- •Table of Contents
- •What’s New in EViews 5.0
- •What’s New in 5.0
- •Compatibility Notes
- •EViews 5.1 Update Overview
- •Overview of EViews 5.1 New Features
- •Preface
- •Part I. EViews Fundamentals
- •Chapter 1. Introduction
- •What is EViews?
- •Installing and Running EViews
- •Windows Basics
- •The EViews Window
- •Closing EViews
- •Where to Go For Help
- •Chapter 2. A Demonstration
- •Getting Data into EViews
- •Examining the Data
- •Estimating a Regression Model
- •Specification and Hypothesis Tests
- •Modifying the Equation
- •Forecasting from an Estimated Equation
- •Additional Testing
- •Chapter 3. Workfile Basics
- •What is a Workfile?
- •Creating a Workfile
- •The Workfile Window
- •Saving a Workfile
- •Loading a Workfile
- •Multi-page Workfiles
- •Addendum: File Dialog Features
- •Chapter 4. Object Basics
- •What is an Object?
- •Basic Object Operations
- •The Object Window
- •Working with Objects
- •Chapter 5. Basic Data Handling
- •Data Objects
- •Samples
- •Sample Objects
- •Importing Data
- •Exporting Data
- •Frequency Conversion
- •Importing ASCII Text Files
- •Chapter 6. Working with Data
- •Numeric Expressions
- •Series
- •Auto-series
- •Groups
- •Scalars
- •Chapter 7. Working with Data (Advanced)
- •Auto-Updating Series
- •Alpha Series
- •Date Series
- •Value Maps
- •Chapter 8. Series Links
- •Basic Link Concepts
- •Creating a Link
- •Working with Links
- •Chapter 9. Advanced Workfiles
- •Structuring a Workfile
- •Resizing a Workfile
- •Appending to a Workfile
- •Contracting a Workfile
- •Copying from a Workfile
- •Reshaping a Workfile
- •Sorting a Workfile
- •Exporting from a Workfile
- •Chapter 10. EViews Databases
- •Database Overview
- •Database Basics
- •Working with Objects in Databases
- •Database Auto-Series
- •The Database Registry
- •Querying the Database
- •Object Aliases and Illegal Names
- •Maintaining the Database
- •Foreign Format Databases
- •Working with DRIPro Links
- •Part II. Basic Data Analysis
- •Chapter 11. Series
- •Series Views Overview
- •Spreadsheet and Graph Views
- •Descriptive Statistics
- •Tests for Descriptive Stats
- •Distribution Graphs
- •One-Way Tabulation
- •Correlogram
- •Unit Root Test
- •BDS Test
- •Properties
- •Label
- •Series Procs Overview
- •Generate by Equation
- •Resample
- •Seasonal Adjustment
- •Exponential Smoothing
- •Hodrick-Prescott Filter
- •Frequency (Band-Pass) Filter
- •Chapter 12. Groups
- •Group Views Overview
- •Group Members
- •Spreadsheet
- •Dated Data Table
- •Graphs
- •Multiple Graphs
- •Descriptive Statistics
- •Tests of Equality
- •N-Way Tabulation
- •Principal Components
- •Correlations, Covariances, and Correlograms
- •Cross Correlations and Correlograms
- •Cointegration Test
- •Unit Root Test
- •Granger Causality
- •Label
- •Group Procedures Overview
- •Chapter 13. Statistical Graphs from Series and Groups
- •Distribution Graphs of Series
- •Scatter Diagrams with Fit Lines
- •Boxplots
- •Chapter 14. Graphs, Tables, and Text Objects
- •Creating Graphs
- •Modifying Graphs
- •Multiple Graphs
- •Printing Graphs
- •Copying Graphs to the Clipboard
- •Saving Graphs to a File
- •Graph Commands
- •Creating Tables
- •Table Basics
- •Basic Table Customization
- •Customizing Table Cells
- •Copying Tables to the Clipboard
- •Saving Tables to a File
- •Table Commands
- •Text Objects
- •Part III. Basic Single Equation Analysis
- •Chapter 15. Basic Regression
- •Equation Objects
- •Specifying an Equation in EViews
- •Estimating an Equation in EViews
- •Equation Output
- •Working with Equations
- •Estimation Problems
- •Chapter 16. Additional Regression Methods
- •Special Equation Terms
- •Weighted Least Squares
- •Heteroskedasticity and Autocorrelation Consistent Covariances
- •Two-stage Least Squares
- •Nonlinear Least Squares
- •Generalized Method of Moments (GMM)
- •Chapter 17. Time Series Regression
