Testing and Diagnostics

Linearity and Constancy Tests

EViews has provided tests of equations for linearity and testing for parameter constancy for many years as represented by the existing Ramsey reset linearity tests, and the Chow breakpoint, Quandt-Andrews, Bai, Bai-Perron, and CUSUM tests.

EViews 10 adds several new tests of linearity and parameter constancy against smooth threshold alternatives (see Teräsvirta (1994), Eitrheim and Teräsvirta (1996), Escribano and Jorda (1999), van Dijk, Teräsvirta, and Franses (2002)). As all of these tests involve a smooth transition regression (STR) alternative, they are implemented within EViews as tests of model specification for an estimated STR, but they are generally applicable as alternatives to the existing tests.

Linearity Tests

To perform a test of linearity, you will first estimate a STR equation (“Smooth Threshold Regression Estimation”). The linearity and parameter constancy tests are then available as views off of your equation.

For linearity testing against the smooth transition alternative, click on View/Stability Diagnostics/Linearity Tests:

EViews computes the Luukkonen, Saikkonen, and Teräsvirta linearity tests of the joint hypothesis test for significance of the elements of the Taylor approximation, Teräsvirta tests are a sequential set of general-to-specific tests, and Escribano-Jorda tests which test for nonlinearity and to discriminate between alternative choices for the transition function.

Remaining Nonlinearity Tests

Given estimation of a two-regime STR model we may wish to test for whether there is additional unmodeled nonlinearity. One popular approach is to test the estimated model against a model with additional regimes. EViews follows van Dijk, Teräsvirta, and Franses (2002) in distinguishing between two forms of the test, the additive and the encapsulated tests, which offer different specifications of the multiple regime alternative.

Click on View/Stability Diagnostics/Remaining Nonlinearity Test/Additive Nonlinearity Test or View/Stability Diagnostics/Remaining Nonlinearity Test/Encapsulated Nonlinearity Test to perform the test.

Parameter Constancy Test

One interesting variant of the STR model is the time-varying coefficient specification which is obtained by choosing time to be the threshold variable. This model allows for structural instability in which regression parameters evolve smoothly over time.

To perform this test, select View/Stability Diagnostics/Parameter Constancy Test:

• See “Stability Diagnostics” .

• See Equation::strconstant for constancy testing.

• See Equation::strlinear for linearity testing.

• See Equation::strnonlin for additional nonlinearity testing.

VAR Tools for Structural Residuals

Structural residuals play an important role in VAR analysis, and their computation is required for a wide range of VAR analysis, including impulse response, forecast variance decomposition, and historical decomposition.

While EViews has long computed these transformed residuals for internal use, EViews 10 now makes structural residuals available to users.

You may display the Structural Residuals views to examine these residuals in graph and spreadsheet form. If the are the ordinary residuals, we display the structural residuals based on factor loadings ,

(0.2) |

or based on weights ,

(0.3) |

When producing results for the Structural Residuals views, you will be prompted to choose a transformation.

In addition, you may use the Make Structural Residuals... entry on the proc menu to save these series into the workfile.

Improved VAR Serial Correlation Testing

Prior versions of EViews computed the multivariate LM test statistic for residual correlation at a specified order using the LR form of the Breusch-Godfrey test with an Edgeworth expansion correction (Johansen 1995, Edgerton and Shukur 1999).

EViews 10 offers two substantive improvements for testing VAR serial correlation.

• First, in addition to testing for autocorrelation at specified orders , EViews now also tests jointly for autocorrelation for lags 1 to . .

• Second, EViews augments the Edgeworth LR form of the test with the Rao F-test version of the LM statistic as described Edgerton and Shukur (1999) whose simulations suggest it performs best among the many variants they consider.

To perform the tests, simply select View/Residual Tests/Autocorrelation LM Test... in your estimated VAR object window. EViews will prompt you for the lag order . Enter a value and click on OK:

• See Var::arlm

VAR Historical and Variance Decomposition

Historical Decomposition

One method of innovation accounting is to decompose the observed series into the components corresponding to each structural shock. Burbridge and Harrison (1985) propose transforming observed residuals to structural residuals, and then for each observation beyond some point in the estimation sample, computing the contribution of the different accumulated structural shocks to each observed variable.

EViews 10 adds built-in support for computing historical decompositions. To obtain the historical decomposition, select View/Historical Decomposition... from the var object toolbar:

As with impulse response analysis, you may choose between various weighting methods such as Cholesky or generalized residual weights, and you can customize the display to show subsets of forecast errors and components, and only the error decomposition or the decomposition inclusive of the baseline forecasts.

A multiple graph decomposition of the stochastic component will look something like:

while the corresponding combined graph is given by

Including the baseline in the combined graph gives

• See “Historical Decomposition” and for discussion.

• See Var::hdecomp

Variance Decomposition

EViews 10 adds to the existing variance decomposition tools the ability to produce automatically the popular stacked graph showing the results for the decomposition.

• See “Variance Decomposition” for discussion.

• See Var::decomp

Nonlinear Dynamic Forecasting Simulation

When forecasting from an equation object with a nonlinear dynamic specification, EViews 10 provides easy-to-use tools for performing stochastic simulation to obtain the mean and standard error of the forecast.

Simply click on the Forecast button as always, and click on the click on the Stochastic simulation checkbox and enter the number of Repetitions and Failed reps prop. before halting as desired:

• See “Dynamic Forecasting” for discussion.

• See Equation::forecast

STL Decomposition and MoveReg Seasonal Adjustment

EViews 10 features two new seasonal adjustment methods: STL decomposition and MoveReg. To access these methods, from the series menu, select Proc/Seasonal Adjustment.

STL decomposition (Cleveland, Cleveland, McRae and Terpenning, 1990) assumes an additive relationship between the seasonal, trend and remainder components of a series. A filtering algorithm based upon LOESS regressions is used to estimate those three components.

STL offers two important advantages over other seasonal adjustment methods; it works on any frequency of data, and can be calculated on time series data with irregular patterns and missing values.

EViews 10 also provides a front-end interface to the MoveReg program, a weekly seasonal adjustment program developed by the U.S. Bureau of Labor. Most seasonal adjustment routines, including the U.S. Census Bureau’s X-11, X-12 and X-13 packages, require the data be sampled at a monthly or quarterly frequency. However, many economic series are sampled on a weekly basis, meaning that these seasonal adjustment techniques cannot be used. MoveReg fills this void by offering a seasonal adjustment method aimed directly at weekly data.

Model Bounds Checking

EViews 10 lets you specify boundaries for endogenous variables in a model through a new Boundaries dialog page.

Although the solver will not enforce the boundaries while solving the model, EViews will warn you if any variable crosses its boundaries (i.e., solves to a value higher than the upper boundary or less than the lower boundary) for any observation in the solve sample.

Boundary violations may be examined in detail using the Check Solution Bounds view after the solve is complete.

• See “Boundaries” for discussion.

• See Model::checkbounds.

• See Model::setbounds.

Improved Distribution Function and Special Function Calculations

EViews 10 offers new functions for numerically stable computation of tails of cumulative distribution functions, special functions, and expressions involving logs and exponentials when evaluated in regions where the standard functions will show a loss of precision: