Perform either (1) Johansen’s system cointegration test, (2) Engle-Granger or Phillips-Ouliaris single equation cointegration testing, or (3) Pedroni, Kao, or Fisher panel cointegration testing for the specified series.

Syntax

There are three forms for the coint command which depend on the form of the test you wish to perform:

Johansen Cointegration Test Syntax

coint(test_option, n, option) ser1 ser2 [...ser3 ser4 ...] [@ x1 x2 x3 ...]

uses the coint keyword followed by the test_option and the number of lags n, and if desired, an “@”-sign followed by a list of exogenous variables. The first option must be one of the following six test options:

a | No deterministic trend in the data, and no intercept or trend in the cointegrating equation. |

b | No deterministic trend in the data, and an intercept but no trend in the cointegrating equation. |

c | Linear trend in the data, and an intercept but no trend in the cointegrating equation. |

d | Linear trend in the data, and both an intercept and a trend in the cointegrating equation. |

e | Quadratic trend in the data, and both an intercept and a trend in the cointegrating equation. |

s | Summarize the results of all 5 options (a-e). |

Options for the Johansen Test

restrict | Impose restrictions as specified by the append (coint) proc. |

m = integer | Maximum number of iterations for restricted estimation (only valid if you choose the restrict option). |

c = scalar | Convergence criterion for restricted estimation. (only valid if you choose the restrict option). |

save = mat_name | Stores test statistics as a named matrix object. The save= option stores a matrix, where is the number of endogenous variables in the VAR. The first column contains the eigenvalues, the second column contains the maximum eigenvalue statistics, the third column contains the trace statistics, and the fourth column contains the log likelihood values. The i-th row of columns 2 and 3 are the test statistics for rank . The last row is filled with NAs, except the last column which contains the log likelihood value of the unrestricted (full rank) model. |

cvtype=ol | Display 0.05 and 0.01 critical values from Osterwald-Lenum (1992). This option reproduces the output from version 4. The default is to display critical values based on the response surface coefficients from MacKinnon-Haug-Michelis (1999). Note that the argument on the right side of the equals sign are letters, not numbers 0-1). |

cvsize=arg (default=0.05) | Specify the size of MacKinnon-Haug-Michelis (1999) critical values to be displayed. The size must be between 0.0001 and 0.9999; values outside this range will be reset to the default value of 0.05. This option is ignored if you set “cvtype=ol”. |

prompt | Force the dialog to appear from within a program. |

p | Print results. |

This type of cointegration testing may be used in a non-panel workfile. For Fisher combined testing using the Johansen framework, see below. The remaining options for the Johansen cointegration test are outlined below (“Options for the Johansen Test”).

Note that the output for cointegration tests displays p-values for the rank test statistics. These p-values are computed using the response surface coefficients as estimated in MacKinnon, Haug, and Michelis (1999). The 0.05 critical values are also based on the response surface coefficients from MacKinnon-Haug-Michelis. Note: the reported critical values assume no exogenous variables other than an intercept and trend.

Single Equation Test Syntax

coint(method=arg, options) ser1 ser2 [...ser3 ser4 ...] [@determ determ_spec] [@regdeterm regdeterm_spec]

where

method=arg | Test method: Engle-Granger residual test (“eg”), Phillips-Ouliaris residual test (“po”). |

Cointegrating equation specifications that include a constant, linear, or quadratic trends, should use the “trend=” option to specify those terms. If any of those terms are in the stochastic regressors equations but not in the cointegrating equation, they should be specified using the “regtrend=” option.

Deterministic trend regressors that are not covered by the list above may be specified using the keywords @determ and @regdeterm. To specify deterministic trend regressors that enter into the regressor and cointegrating equations, you should add the keyword @determ followed by the list of trend regressors. To specify deterministic trends that enter in the regressor equations but not the cointegrating equation, you should include the keyword @regdeterm followed by the list of trend regressors.

Note that the p-values for the test statistics are based on simulations, and do not account for any user-specified deterministic regressors.