- •Serial Correlation Theory
- •Testing for Serial Correlation
- •Estimating AR Models
- •ARIMA Theory
- •Estimating ARIMA Models
- •ARMA Equation Diagnostics
- •Nonstationary Time Series
- •Unit Root Tests
- •Panel Unit Root Tests
- •Chapter 18. Forecasting from an Equation
- •Forecasting from Equations in EViews
- •An Illustration
- •Forecast Basics
- •Forecasting with ARMA Errors
- •Forecasting from Equations with Expressions
- •Forecasting with Expression and PDL Specifications
- •Chapter 19. Specification and Diagnostic Tests
- •Background
- •Coefficient Tests
- •Residual Tests
- •Specification and Stability Tests
- •Applications
- •Part IV. Advanced Single Equation Analysis
- •Chapter 20. ARCH and GARCH Estimation
- •Basic ARCH Specifications
- •Estimating ARCH Models in EViews
- •Working with ARCH Models
- •Additional ARCH Models
- •Examples
- •Binary Dependent Variable Models
- •Estimating Binary Models in EViews
- •Procedures for Binary Equations
- •Ordered Dependent Variable Models
- •Estimating Ordered Models in EViews
- •Views of Ordered Equations
- •Procedures for Ordered Equations
- •Censored Regression Models
- •Estimating Censored Models in EViews
- •Procedures for Censored Equations
- •Truncated Regression Models
- •Procedures for Truncated Equations
- •Count Models
- •Views of Count Models
- •Procedures for Count Models
- •Demonstrations
- •Technical Notes
- •Chapter 22. The Log Likelihood (LogL) Object
- •Overview
- •Specification
- •Estimation
- •LogL Views
- •LogL Procs
- •Troubleshooting
- •Limitations
- •Examples
- •Part V. Multiple Equation Analysis
- •Chapter 23. System Estimation
- •Background
- •System Estimation Methods
- •How to Create and Specify a System
- •Working With Systems
- •Technical Discussion
- •Vector Autoregressions (VARs)
- •Estimating a VAR in EViews
- •VAR Estimation Output
- •Views and Procs of a VAR
- •Structural (Identified) VARs
- •Cointegration Test
- •Vector Error Correction (VEC) Models
- •A Note on Version Compatibility
- •Chapter 25. State Space Models and the Kalman Filter
- •Background
- •Specifying a State Space Model in EViews
- •Working with the State Space
- •Converting from Version 3 Sspace
- •Technical Discussion
- •Chapter 26. Models
- •Overview
- •An Example Model
- •Building a Model
- •Working with the Model Structure
- •Specifying Scenarios
- •Using Add Factors
- •Solving the Model
- •Working with the Model Data
- •Part VI. Panel and Pooled Data
- •Chapter 27. Pooled Time Series, Cross-Section Data
- •The Pool Workfile
- •The Pool Object
- •Pooled Data
- •Setting up a Pool Workfile
- •Working with Pooled Data
- •Pooled Estimation
- •Chapter 28. Working with Panel Data
- •Structuring a Panel Workfile
- •Panel Workfile Display
- •Panel Workfile Information
- •Working with Panel Data
- •Basic Panel Analysis
- •Chapter 29. Panel Estimation
- •Estimating a Panel Equation
- •Panel Estimation Examples
- •Panel Equation Testing
- •Estimation Background
- •Appendix A. Global Options
- •The Options Menu
- •Print Setup
- •Appendix B. Wildcards
- •Wildcard Expressions
- •Using Wildcard Expressions
- •Source and Destination Patterns
- •Resolving Ambiguities
- •Wildcard versus Pool Identifier
- •Appendix C. Estimation and Solution Options
- •Setting Estimation Options
- •Optimization Algorithms
- •Nonlinear Equation Solution Methods
- •Appendix D. Gradients and Derivatives
- •Gradients
- •Derivatives
- •Appendix E. Information Criteria
- •Definitions
- •Using Information Criteria as a Guide to Model Selection
- •References
- •Index
- •Symbols
- •.DB? files 266
- •.EDB file 262
- •.RTF file 437
- •.WF1 file 62
- •@obsnum
- •Panel
- •@unmaptxt 174
- •~, in backup file name 62, 939
- •Numerics
- •3sls (three-stage least squares) 697, 716
- •Abort key 21
- •ARIMA models 501
- •ASCII
- •file export 115
- •ASCII file
- •See also Unit root tests.
