Introduction to Time Series Using

Transcription

1 Introduction to Time Series Using Olclticl SEAN BECKETTI?TV) A Stata Press Publication StataCorp LP College Station, Texas

2 Contents List of tables xiii List of figures xv Preface xxi Acknowledgments xxvii 1 Just enough Stata Getting started Action first, explanation later Now some explanation Navigating the interface The gestalt of Stata The parts of Stata speech All about data Looking at data Statistics Basics Estimation Odds and ends Making a date How to look good Transformers Typing dates and date variables Looking ahead 69 2 Just enough statistics Random variables and their moments 72

3 vi Contents 2.2 Hypothesis tests Linear regression Ordinary least squares Instrumental variables FGLS Multiple-equation models Time series White noise, autocorrelation, and stationarity ARMA models 82 3 Filtering time-series data Preparing to analyze a time series Questions for all types of data 87 How are the variables defined? 87 What is the relationship between the data and the phenomenon of interest? 88 Who compiled the data? 90 What processes generated the data? Questions specifically for time-series data 91 What is the frequency of measurement? 91 Are the data seasonally adjusted? 91 Are the data revised? The four components of a time series 92 Trend 93 Cycle 95 Seasonal Some simple filters Smoothing a trend Smoothing a cycle Smoothing a seasonal pattern Smoothing real data 115

4 Contents vii 3.4 Additional filters ma: Weighted moving averages EWMAs 125 exponential: EWMAs 126 dexponential: Double-exponential moving averages Holt-Winters smoothers 131 hwinters: Holt-Winters smoothers without a seasonal component 131 shwinters: Holt-Winters smoothers including a seasonal component Points to remember A first pass at forecasting Forecast fundamentals Types of forecasts Measuring the quality of a forecast Elements of a forecast Filters that forecast Forecasts based on EWMAs Forecasting a trending series with a seasonal component Points to remember Looking ahead Autocorrelated disturbances Autocorrelation Example: Mortgage rates Regression models with autocorrelated disturbances First-order autocorrelation Example: Mortgage rates (cont.) Testing for autocorrelation Other tests Estimation with first-order autocorrelated data 178

5 viii Contents Model 1: Strictly exogenous regressors and autocorrelated disturbances 179 The OLS strategy 181 The transformation strategy 183 The FGLS strategy 185 Comparison of estimates of model Model 2: A lagged dependent variable and i.i.d. errors Model 3: A lagged dependent variable with AR(1) errors The transformation strategy 193 The IV strategy Estimating the mortgage rate equation Points to remember Univariate time-series models The general linear process Lag polynomials: Notation or prestidigitation? The ARMA model Stationarity and invertibility What can ARMA models do? Points to remember Looking ahead Modeling a real-world time series Getting ready to model a time series The Box-Jenkins approach Specifying an ARMA model Step 1: Induce stationarity (ARMA becomes ARIMA) Step 2: Mind your p's and q's Estimation Looking for trouble: Model diagnostic checking Overrating Tests of the residuals 254

6 Contents ix 7.6 Forecasting with ARIMA models Comparing forecasts Points to remember What have we learned so far? Looking ahead Time-varying volatility Examples of time-varying volatility ARCH: A model of time-varying volatility Extensions to the ARCH model GARCH: Limiting the order of the model Other extensions 292 Asymmetric responses to "news" 293 Variations in volatility affect the mean of the observable series 295 Nonnormal errors 296 Odds and ends Points to remember Models of multiple time series Vector autoregressions Three types of VARs A VAR of the U.S. macroeconomy Using Stata to estimate a reduced-form VAR Testing a VAR for stationarity 309 Other tests Forecasting 316 Evaluating a VAR forecast Who's on first? Cross correlations Summarizing temporal relationships in a VAR 335 Granger causality 336

7 x Contents How to impose order 339 FEVDs 343 Using Stata to calculate IRFs and FEVDs SVARs Examples of a short-run SVAR Examples of a long-run SVAR Points to remember Looking ahead Models of nonstationary time series Trends and unit roots Testing for unit roots Cointegration: Looking for a long-term relationship Cointegrating relationships and VECMs Deterministic components in the VECM From intuition to VECM: An example 392 Step 1: Confirm the unit root 397 Step 2: Identify the number of lags 399 Step 3: Identify the number of cointegrating relationships. 400 Step 4: Fit a VECM 404 Step 5: Test for stability and white-noise residuals 414 Step 6: Review the model implications for reasonableness Points to remember Looking ahead Closing observations Making sense of it all What did we miss? Advanced time-series topics Additional Stata time-series features Data management tools and utilities 429 Univariate models 430

8 Contents XI Multivariate models Farewell 431 References 433 Author index 437 Subject index 439