Time Series Analysis: Univariate And Multivariate Methods by William W.s. WeiTime Series Analysis: Univariate And Multivariate Methods by William W.s. Wei

Time Series Analysis: Univariate And Multivariate Methods

byWilliam W.s. Wei

Paperback | July 7, 2005

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With its broad coverage of methodology, this comprehensive book is a useful learning and reference tool for those in applied sciences where analysis and research of time series is useful. Its plentiful examples show the operational details and purpose of a variety of univariate and multivariate time series methods. Numerous figures, tables and real-life time series data sets illustrate the models and methods useful for analyzing, modeling, and forecasting data collected sequentially in time. The text also offers a balanced treatment between theory and applications.


Overview. Fundamental Concepts. Stationary Time Series Models. Nonstationary Time Series Models. Forecasting. Model Identification. Parameter Estimation, Diagnostic Checking, and Model Selection. Seasonal Time Series Models. Testing for a Unit Root. Intervention Analysis and Outlier Detection. Fourier Analysis. Spectral Theory of Stationary Processes. Estimation of the Spectrum. Transfer Function Models. Time Series Regression and GARCH Models. Vector Time Series Models. More on Vector Time Series. State Space Models and the Kalman Filter. Long Memory and Nonlinear Processes. Aggregation and Systematic Sampling in Time Series.


For all readers interested in time series analysis.
Title:Time Series Analysis: Univariate And Multivariate MethodsFormat:PaperbackDimensions:624 pages, 9.2 × 6.8 × 1.4 inPublished:July 7, 2005Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321322169