This type of cointegration testing may be used in a non-panel workfile. The remaining options for the single equation cointegration tests are outlined below.

Options for Single Equation Tests

Options for the Engle-Granger Test

The following options determine the specification of the Engle-Granger test (Augmented Dickey-Fuller) equation and the calculation of the variances used in the test statistic.

trend=arg (default=“const”) | Specification for the powers of trend to include in the cointegrating equation: None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Note that the specification implies all trends up to the specified order so that choosing a quadratic trend instructs EViews to include a constant and a linear trend term along with the quadratic. |

regtrend=arg (default=“none”) | Additional trends to include in the regressor equations (but not the cointegrating equation): None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Only trend orders higher than those specified by “trend=” will be considered. Note that the specification implies all trends up to the specified order so that choosing a quadratic trend instructs EViews to include a constant and a linear trend term along with the quadratic. |

lag=arg (default=“a”) | Method of selecting the lag length (number of first difference terms) to be included in the regression: “a” (automatic information criterion based selection), or integer (user-specified lag length). |

lagtype=arg (default=“sic”) | Information criterion or method to use when computing automatic lag length selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn), “msaic” (Modified Akaike), “msic” (Modified Schwarz), “mhqc” (Modified Hannan-Quinn), “tstat” (t-statistic). |

maxlag=integer | Maximum lag length to consider when performing automatic lag-length selection default= where is the number of coefficients in the cointegrating equation. Applicable when “lag=a”. |

lagpval=number (default=0.10) | Probability threshold to use when performing automatic lag-length selection using a t-test criterion. Applicable when both “lag=a” and “lagtype=tstat”. |

nodf | Do not degree-of-freedom correct estimates of the variances. |

prompt | Force the dialog to appear from within a program. |

p | Print results. |

Options for the Phillips-Ouliaris Test

The following options control the computation of the symmetric and one-sided long-run variances in the Phillips-Ouliaris test.

Basic Options:

trend=arg (default=“const”) | Specification for the powers of trend to include in the cointegrating equation: None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Note that the specification implies all trends up to the specified order so that choosing a quadratic trend instructs EViews to include a constant and a linear trend term along with the quadratic. |

regtrend=arg (default=“none”) | Additional trends to include in the regressor equations (but not the cointegrating equation): None (“none”), Constant (“const”), Linear trend (“linear”), Quadratic trend (“quadratic”). Only trend orders higher than those specified by “trend=” will be considered. |

nodf | Do not degree-of-freedom correct the coefficient covariance estimate. |

prompt | Force the dialog to appear from within a program. |

p | Print results. |

HAC Whitening Options:

lag=arg (default=0) | Lag specification: integer (user-specified lag value), “a” (automatic selection). |

infosel=arg (default=“aic”) | Information criterion for automatic selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn) (if “lag=a”). |

maxlag=integer | Maximum lag-length for automatic selection (optional) (if “lag=a”). The default is an observation-based maximum. |

HAC Kernel Options:

kern=arg (default=“bart”) | Kernel shape: “none” (no kernel), “bart” (Bartlett, default), “bohman” (Bohman), “daniell” (Daniel), “parzen” (Parzen), “parzriesz” (Parzen-Riesz), “parzgeo” (Parzen-Geometric), “parzcauchy” (Parzen-Cauchy), “quadspec” (Quadratic Spectral), “trunc” (Truncated), “thamm” (Tukey-Hamming), “thann” (Tukey-Hanning), “tparz” (Tukey-Parzen). |

bw=arg (default=“nwfixed”) | Bandwidth: “fixednw” (Newey-West fixed), “andrews” (Andrews automatic), “neweywest” (Newey-West automatic), number (User-specified bandwidth). |

nwlag=integer | Newey-West lag-selection parameter for use in nonparametric bandwidth selection (if “bw=neweywest”). |

bwint | Use integer portion of bandwidth. |

Panel Syntax

coint(option) ser1 ser2 [...ser3 ser4 ...]

