Examination

    Evidence of academic achievements: Two hour writtenexam both for the univariate and multivariate partSchedule for the Univariate Exam: 30/05 (to beconfirmed!!!)

    11 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Prerequisites

    Basic Knowledge (ideas) of OLS, maximum likelihoodestimation, heteroscedasticity, autocorrelation.Some algebra

    12 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Software

    Where you have to pay:STATAEviewsMatlab (Student version available, about 80 Euro)

    Free software:R (www.r-project.org)Jmulti (www.jmulti) (Based on the book by Ltkepohl(2005))

    13 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Tools used in this lecture

    usual standard lecture (as you might expected)derivations using the whiteboard (not available in thescript!)live demonstrations (examples) using Excel, Matlab,Eviews, Stata and JMultilive programming using Matlab

    14 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Outline

    IntroductionLinear ModelsModeling ARIMA Processes: The Box-Jenkins ApproachPrediction (Forecasting)Nonstationarity (Unit Roots)Financial Time Series

    15 / 442

  • Univariate Time Series Analysis

    Organizational Details and Outline

    Goals

    After the lecture you should be able to ...... identify time series characteristics and dynamics... build a time series model... estimate a model... check a model... do forecasts... understand financial time series

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  • Univariate Time Series Analysis

    Organizational Details and Outline

    Questions to keep in mind

    General Question Follow-up QuestionsAll types of data

    How are the variables de-fined?

    What are the units of measurement? Do the data com-prise a sample? Ifo so, how was the sample drawn?

    What is the relationship be-tween the data and the phe-nomenon of interest?

    Are the variables direct measurements of the phe-nomenon of interest, proxies, correlates, etc.?

    Who compiled the data? Is the data provider unbiased? Does the provider pos-sess the skills and resources to enure data quality andintegrity?

    What processes generatedthe data?

    What theory or theories can account for the relationshipsbetween the variables in the data?

    Time Series dataWhat is the frequency ofmeasurement

    Are the variables measured hourly, daily monthly, etc.?How are gaps in the data (for example, weekends andholidays) handled?

    What is the type of mea-surement?

    Are the data a snapshot at a point in time, an averageover time, a cumulative value over time, etc.?

    Are the data seasonally ad-justed?

    If so, what is the adjustment method? Does this methodintroduce artifacts in the reported series?

    17 / 442

  • Univariate Time Series Analysis

    An (unconventional) introduction

    Table of content I1 Organizational Details and Outline

    2 An (unconventional) introductionTime series CharacteristicsNecessity of (economic) forecastsComponents of time series dataSome simple filtersTrend extractionCyclical ComponentSeasonal ComponentIrregular ComponentSimple Linear Models

    3 A more formal introduction

    4 (Univariate) Linear ModelsNotation and Terminology

    18 / 442

  • Univariate Time Series Analysis

    An (unconventional) introduction

    Table of content IIStationarity of ARMA ProcessesIdentification Tools

    5 Modeling ARIMA Processes: The Box-Jenkins ApproachEstimation of Identification FunctionsIdentificationEstimation

    Yule-Walker EstimationLeast Squares EstimatorsMaximum Likelihood Estimator (MLE)

    Model specification