ISBN - 13:9780321322166

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Overview intrigue n. 1. The quality or power of arousing curiosity or interest. 2. The events and situations that complicate the plot of a story. 3. A plotting or scheming by secret or underhand means. 4. A secret or illicit love affair. (Funk & Wagnall's Standard College Dictionary) intrigue n.f. 1. Menees secretes pour faire reussir ou echouer une affaire. 2. Liaison secrete. 3. Combinaison des differents incidents qui forment le sujet dune piece, d'un roman, d'un film. (Dictionnaire Hachette) Intrigue is essentially a mystery story. It is the story of a Frenchman named Jean-Louis and a Quebecoise graduate student named Claire who meet, seemingly coincidentally, in New Orleans. One in search of a rare original manuscript written by a famous eighteenth-century author, and the other with hidden motives, the two become entangled in a web of adventures that take them from Louisiana to the Caribbean, West Africa, Europe, and Canada. The protagonists discover, in the course of these travels, that their meeting was not entirely coincidental and that they themselves are part of a larger international scheme of intrigue and deception. This mystery story, however, is not written in a traditional narrative format. Rather, it evolves through the chapter dialogues, listening comprehension selections, communicative activities, and even grammar exercises of the textbook. With each activity in each chapter, the story progresses, and the students learn more about the characters' motives as they pick up clues related to the twists and turns of the story line. As they become interested in the evolving mystery story, they become engaged in learning French language and in discovering French-speaking cultures around the globe. As the title indicates, Intrigue aims to arouse the student's curiosity by offering a complex mystery plot in which characters use underhand means to accomplish their objectives. By offering continuity between readings, student listening recordings, classroom activities, and homework exercises, Intrigue draws students into using the French-language in meaningful situations and understanding the cultures of the French-speaking world. In Intrigue, readings and activities are contextualized and relevant to the story line. Intrigue is a comprehensive and flexible intermediate-level textbook that develops the four basic communicative skills: reading, writing, speaking, and listening. Its proficiency-oriented methodology focuses on communication, linguistic functions, and interactive exchanges. Rather than split the contents between a grammar-intensive workbook and communication-focused classroom text, thereby isolating grammar review from communicative activities, Intrigue incorporates it all into one comprehensive textbook. The plot of the mystery story ties together the numerous objectives of an intermediate-level French textbook and provides a meaningful context for the presentation of language functions, vocabulary, grammar explanations, authentic literary excerpts, and cultural information. Students are introduced first to episodes of the story and then to the vocabulary, grammatical tools, and cultural information needed to fully comprehend what they are reading and to imagine themselves functioning in similar linguistic situations. Student learning is natural, as the text builds skills and recycles grammar points and functions in order to reinforce learning. Interspersed throughout the chapters are "Centre d'information" blocks that provide grammatical tips, explain idiomatic expressions, or present vocabulary or cultural / historical information. In each chapter, personal opinion questions help the students to relate to the information presented, allow them to express ideas, encourage them to adapt vocabulary to their own circumstances, and foster critical thinking. Authentic materials are presented in conjunction with various episodes in the mystery story, and challenging literary readings also relate to the mystery story or chapter themes. These help to prepare intermediate-level language students for future upper-level courses in French literature or civilization. Vocabulary pools build upon the basics (work, travel, food, family life, clothes) and introduce some new topics (introductory business French, describing political movements, quebecismes). Process-writing activities, plus pre-reading and post-reading exercises, foster improvement in reading and writing skills. The Cahier presents additional oral and written review activities that target grammatical tools, vocabulary, verb conjugations, as well as supplementary culture and literature review activities. The online Cahier Electronique offers a multitude of optional "Pour aller plus loin" content-based expansion activities. These may be Internet activities or the study of additional literary texts, works of art, radio programs, news, music, films, or other cultural texts. The online "Pour aller plus loin" activities offer endless opportunities for student interaction with authentic texts in French. The "Pour agir" section, also included in the Cahier Electronique, suggests related experiential, community-based, or service-learning projects. The idea of encouraging students to get out of the classroom and act on what they have learned is a truly unique feature of Intrigue. The aim of these projects is as much to enrich the overall educational experience of the students as to reinforce the learning of French language and Francophone cultures. While Intrigue prepares students for upper-level French courses, for many, the intermediate language course is merely a college requirement. Ten years after taking Intermediate French in college, most students will not remember how to conjugate the subjunctive. However, they may remember a volunteer project or a group outing of which they were a part. Experiential learning, which requires students to act on the knowledge and skills they have developed, not only makes learning French something "real" but also helps to instill more fundamental concepts such as awareness of cultural differences, openness to new ideas ... and perhaps even the desire to continue studying French at the upper levels. The activities in the textbook are designed to reach a broad range of learners, addressing those with diverse learning styles, those with varying levels of preparation in French, and