- •Auto-search
- •Auto-series
- •in groups 144
- •Auto-updating series
- •and databases 152
- •Backcast
- •Berndt-Hall-Hall-Hausman (BHHH). See Optimization algorithms.
- •Bias proportion 554
- •fitted index 634
- •Binning option
- •classifications 313, 382
- •Boxplots 409
- •By-group statistics 312, 886, 893
- •coef vector 444
- •Causality
- •Granger's test 389
- •scale factor 649
- •Census X11
- •Census X12 337
- •Chi-square
- •Cholesky factor
- •Classification table
- •Close
- •Coef (coefficient vector)
- •default 444
- •Coefficient
- •Comparison operators
- •Conditional standard deviation
- •graph 610
- •Confidence interval
- •Constant
- •Copy
- •data cut-and-paste 107
- •table to clipboard 437
- •Covariance matrix
- •HAC (Newey-West) 473
- •heteroskedasticity consistent of estimated coefficients 472
- •Create
- •Cross-equation
- •Tukey option 393
- •CUSUM
- •sum of recursive residuals test 589
- •sum of recursive squared residuals test 590
- •Data
- •Database
- •link options 303
- •using auto-updating series with 152
- •Dates
- •Default
- •database 24, 266
- •set directory 71
- •Dependent variable
- •Description
- •Descriptive statistics
- •by group 312
- •group 379
- •individual samples (group) 379
- •Display format
- •Display name
- •Distribution
- •Dummy variables
- •for regression 452
- •lagged dependent variable 495
- •Dynamic forecasting 556
- •Edit
- •See also Unit root tests.
- •Equation
- •create 443
- •store 458
- •Estimation
- •EViews
- •Excel file
- •Excel files
- •Expectation-prediction table
- •Expected dependent variable
- •double 352
- •Export data 114
- •Extreme value
- •binary model 624
- •Fetch
- •File
- •save table to 438
- •Files
- •Fitted index
- •Fitted values
- •Font options
- •Fonts
- •Forecast
- •evaluation 553
- •Foreign data
- •Formula
- •forecast 561
- •Freq
- •DRI database 303
- •F-test
- •for variance equality 321
- •Full information maximum likelihood 698
- •GARCH 601
- •ARCH-M model 603
- •variance factor 668
- •system 716
- •Goodness-of-fit
- •Gradients 963
- •Graph
- •remove elements 423
- •Groups
- •display format 94
- •Groupwise heteroskedasticity 380
- •Help
- •Heteroskedasticity and autocorrelation consistent covariance (HAC) 473
- •History
- •Holt-Winters
- •Hypothesis tests
- •F-test 321
- •Identification
- •Identity
- •Import
- •Import data
- •See also VAR.
- •Index
- •Insert
- •Instruments 474
- •Iteration
- •Iteration option 953
- •in nonlinear least squares 483
- •J-statistic 491
- •J-test 596
- •Kernel
- •bivariate fit 405
- •choice in HAC weighting 704, 718
- •Kernel function
- •Keyboard
- •Kwiatkowski, Phillips, Schmidt, and Shin test 525
- •Label 82
- •Last_update
- •Last_write
- •Latent variable
- •Lead
- •make covariance matrix 643
- •List
- •LM test
- •ARCH 582
- •for binary models 622
- •LOWESS. See also LOESS
- •in ARIMA models 501
- •Mean absolute error 553
- •Metafile
- •Micro TSP
- •recoding 137
- •Models
- •add factors 777, 802
- •solving 804
- •Mouse 18
- •Multicollinearity 460
- •Name
- •Newey-West
- •Nonlinear coefficient restriction
- •Wald test 575
- •weighted two stage 486
- •Normal distribution
- •Numbers
- •chi-square tests 383
- •Object 73
- •Open
- •Option setting
- •Option settings
- •Or operator 98, 133
- •Ordinary residual
- •Panel
- •irregular 214
- •unit root tests 530
- •Paste 83
- •PcGive data 293
- •Polynomial distributed lag
- •Pool
- •Pool (object)
- •PostScript
- •Prediction table
- •Principal components 385
- •Program
- •p-value 569
- •for coefficient t-statistic 450
- •Quiet mode 939
- •RATS data
- •Read 832
- •CUSUM 589
- •Regression
- •Relational operators
- •Remarks
- •database 287
- •Residuals
- •Resize
- •Results
- •RichText Format
- •Robust standard errors
- •Robustness iterations
- •for regression 451
- •with AR specification 500
- •workfile 95
- •Save
- •Seasonal
- •Seasonal graphs 310
- •Select
- •single item 20
- •Serial correlation
- •theory 493
- •Series
- •Smoothing
- •Solve
- •Source
- •Specification test
- •Spreadsheet
- •Standard error
- •Standard error
- •binary models 634
- •Start
- •Starting values
- •Summary statistics
- •for regression variables 451
- •System
- •Table 429
- •font 434
- •Tabulation
- •Template 424
- •Tests. See also Hypothesis tests, Specification test and Goodness of fit.
