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Introduction to Time Series Using Stata
Comment from the Stata technical group
Introduction to Time Series Using Stata, by Sean Becketti, provides a practical guide to working with time-series data using Stata and will appeal to a broad range of users. The many examples, concise explanations that focus on intuition, and useful tips based on the author’s decades of experience using time-series methods make the book insightful not just for academic users but also for practitioners in industry and government.
The book is appropriate both for new Stata users and for experienced users who are new to time-series analysis.
Chapter 1 provides a mild yet fast-paced introduction to Stata, highlighting all the features a user needs to know to get started using Stata for time-series analysis. Chapter 2 is a quick refresher on regression and hypothesis testing, and it defines key concepts such as white noise, autocorrelation, and lag operators.
Chapter 3 begins the discussion of time series, using moving-average and Holt–Winters techniques to smooth and forecast the data. Becketti also introduces the concepts of trends, cyclicality, and seasonality and shows how they can be extracted from a series. Chapter 4 focuses on using these methods for forecasting and illustrates how the assumptions regarding trends and cycles underlying the various moving-average and Holt–Winters techniques affect the forecasts produced. Although these techniques are sometimes neglected in other time-series books, they are easy to implement, can be applied to many series quickly, often produce forecasts just as good as more complicated techniques, and as Becketti emphasizes, have the distinct advantage of being easily explained to colleagues and policy makers without backgrounds in statistics.
Chapters 5 through 8 encompass single-equation time-series models. Chapter 5 focuses on regression analysis in the presence of autocorrelated disturbances and details various approaches that can be used when all the regressors are strictly exogenous but the errors are autocorrelated, when the set of regressors includes a lagged dependent variable and independent errors, and when the set of regressors includes a lagged dependent variable and autocorrelated errors. Chapter 6 describes the ARIMA model and Box–Jenkins methodology, and chapter 7 applies those techniques to develop an ARIMA-based model of U.S. GDP. Chapter 7 in particular will appeal to practitioners because it goes step by step through a real-world example: here is my series, now how do I fit an ARIMA model to it? Chapter 8 is a self-contained summary of ARCH/GARCH modeling.
In the final portion of the book, Becketti discusses multiple-equation models, particularly VARs and VECs. Chapter 9 focuses on VAR models and illustrates all key concepts, including model specification, Granger causality, impulse-response analyses, and forecasting, using a simple model of the U.S. economy; structural VAR models are illustrated by imposing a Taylor rule on interest rates. Chapter 10 presents nonstationary time-series analysis. After describing nonstationarity and unit-root tests, Becketti masterfully navigates the reader through the often-confusing task of specifying a VEC model, using an example based on construction wages in Washington, DC, and surrounding states. Chapter 11 concludes.
Sean Becketti is a financial industry veteran with three decades of experience in academics, government, and private industry. He was a developer of Stata in its infancy, and he was Editor of the Stata Technical Bulletin, the precursor to the Stata Journal, between 1993 and 1996. He has been a regular Stata user since its inception, and he wrote many of the first time-series commands in Stata.
Introduction to Time Series Using Stata, by Sean Becketti, is a first-rate, example-based guide to time-series analysis and forecasting using Stata. It can serve as both a reference for practitioners and a supplemental textbook for students in applied statistics courses.
Table of contents
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List of tables
List of figures
1 Just enough Stata
1.1 Getting started
1.1.1 Action first, explanation later1.2 All about data
1.1.2 Now some explanation
1.1.3 Navigating the interface
1.1.4 The gestalt of Stata
1.1.5 The parts of Stata speech
1.3 Looking at data
1.4.1 Basics1.5 Odds and ends
1.6 Making a date
1.6.1 How to look good1.7 Typing dates and date variables
1.8 Looking ahead
2 Just enough statistics
2.1 Random variables and their moments
2.2 Hypothesis tests
2.3 Linear regression
2.3.1 Ordinary least squares2.4 Multiple-equation models
2.3.2 Instrumental variables
2.5 Time series
2.5.1 White noise, autocorrelation, and stationarity
2.5.2 ARMA models
3 Filtering time-series data
3.1 Preparing to analyze a time series
3.1.1 Questions for all types of data3.2 The four components of a time series
How are the variables defined?3.1.2 Questions specifically for time-series data
What is the relationship between the data and the phenomenon of interest?
Who compiled the data?
What processes generated the data?
What is the frequency of measurement?