nontraditional adult students. Activities to practice each function or grammar point are scaled to different levels—each one including inductive activities, discrete activities, open-ended and interactive exercises—and are varied to reach students who may be visual or tactile learners, linear thinkers, or inductive reasoners. Instructors may choose the activities that best address the needs of their students. The design and subject of the textbook are geared toward college-level and adult students, partly in response to the growing number of nontraditional older students in today's universities and partly to offer traditional-age college students material that they will find challenging and interesting. Not cluttered with cartoons or irrelevant "eye-catching" visual material that can be distracting, the story is what will draw the students to the page. The text assumes an intellectually mature and perceptive reader hindered only by his or her limited knowledge of French. The material presented to students in Intrigue aims to incite lively interaction and critical reflection, encouraging students to draw on their own life experiences, thereby rendering the subject of the course relevant to them personally. Intrigue may be used for a full-year intermediate course or compressed into an intensive one-semester grammar review. The text and workbook alone offer opportunities for a basic intermediate course. Or the text and workbook can be used with a selection of the texts and activities suggested in "Pour aller plus loin" or "Pour agir," as a standard intermediate French course or a more challenging content-based intermediate course. The "Interlude" section—which offers short synopses of the plot events, a time line, and brief descriptions of the main characters—may be used as a mid-year review for a two-semester course. This way, a student who is beginning language study at the second-semester intermediate level can quickly get up to speed on the plot and skills reviewed in the first five chapters, or a student returning from a long break can refresh his or her memory. As concerned educators in an age dominated by pop culture, true crime stories, action-adventure mysteries, and courtroom dramas, we want to reach out to our students and help them engage with the course material. Intrigue allows us to offer our students the best of both worlds: all of the fun of a mystery story combined with all of the educational value of a communicative French textbook. Important Features of Intrigue This innovative mystery-story textbook arouses student curiosity and encourages students to participate actively in understanding the story and related authentic documents, to discuss the content of chapter readings, to write about their opinions and reactions, and even to complete grammar review activities—all of which advance the plot and offer clues to solving the mystery. Students engage with the material as they work through the contextualized activities, which foster active communication and collaborative learning while lowering the affective filter. The textbook is designed to meet the "five C's" of the standards for foreign language learning: Communication (accurate language use, achieved through contextualized language activities), Cultures (understanding different cultural perspectives, achieved through contextualized cultural information and authentic texts), Connections (interdisciplinary explorations, presented in the text and expanded in the "Pour alter plus loin" activities), Comparisons (insight into the nature of language / culture, achieved through comparative questions in the text and workbook), and Communities (use of language beyond the classroom setting, targeted by the "Pour agir" experiential learning suggestions). Vocabulary-building activities in the first episode of each chapter encourage students to draw on their knowledge of basic vocabulary and add new vocabulary pools, including quebecismes, literary analysis, and an introduction to Business French! Process-writing activities in each chapter, at the end of each episode, guide students through the writing process. The "A 1'ecrit" activities successively target vocabulary development, question formation, and practical writing. These first three activities lead to a more formal essay or letter-writing assignment in the final section of each chapter. Pre-reading and post-reading activities assist students in developing strategies for understanding meaning from context. Original readings that expose the plot of the mystery story are accompanied by realia and other authentic texts such as newspaper articles, songs, poems, or literary excerpts. Readings become progressively more complex in each subsequent chapter and include examples of the grammatical structures or language functions learned in the chapter. Grammar review and language function activities are designed to address the needs of students with varying levels of language preparation and diverse learning styles. Grammar explanations in English ensure students will have a clear understanding of the structures, but students are also exposed to grammatical terminology in French to facilitate in-class discussions of grammar in the target language. All activities are incorporated into one convenient and comprehensive textbook, including a student audio program that allows students to hear dialogues read by native speakers. It also presents listening comprehension selections that correspond to activities in the text and further advance the story. Students are drawn into the vibrancy and diversity of cultures in the Frenchspeaking world through the characters presented in context of the mystery story. The "Centre d'information " blocks offer historical and cultural background information about Francophone cultures or useful tips about French language usage. The workbook includes oral and written review activities and there are endless opportunities for student contact with authentic documents and texts in the online workbook or Cahier electronique. The "Pour aller plus loin" content-based activities encourage students to explore other literary texts, works of art, films, music, interdisciplinary topics, and websites that relate to the chapter topics. Also online are the "Pour agir " suggestions for community exchanges, service-learning projects, or other experiential learning activities designed to engage the students' minds and bodies in learning about