- •Text file
- •open as workfile 54
- •Type
- •field in database query 282
- •Units
- •Update
- •Valmap
- •find label for value 173
- •find numeric value for label 174
- •Value maps 163
- •estimating 749
- •View
- •Wald test 572
- •nonlinear restriction 575
- •Watson test 323
- •Weighting matrix
- •heteroskedasticity and autocorrelation consistent (HAC) 718
- •kernel options 718
- •White
- •Window
- •Workfile
- •storage defaults 940
- •Write 844
- •XY line
- •Yates' continuity correction 321
Chapter 17. Time Series Regression
In this section, we discuss single equation regression techniques that are important for the analysis of time series data: testing for serial correlation, estimation of ARMA models, using polynomial distributed lags, and testing for unit roots in potentially nonstationary time series.
The chapter focuses on the specification and estimation of time series models. A number of related topics are discussed elsewhere. For example, standard multiple regression techniques are discussed in Chapter 15, “Basic Regression”, on page 443 and Chapter 16, “Additional Regression Methods”, on page 461, while forecasting and inference are discussed extensively in Chapter 18, “Forecasting from an Equation”, on page 543.
Serial Correlation Theory
A common finding in time series regressions is that the residuals are correlated with their own lagged values. This serial correlation violates the standard assumption of regression theory that disturbances are not correlated with other disturbances. The primary problems associated with serial correlation are:
•OLS is no longer efficient among linear estimators. Furthermore, since prior residuals help to predict current residuals, we can take advantage of this information to form a better prediction of the dependent variable.
•Standard errors computed using the textbook OLS formula are not correct, and are generally understated.
•If there are lagged dependent variables on the right-hand side, OLS estimates are biased and inconsistent.
EViews provides tools for detecting serial correlation and estimation methods that take account of its presence.
In general, we will be concerned with specifications of the form:
yt = xt′β + ut
(17.1)
ut = zt − 1′γ + t
where xt is a vector of explanatory variables observed at time t , zt − 1 is a vector of variables known in the previous period, β and γ are vectors of parameters, ut is a disturbance term, and t is the innovation in the disturbance. The vector zt − 1 may contain lagged values of u , lagged values of , or both.
494—Chapter 17. Time Series Regression
The disturbance ut is termed the unconditional residual. It is the residual based on the structural component ( x′tβ ) but not using the information contained in zt − 1 . The innovation t is also known as the one-period ahead forecast error or the prediction error. It is the difference between the actual value of the dependent variable and a forecast made on the basis of the independent variables and the past forecast errors.
The First-Order Autoregressive Model
The simplest and most widely used model of serial correlation is the first-order autoregressive, or AR(1), model. The AR(1) model is specified as:
yt = xt′β + ut
(17.2)
ut = ρut − 1 + t
The parameter ρ is the first-order serial correlation coefficient. In effect, the AR(1) model incorporates the residual from the past observation into the regression model for the current observation.
Higher-Order Autoregressive Models
More generally, a regression with an autoregressive process of order p , AR( p ) error is given by:
yt = xt′β + ut
(17.3)
ut = ρ1ut − 1 + ρ2ut − 2 + … + ρput − p + t
The autocorrelations of a stationary AR(p ) process gradually die out to zero, while the partial autocorrelations for lags larger than p are zero.
Testing for Serial Correlation
Before you use an estimated equation for statistical inference (e.g. hypothesis tests and forecasting), you should generally examine the residuals for evidence of serial correlation. EViews provides several methods of testing a specification for the presence of serial correlation.
The Durbin-Watson Statistic
EViews reports the Durbin-Watson (DW) statistic as a part of the standard regression output. The Durbin-Watson statistic is a test for first-order serial correlation. More formally, the DW statistic measures the linear association between adjacent residuals from a regression model. The Durbin-Watson is a test of the hypothesis ρ = 0 in the specification:
ut = ρut − 1 + t . |
(17.4) |
Testing for Serial Correlation—495
If there is no serial correlation, the DW statistic will be around 2. The DW statistic will fall below 2 if there is positive serial correlation (in the worst case, it will be near zero). If there is negative correlation, the statistic will lie somewhere between 2 and 4.
