Hi,

I have a question regarding the usage of 'p' argument in adf function.

I am checking the stationarity of an electricity spot price over a 5 years period (as a first step of performing cointegration analysis). Intuitively speaking, the price should be non-stationary.

I apply the Dickey Fuller test as the unit root test, using the function 'adf' from Spatial Econometrics Toolbox. Since the time series has a non-zero mean, I use p=0, i.e., a constant term is included in the test. According to ADF t-statistics, the time series is integrated only for very large values of lag (lag>50). For small values, it is stationary. However, if I use p=-1 instead, i.e., no deterministic part considered in the test, the time series is integrated for any lag value.

So, even though p=0 should be used in the test due to non-zero mean, p=-1 seems to give more reasonable results. Can I trust the results with p=-1 even though the time series has a non-zero mean? Or one should definitely avoid using p=-1 in case of non-zero mean?

Best,

Akin

Hi Akin:

First of all, Spatial Econometrics Toolbox is not a MathWorks product, and we do not support it.

Regarding your question about choosing an appropriate model and number of lags for the Dickey-Fuller test, I share with you a couple of notes from the help for the MathWorks Econometrics Toolbox function ADFTEST:

o A suitable value for 'lags' must be determined in order to draw valid inferences from the test. One method is to begin with a maximum lag,  such as the one recommended by Schwert [7], and then test down by assessing the significance of the coefficient of the largest lagged change in y, bp. The usual t statistic is appropriate, as reported in the reg output structure. Another method is to combine a measure of fit, such as SSR, with information criteria such as AIC, BIC, and HQC. These statistics are also reported in the reg output structure. Ng and Perron [6] provide further guidelines.

o The value of 'model' is determined by the growth characteristics of  the time series being tested, and should be chosen with a specific testing strategy in mind. As discussed in Elder & Kennedy [4], including too many regressors results in lost power, while including too few biases the test in favor of the null. In general, if a series is growing, the 'TS' model provides a reasonable trend-stationary alternative to a unit-root process with drift. If a series is not  growing, 'AR' and 'ARD' models provide reasonable stationary alternatives to a unit-root process without drift. The 'ARD' alternative has mean c/(1-a); the 'AR' alternative has mean 0.

See

http://www.mathworks.com/access/helpdesk/help/toolbox/econ/adftest.html

for the ADFTEST reference page. Also see the section of the Econometrics Toolbox User's Guide on unit root testing at

http://www.mathworks.com/access/helpdesk/help/toolbox/econ/bsf2u3f-1.html#bsf2u3f-3

I list the cited references below. I especially recommend the Elder & Kennedy article as an accessible introduction to choosing an appropriate model.

[4] Elder, J., and P. E. Kennedy. "Testing for Unit Roots: What Should Students Be Taught?" Journal of Economic Education. Vol. 32, 2001,  pp. 137-146.

[6] Ng, S., and P. Perron. "Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag." Journal of the American Statistical Association. Vol. 90, 1995, pp. 268-281.

 [7] Schwert, W. "Tests for Unit Roots: A Monte Carlo Investigation."  Journal of Business and Economic Statistics. Vol. 7, 1989,  pp. 147-159.

  Best,

  Bill Mueller
  MathWorks Computational Finance Group

Hi William,

Thanks a lot for your reply. I will check the references in detail.

In fact, the reason why I am using the Spatial Econometrics Toolbox is that conintegration methods and error correction models are not covered within MathWorks Econometrics Toolbox. Therefore, I did not even know the unit root test existed in MathWorks Econometrics Toolbox. 

The cointegration tests and ECM are included in most of the Econometrics software packages, I would say it is more or less standard... Are you planning to include them in the future releases? Or are there already some reliable Matlab functions that can be added in your toolbox.

Best, 

Akin 

"William Mueller" <wmueller@mathworks.com> wrote in message <i5o145$c0h$1@fred.mathworks.com>...
> Hi Akin:
> 
> First of all, Spatial Econometrics Toolbox is not a MathWorks product, and we do not support it.
> 
> Regarding your question about choosing an appropriate model and number of lags for the Dickey-Fuller test, I share with you a couple of notes from the help for the MathWorks Econometrics Toolbox function ADFTEST:
> 
> o A suitable value for 'lags' must be determined in order to draw valid inferences from the test. One method is to begin with a maximum lag,  such as the one recommended by Schwert [7], and then test down by assessing the significance of the coefficient of the largest lagged change in y, bp. The usual t statistic is appropriate, as reported in the reg output structure. Another method is to combine a measure of fit, such as SSR, with information criteria such as AIC, BIC, and HQC. These statistics are also reported in the reg output structure. Ng and Perron [6] provide further guidelines.
> 
> o The value of 'model' is determined by the growth characteristics of  the time series being tested, and should be chosen with a specific testing strategy in mind. As discussed in Elder & Kennedy [4], including too many regressors results in lost power, while including too few biases the test in favor of the null. In general, if a series is growing, the 'TS' model provides a reasonable trend-stationary alternative to a unit-root process with drift. If a series is not  growing, 'AR' and 'ARD' models provide reasonable stationary alternatives to a unit-root process without drift. The 'ARD' alternative has mean c/(1-a); the 'AR' alternative has mean 0.
> 
> See
> 
> http://www.mathworks.com/access/helpdesk/help/toolbox/econ/adftest.html
> 
> for the ADFTEST reference page. Also see the section of the Econometrics Toolbox User's Guide on unit root testing at
> 
> http://www.mathworks.com/access/helpdesk/help/toolbox/econ/bsf2u3f-1.html#bsf2u3f-3
> 
> I list the cited references below. I especially recommend the Elder & Kennedy article as an accessible introduction to choosing an appropriate model.
> 
> [4] Elder, J., and P. E. Kennedy. "Testing for Unit Roots: What Should Students Be Taught?" Journal of Economic Education. Vol. 32, 2001,  pp. 137-146.
> 
> [6] Ng, S., and P. Perron. "Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag." Journal of the American Statistical Association. Vol. 90, 1995, pp. 268-281.
> 
>  [7] Schwert, W. "Tests for Unit Roots: A Monte Carlo Investigation."  Journal of Business and Economic Statistics. Vol. 7, 1989,  pp. 147-159.
> 
>   Best,
> 
>   Bill Mueller
>   MathWorks Computational Finance Group

Hi Akin:

I'm not allowed to say much about what's under development here, but look for tools for cointegration analysis and error-correction modeling in an upcoming release of our Econometrics Toolbox. ;-)

  -Bill Mueller
   MathWorks Computational Finance Group