Francophone cultures. The instructor may choose to incorporate any or all of these materials into the course, depending on his or her own teaching style and pedagogical goals. The content and design of the textbook are age-appropriate for college-level students and adult (nontraditional) students. How Are the Chapters Organized? Each of the ten chapters is composed of a short preview called "Avant-Propos," three main sections or "Episodes," and a "Denouement" or synthesis section. Each section develops the story and all four language skills, while focusing on particular skills and / or language functions. Interspersed throughout the four sections are relevant visuals to aid in learning, "Centre d' information' blocks that offer cultural background or language tips, and "Pour aller plus loin" blocks that suggest optional content-based expansion activities found on the text's website. The student workbook offers oral and written review activities. The workbook website, or Calder electronique, houses the "Pour aller plus loin" and "Pour agir" expansion activities. The instructor's resource manual includes rationales and suggestions for using the chapter activities, as well as tapescripts, sample tests, and other resources. As you read through the text, notice that the story line develops principally in the four main reading / listening texts of each episode ("Lecture," "A 1'ecoute," "Correspondance," and "A suivre") but also in many of the student activities. The textbook is designed such that the main reading / listening sections are crucial to following the mystery story plot, but the plot developments in the grammar review activities are not essential to follow the story. This way, instructors and students are not obliged to complete all of the textbook activities in class, and instructors may select activities that work best in their particular classrooms. Chapter Structure Avant-propos : Introduction / Schema This one-page preview to the chapter begins with a proverb, saying, or quotation that serves the dual purpose of introducing the cultural context of the chapter and providing a clue to the story. The instructor's resource guide suggests ways to use the proverb to introduce the cultural context and pique student interest. It also offers pronunciation work, as students may repeat aloud or memorize the saying. The preview page also offers a synopsis of the developments of the mystery story in each chapter, without giving away the plot twists, to give students a pre-reading context and to entice them to read on. Episode 1 Exposition The first section introduces a new episode in the development of the mystery story, a cultural context, and a pool of vocabulary. Activities practice all four skills, but the focus is on reading skills and vocabulary building, including a quick writing activity to brainstorm vocabulary for upcoming writing assignments. The opening episode in the story also introduces all of the grammar tools and language functions that will be the focus of the chapter, thereby providing rich inductive material. Episode 2 Developpement In this section, students will draw on the vocabulary presented in the first episode and concentrate on developing correct usage of the grammatical tools (articles, pronouns, and so on) that are needed for the chapter language functions. Again, activities span all four skills, but the focus in this section is on aural / oral skills. A listening comprehension activity (full text available in instructor's resource manual only) continues the mystery story and requires attentive listening. Oral and written activities are designed to target conversational speaking and informal writing. Episode 3 Noeud The third section also emphasizes structures needed for the language functions of the chapter, with a particular focus on verb conjugations and accurate use of verb tenses in practical speaking / writing contexts. Some activities in this section of each chapter will intermingle tenses, ensuring that students remember how to form those learned earlier in the course and can demonstrate proper usage in realistic situations. A short reading in this section in the form of real-life correspondence (a letter, email, fax) brings the action of the mystery story to a peak, further involving the students in the mystery plot, and serves as an example for a practical writing activity that includes the vocabulary and structures practiced in the two earlier episodes. Denouement: Conclusion/Synthese The final section of each chapter offers activities that synthesize the material presented in the chapter (vocabulary, grammar structures, language functions, cultural information). Interactive activities, such as games, role-playing, and debates, recycle chapter functions and themes in a meaningful and fun way. Writing activities, including a more formal essay-writing assignment, also recycle the material learned in this and previous episodes. A literary excerpt related to the chapter material further expands students' reading and speaking skills while introducing them to major authors of the Francophone world. A final short conclusion to the chapter's mystery story episode is an open-ended "A suivre" section with questions that allow students to reflect critically on the character's actions thus far and to hypothesize about upcoming events or scenarios. Ancillaries Intrigue Student Audio Program: The student CD, which accompanies the textbook, contains the "Dialogue" listening comprehension selection (found in Episode 2 of each chapter). Intrigue Cahier: This print version of the student workbook contains the "Pour reviser" oral and written review activities that target vocabulary, language functions, grammar structures, culture, and literature. Intrigue Cahier Audio Program: A master CD contains the audio material for the oral review section of the workbook ("Pour reviser: activites orales"). Intrigue Cahier Electronique: The student "online workbook" website contains the "Pour aller plus loin" content-based, expansion activities, the "Pour agir" experiential, community-based or service project suggestions, and the "Pour vous aider " online French-English and French dictionary tools. Intrigue Instructor's Resource Manual: The manual contains rationales for each activity (whether structured input, inductive, discrete, open-ended, or creative), teaching suggestions, dialogue tapescripts, sample tests, and additional resources for instructors.