Are the data seasonally adjusted?
Are the data revised?
Trend3.3 Some simple filters
3.3.1 Smoothing a trend3.4 Additional filters
3.3.2 Smoothing a cycle
3.3.3 Smoothing a seasonal pattern
3.3.4 Smoothing real data
3.4.1 ma: Weighted moving averages3.5 Points to remember
exponential: EWMAs3.4.3 Holt–Winters smoothers
dexponential: Double-exponential moving averages
hwinters: Holt–Winters smoothers without a seasonal component
shwinters: Holt–Winters smoothers including a seasonal component
4 A first pass at forecasting
4.1 Forecast fundamentals
4.1.1 Types of forecasts4.2 Filters that forecast
4.1.2 Measuring the quality of a forecast
4.1.3 Elements of a forecast
4.2.1 Forecasts based on EWMAs4.3 Points to remember
4.2.2 Forecasting a trending series with a seasonal component
4.4 Looking ahead
5 Autocorrelated disturbances
5.1.1 Example: Mortgage rates5.2 Regression models with autocorrelated disturbances
5.2.1 First-order autocorrelation5.3 Testing for autocorrelation
5.2.2 Example: Mortgage rates (cont.)
5.3.1 Other tests5.4 Estimation with first-order autocorrelated data
5.4.1 Model 1: Strictly exogenous regressors and autocorrelated disturbances5.5 Estimating the mortgage rate equation
The OLS strategy5.4.2 Model 2: A lagged dependent variable and i.i.d. errors
The transformation strategy
The FGLS strategy
Comparison of estimates of model
5.4.3 Model 3: A lagged dependent variable with AR(1) errors
The transformation strategy
The IV strategy
5.6 Points to remember
6 Univariate time-series models
6.1 The general linear process
6.2 Lag polynomials: Notation or prestidigitation?
6.3 The ARMA model
6.4 Stationarity and invertibility
6.5 What can ARMA models do?
6.6 Points to remember
6.7 Looking ahead
7 Modeling a real-world time series
7.1 Getting ready to model a time series
7.2 The Box–Jenkins approach
7.3 Specifying an ARMA model
7.3.1 Step 1: Induce stationarity (ARMA becomes ARIMA)7.4 Estimation
7.3.2 Step 2: Mind your p’s and q’s
7.5 Looking for trouble: Model diagnostic checking
7.5.1 Overfitting7.6 Forecasting with ARIMA models
7.5.2 Tests of the residuals
7.7 Comparing forecasts
7.8 Points to remember
7.9 What have we learned so far?
7.10 Looking ahead
8 Time-varying volatility
8.1 Examples of time-varying volatility
8.2 ARCH: A model of time-varying volatility
8.3 Extensions to the ARCH model
8.3.1 GARCH: Limiting the order of the model8.4 Points to remember
8.3.2 Other extensions
Asymmetric responses to “news”
Variations in volatility affect the mean of the observable series
Odds and ends
9 Models of multiple time series
9.1 Vector autoregressions
9.1.1 Three types of VARs9.2 A VAR of the U.S. macroeconomy
9.2.1 Using Stata to estimate a reduced-form VAR9.3 Who’s on first?
9.2.2 Testing a VAR for stationarity
Other tests9.2.3 Forecasting
Evaluating a VAR forecast
9.3.1 Cross correlations9.4 SVARs
9.3.2 Summarizing temporal relationships in a VAR
How to impose order
Using Stata to calculate IRFs and FEVDs
9.4.1 Examples of a short-run SVAR9.5 Points to remember
9.4.2 Examples of a long-run SVAR
9.6 Looking ahead
10 Models of nonstationary time series
10.1 Trends and unit roots
10.2 Testing for unit roots
10.3 Cointegration: Looking for a long-term relationship
10.4 Cointegrating relationships and VECMs
10.4.1 Deterministic components in the VECM
10.5 From intuition to VECM: An example
Step 1: Confirm the unit root10.6 Points to remember
Step 2: Identify the number of lags
Step 3: Identify the number of cointegrating relationships
Step 4: Fit a VECM
Step 5: Test for stability and white-noise residuals
Step 6: Review the model implications for reasonableness
10.7 Looking ahead
11 Closing observations
11.1 Making sense of it all
11.2 What did we miss?
11.2.1 Advanced time-series topics11.3 Farewell
11.2.2 Additional Stata time-series features
Data management tools and utilities