The coint command tests for cointegration among the series in the group. The second form of the command should be used with panel structured workfiles.

Options for the Panel Tests

For panel cointegration tests, you may specify the type using one of the following keywords:

Pedroni (default) | Pedroni (1994 and 2004). |

Kao | Kao (1999) |

Fisher | Fisher - pooled Johansen |

Depending on the type selected above, the following may be used to indicate deterministic trends:

const (default) | Include a constant in the test equation. Applicable to Pedroni and Kao tests. |

trend | Include a constant and a linear time trend in the test equation. Applicable to Pedroni tests. |

none | Do not include a constant or time trend. Applicable to Pedroni tests. |

a, b, c, d, or e | Indicate deterministic trends using the “a”, “b”, “c”, “d”, and “e” keywords, as detailed above in “Options for the Johansen Test”. Applicable to Fisher tests. |

Additional Options:

ac=arg (default=“bt”) | Method of estimating the frequency zero spectrum: “bt” (Bartlett kernel), “pr” (Parzen kernel), “qs” (Quadratic Spectral kernel). Applicable to Pedroni and Kao tests. |

band=arg (default=“nw”) | Method of selecting the bandwidth, where arg may be “nw” (Newey-West automatic variable bandwidth selection), or a number indicating a user-specified common bandwidth. Applicable to Pedroni and Kao tests. |

lag=arg | For Pedroni and Kao tests, the method of selecting lag length (number of first difference terms) to be included in the residual regression. For Fisher tests, a pair of numbers indicating lag. |

infosel=arg (default=“sic”) | Information criterion to use when computing automatic lag length selection: “aic” (Akaike), “sic” (Schwarz), “hqc” (Hannan-Quinn). Applicable to Pedroni and Kao tests. |

maxlag=int | Maximum lag length to consider when performing automatic lag length selection, where int is an integer. The default is where is the length of the cross-section. Applicable to Pedroni and Kao tests. |

disp=arg (default=500) | Maximum number of individual results to be displayed. |

prompt | Force the dialog to appear from within a program. |

p | Print results. |

Examples

Johansen test

coint(s,4) x y z

summarizes the results of the Johansen cointegration test for the series X, Y, and Z for all five specifications of trend. The test equation uses lags of up to order four.

Engle-Granger Test

coint(method=eg) x y z

performs the default Engle-Granger test on the residuals from a cointegrating equation which includes a constant. The number of lags is determined using the SIC criterion and an observation-based maximum number of lags.

coint(method=eg, trend=linear, lag=a, lagtype=tstat, lagpval=.15, maxlag=10) x y z

employs a cointegrating equation that includes a constant and linear trend, and uses a sequential t-test starting at lag 10 with threshold probability 0.15 to determine the number of lags.

coint(method=eg, lag=5) x y z

conducts an Engle-Granger cointegration test on the residuals from a cointegrating equation with a constant, using a fixed lag of 5.

Phillips-Ouliaris Test

coint(method=po) x y z

performs the default Phillips-Ouliaris test on the residuals from a cointegrating equation with a constant, using a Bartlett kernel and Newey-West fixed bandwidth.

coint(method=po, bw=andrews, kernel=quadspec, nodf) x y z

estimates the long-run covariances using a Quadratic Spectral kernel, Andrews automatic bandwidth, and no degrees-of-freedom correction.

coint(method=po, trend=linear, lag=1, bw=4) x y z

estimates a cointegrating equation with a constant and linear trend, and performs the Phillips-Ouliaris test on the residuals by computing the long-run covariances using AR(1) prewhitening, a fixed bandwidth of 4, and the Bartlett kernel.

Panel Tests

For a panel structured workfile,

coint(pedroni,maxlag=3,infosel=sic) x y z

performs Pedroni’s residual-based panel cointegration test with automatic lag selection with a maximum lag limit of 3. Automatic selection based on Schwarz criterion.

Cross-references