Table of Contents

1: Overview

1.1 Introduction

1.2 Examples and Scope of This Book


2: Fundamental Concepts

2.1 Stochastic Processes

2.2 The Autocovariance and Autocorrelation Functions

2.3 The Partial Autocorrelation Function

2.4 White Noise Processes

2.5 Estimation of the Mean, Autocovariances, and Autocorrelations

2.5.1 Sample Mean

2.5.2 Sample Autocovariance Function

2.5.3 Sample Autocorrelation Function

2.5.4 Sample Partial Autocorrelation Function

2.6 Moving Average and Autoregressive Representations of Time Series Processes

2.7 Linear Difference Equations


3: Stationary Time Series Models

3.1 Autoregressive Processes

3.1.1 The First-Order Autoregressive AR(1) Process

3.1.2 The Second-Order Autoregressive AR(2) Process

3.1.3 The General pth-Order Autoregressive AR(p) Process

3.2 Moving Average Processes

3.2.1 The First-Order Moving Average MA(1) Process

3.2.2 The Second-Order Moving Average MA(2) Process

3.2.3 The General qth-Order Moving Average MA(q) Process

3.3 The Dual Relationship Between AR(p) and MA(q) Processes

3.4 Autoregressive Moving Average ARMA(p, q) Processes

3.4.1 The General Mixed ARMA(p, q) Process

3.4.2 The ARMA(1, 1) Process


4: Nonstationary Time Series Models

4.1 Nonstationarity in the Mean

4.1.1 Deterministic Trend Models

4.1.2 Stochastic Trend Models and Differencing

4.2 Autoregressive Integrated Moving Average (ARIMA) Models

4.2.1 The General ARIMA Model

4.2.2 The Random Walk Model

4.2.3 The ARIMA(0, 1, 1) or IMA(1, 1) Model

4.3 Nonstationarity in the Variance and the Autocovariance

4.3.1 Variance and Autocovariance of the ARIMA Models

4.3.2 Variance Stabilizing Transformations


5: Forecasting

5.1 Introduction

5.2 Minimum Mean Square Error Forecasts

5.2.1 Minimum Mean Square Error Forecasts for ARMA Models

5.2.2 Minimum Mean Square Error Forecasts for ARIMA Models

5.3 Computation of Forecasts

5.4 The ARIMA Forecast as a Weighted Average of Previous Observations

5.5 Updating Forecasts

5.6 Eventual Forecast Functions

5.7 A Numerical Example


6: Model Identification

6.1 Steps for Model Identification

6.2 Empirical Examples

6.3 The Inverse Autocorrelation Function (IACF)

6.4 Extended Sample Autocorrelation Function and Other Identification Procedures

6.4.1 The Extended Sample Autocorrelation Function (ESACF)

6.4.2 Other Identification Procedures


7: Parameter Estimation, Diagnostic Checking, and Model Selection

7.1 The Method of Moments

7.2 Maximum Likelihood Method

7.2.1 Conditional Maximum Likelihood Estimation

7.2.2 Unconditional Maximum Likelihood Estimation and Backcasting Method

7.2.3 Exact Likelihood Functions

7.3 Nonlinear Estimation

7.4 Ordinary Least Squares (OLS) Estimation in Time Series Analysis

7.5 Diagnostic Checking

7.6 Empirical Examples for Series W1—W7

7.7 Model Selection Criteria



8: Seasonal Time Series Models

8.1 General Concepts

8.2 Traditional Methods

8.2.1 Regression Method

8.2.2 Moving Average Method

8.3 Seasonal ARIMA Models

8.4 Empirical Examples


9: Testing for a Unit Root

9.1 Introduction

9.2 Some Useful Limiting Distributions

9.3 Testing for a Unit Root in the AR(1) Model

9.3.1 Testing the AR(1) Model without a Constant Term

9.3.2 Testing the AR(1) Model with a Constant Term

9.3.3 Testing the AR(1) Model with a Linear Time Trend

9.4 Testing for a Unit Root in a More General Model

9.5 Testing for a Unit Root in Seasonal Time Series Models

9.5.1 Testing the Simple Zero Mean Seasonal Model

9.5.2 Testing the General Multiplicative Zero Mean Seasonal Model


10: Intervention Analysis and Outlier Detection

10.1 Intervention Models

10.2 Examples of Intervention Analysis

10.3 Time Series Outliers

10.3.1 Additive and Innovational Outliers

10.3.2 Estimation of the Outlier Effect When the Timing of the Outlier Is Known

10.3.3 Detection of Outliers Using an Iterative Procedure

10.4 Examples of Outlier Analysis

10.5 Model Identification in the Presence of Outliers


11: Fourier Analysis

11.1 General Concepts

11.2 Orthogonal Functions

11.3 Fourier Representation of Finite Sequences

11.4 Fourier Representation of Periodic Sequences

11.5 Fourier Representation of Nonperiodic Sequences: The Discrete-Time Fourier Transform

11.6 Fourier Representation of Continuous-Time Functions

11.6.1 Fourier Representation of Periodic Functions

11.6.2 Fourier Representation of Nonperiodic Functions: The Continuous-Time Fourier Transform

11.7 The Fast Fourier Transform


12: Spectral Theory of Stationary Processes

12.1 The Spectrum

12.1.1 The Spectrum and Its Properties

12.1.2 The Spectral Representation of Autocovariance Functions: The Spectral Distribution Function

12.1.3 Wold’s Decomposition of a Stationary Process

12.1.4 The Spectral Representation of Stationary Processes

12.2 The Spectrum of Some Common Processes

12.2.1 The Spectrum and the Autocovariance Generating Function

12.2.2 The Spectrum of ARMA Models

12.2.3 The Spectrum of the Sum of Two Independent Processes

12.2.4 The Spectrum of Seasonal Models

12.3 The Spectrum of Linear Filters

12.3.1 The Filter Function

12.3.2 Effect of Moving Average

12.3.3 Effect of Differencing

12.4 Aliasing


13: Estimation of the Spectrum

13.1 Periodogram Analysis

13.1.1 The Periodogram

13.1.2 Sampling Properties of the Periodogram

13.1.3 Tests for Hidden Periodic Components

13.2 The Sample Spectrum

13.3 The Smoothed Spectrum

13.3.1 Smoothing in the Frequency Domain: The Spectral Window

13.3.2 Smoothing in the Time Domain: The Lag Window

13.3.3 Some Commonly Used Windows

13.3.4 Approximate Confidence Intervals for Spectral Ordinates

13.4 ARMA Spectral Estimation


14: Transfer Function Models

14.1 Single-Input Transfer Function Models

14.1.1 General Concepts

14.1.2 Some Typical Impulse Response Functions

14.2 The Cross-Correlation Function and Transfer Function Models

14.2.1 The Cross-Correlation Function (CCF)

14.2.2 The Relationship between the Cross-Correlation Function and the Transfer Function

14.3 Construction of Transfer Function Models

14.3.1 Sample Cross-Correlation Function

14.3.2 Identification of Transfer Function Models

14.3.3 Estimation of Transfer Function Models

14.3.4 Diagnostic Checking of Transfer Function Models

14.3.5 An Empirical Example

14.4 Forecasting Using Transfer Function Models

14.4.1 Minimum Mean Square Error Forecasts for Stationary Input and Output Series

14.4.2 Minimum Mean Square Error Forecasts for Nonstationary Input and Output Series

14.4.3 An Example

14.5 Bivariate Frequency-Domain Analysis

14.5.1 Cross-Covariance Generating Functions and the Cross-Spectrum

14.5.2 Interpretation of the Cross-Spectral Functions


14.5.4 Estimation of the Cross-Spectrum

14.6 The Cross-Spectrum and Transfer Function Models

14.6.1 Construction of Transfer Function Models through Cross-Spectrum Analysis

14.6.2 Cross-Spectral Functions of Transfer Function Models

14.7 Multiple-Input Transfer Function Models


15: Time Series Regression and GARCH Models

15.1 Regression with Autocorrelated Errors

15.2 ARCH and GARCH Models

15.3 Estimation of GARCH Models

15.3.1 Maximum Likelihood Estimation

15.3.2 Iterative Estimation

15.4 Computation of Forecast Error Variance

15.5 Illustrative Examples


16: Vector Time Series Models

16.1 Covariance and Correlation Matrix Functions

16.2 Moving Average and Autoregressive Representations of Vector Processes

16.3 The Vector Autoregressive Moving Average Process

16.3.1 Covariance Matrix Function for the Vector AR(1) Model

16.3.2 Vector AR(p) Models

16.3.3 Vector MA(1) Models

16.3.4 Vector MA(q) Models

16.3.5 Vector ARMA(1, 1) Models

16.4 Nonstationary Vector Autoregressive Moving Average Models

16.5 Identification of Vector Time Series Models

16.5.1 Sample Correlation Matrix Function

16.5.2 Partial Autoregression Matrices

16.5.3 Partial Lag Correlation Matrix Function

16.6 Model Fitting and Forecasting

16.7 An Empirical Example

16.7.1 Model Identification

16.7.2 Parameter Estimation

16.7.3 Diagnostic Checking

16.7.4 Forecasting

16.7.5 Further Remarks

16.8 Spectral Properties of Vector Processes

Supplement 16.A Multivariate Linear Regression Models


17: More on Vector Time Series

17.1 Unit Roots and Cointegration in Vector Processes

17.1.1 Representations of Nonstationary Cointegrated Processes

17.1.2 Decomposition of Z t

17.1.3 Testing and Estimating Cointegration

17.2 Partial Process and Partial Process Correlation Matrices

17.2.1 Covariance Matrix Generating Function

17.2.2 Partial Covariance Matrix Generating Function

17.2.3 Partial Process Sample Correlation Matrix Functions

17.2.4 An Empirical Example: The U.S. Hog Data

17.3 Equivalent Representations of a Vector ARMA Model

17.3.1 Finite-Order Representations of a Vector Time Series Process

17.3.2 Some Implications


18: State Space Models and the Kalman Filter

18.1 State Space Representation

18.2 The Relationship between State Space and ARMA Models

18.3 State Space Model Fitting and Canonical Correlation Analysis

18.4 Empirical Examples

18.5 The Kalman Filter and Its Applications

Supplement 18.A Canonical Correlations


19: Long Memory and Nonlinear Processes

19.1 Long Memory Processes and Fractional Differencing

19.1.1 Fractionally Integrated ARMA Models and Their ACF

19.1.2 Practical Implications of the ARFIMA Processes

19.1.3 Estimation of the Fractional Difference

19.2 Nonlinear Processes

19.2.1 Cumulants, Polyspectrum, and Tests for Linearity and Normality

19.2.2 Some Nonlinear Time Series Models

19.3 Threshold Autoregressive Models

19.3.1 Tests for TAR Models

19.3.2 Modeling TAR Models


20: Aggregation and Systematic Sampling in Time Series

20.1 Temporal Aggregation of the ARIMA Process

20.1.1 The Relationship of Autocovariances between the Nonaggregate and Aggregate Series

20.1.2 Temporal Aggregation of the IMA(d, q) Process

20.1.3 Temporal Aggregation of the AR(p) Process

20.1.4 Temporal Aggregation of the ARIMA(p, d, q) Process

20.1.5 The Limiting Behavior of Time Series Aggregates

20.2 The Effects of Aggregation on Forecasting and Parameter Estimation

20.2.1 Hilbert Space

20.2.2 The Application of Hilbert Space in Forecasting

20.2.3 The Effect of Temporal Aggregation on Forecasting

20.2.4 Information Loss Due to Aggregation in Parameter Estimation

20.3 Systematic Sampling of the ARIMA Process

20.4 The Effects of Systematic Sampling and Temporal Aggregation on Causality

20.4.1 Decomposition of Linear Relationship between Two Time Series

20.4.2 An Illustrative Underlying Model

20.4.3 The Effects of Systematic Sampling and Temporal Aggregation on Causality

20.5 The Effects of Aggregation on Testing for Linearity and Normality

20.5.1 Testing for Linearity and Normality

20.5.2 The Effects of Temporal Aggregation on Testing for Linearity and Normality

20.6 The Effects of Aggregation on Testing for a Unit Root

20.6.1 The Model of Aggregate Series

20.6.2 The Effects of Aggregation on the Distribution of the Test Statistics

20.6.3 The Effects of Aggregation on the Significance Level and the Power of the Test


20.6.5 General Cases and Concluding Remarks

20.7 Further Comments





Time Series Data Used for Illustrations

Statistical Tables

Author Index


Subject Index