Positive serial correlation is the most commonly observed form of dependence. As a rule of thumb, with 50 or more observations and only a few independent variables, a DW statistic below about 1.5 is a strong indication of positive first order serial correlation. See Johnston and DiNardo (1997, Chapter 6.6.1) for a thorough discussion on the Durbin-Watson test and a table of the significance points of the statistic.
There are three main limitations of the DW test as a test for serial correlation. First, the distribution of the DW statistic under the null hypothesis depends on the data matrix x . The usual approach to handling this problem is to place bounds on the critical region, creating a region where the test results are inconclusive. Second, if there are lagged dependent variables on the right-hand side of the regression, the DW test is no longer valid. Lastly, you may only test the null hypothesis of no serial correlation against the alternative hypothesis of first-order serial correlation.
Two other tests of serial correlation—the Q-statistic and the Breusch-Godfrey LM test— overcome these limitations, and are preferred in most applications.
Correlograms and Q-statistics
If you select View/Residual Tests/Correlogram-Q-statistics on the equation toolbar, EViews will display the autocorrelation and partial autocorrelation functions of the residuals, together with the Ljung-Box Q-statistics for high-order serial correlation. If there is no serial correlation in the residuals, the autocorrelations and partial autocorrelations at all lags should be nearly zero, and all Q-statistics should be insignificant with large p-values.
Note that the p-values of the Q-statistics will be computed with the degrees of freedom adjusted for the inclusion of ARMA terms in your regression. There is evidence that some care should be taken in interpreting the results of a Ljung-Box test applied to the residuals from an ARMAX specification (see Dezhbaksh, 1990, for simulation evidence on the finite sample performance of the test in this setting).
Details on the computation of correlograms and Q-statistics are provided in greater detail in Chapter 11, “Series”, on page 328.
Serial Correlation LM Test
Selecting View/Residual Tests/Serial Correlation LM Test… carries out the Breusch-God- frey Lagrange multiplier test for general, high-order, ARMA errors. In the Lag Specification dialog box, you should enter the highest order of serial correlation to be tested.
The null hypothesis of the test is that there is no serial correlation in the residuals up to the specified order. EViews reports a statistic labeled “F-statistic” and an “Obs*R-squared”
496—Chapter 17. Time Series Regression
(NR2 —the number of observations times the R-square) statistic. The NR2 statistic has an asymptotic χ2 distribution under the null hypothesis. The distribution of the F-statistic is not known, but is often used to conduct an informal test of the null.
See “Serial Correlation LM Test” on page 581 for further discussion of the serial correlation LM test.
Example
As an example of the application of these testing procedures, consider the following results from estimating a simple consumption function by ordinary least squares:
Dependent Variable: CS
Method: Least Squares
Date: 08/19/97 Time: 13:03
Sample: 1948:3 1988:4
Included observations: 162
Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
|
|
|
C |
-9.227624 |
5.898177 |
-1.564487 |
0.1197 |
GDP |
0.038732 |
0.017205 |
2.251193 |
0.0257 |
CS(-1) |
0.952049 |
0.024484 |
38.88516 |
0.0000 |
|
|
|
|
|
R-squared |
0.999625 |
Mean dependent var |
1781.675 |
Adjusted R-squared |
0.999621 |
S.D. dependent var |
694.5419 |
S.E. of regression |
13.53003 |
Akaike info criterion |
8.066045 |
Sum squared resid |
29106.82 |
Schwarz criterion |
8.123223 |
Log likelihood |
-650.3497 F-statistic |
212047.1 |
|
Durbin-Watson stat |
1.672255 |
Prob(F-statistic) |
0.000000 |
|
|
|
|
A quick glance at the results reveals that the coefficients are statistically significant and the fit is very tight. However, if the error term is serially correlated, the estimated OLS standard errors are invalid and the estimated coefficients will be biased and inconsistent due to the presence of a lagged dependent variable on the right-hand side. The Durbin-Watson statistic is not appropriate as a test for serial correlation in this case, since there is a lagged dependent variable on the right-hand side of the equation.
Selecting View/Residual Tests/Correlogram-Q-statistics for the first 12 lags from this equation produces the following view: