Tom Starke for providing the inspiration for this article series. The code below is a modification of that which used to be found on his website leinenbock.

The following SAS Data step creates the first lagged, the first differenced and the five lagged-differenced values of the x series. A similar step is needed to create the same variables from the y series.

SAS LAG function simply looks back in the dataset nth number of records and allows you to obtain a previous value of a variable and store it in the current observation. Many times the only thing you want to do with a previous value of a variable is to compare it with the current value to compute the difference.

It is always recommended that the LAG and DIF functions not to be executed conditionally because they could cause unexpected results. If you have to use them with conditional processing of a dataset, first execute the functions and assign their results to a new variable, then use the new variable for the conditional processing.

The DIFn function works the same way as LAGn, but rather than simply assigning a value, it assigns the difference between the current value and a previous value of a variable.

Both LAG and DIF functions should only be used on the right hand side of assignment statements and again should not be executed conditionally.

The regression model used here was set as a relationship in which the value of x at the preceding time period lagged value 3 NESUG Posters of x is the dependent variable and the independent variables are the set of 5 previous-differenced values of the x series. Compare this t-value to the Critical Values see Dickey and Fuller, for the critical values to test the hypotheses that the x series is: Stationary In our example the t-value of We would fail to reject the null hypothesis and conclude that the x series is a non-stationary process when tested at level.

Differencing of a series normally transforms it from non-stationarity to stationarity. The order of integration is the number of unit roots contained in the series, or the number of differencing operations it takes to make the series stationary.

For our purpose here, since we will difference our example series once, there is one unit root, so it is an I 1 series. Once both x and y determined non-stationary at their level, we will move further to examine the nature of their linear combination.

Specifically we will be interested in examining the linear combination between the non-stationary x and y, if such a linear combination exists, then x and y series are said to be cointegrated.

The linear combination between them is the cointegrating equation and may be interpreted as the long-run equilibrium relationship among the 2 variables.

Fortunately, this test can also be accomplished using the Augmented Dickey-Fuller test and will be the subject of discussion of the second part of this series of articles. Results of this code are shown in the next page.See Dickey and Fuller (), Dickey, Hasza, and Fuller (), and Hamilton () for more information about the Dickey-Fuller test null distribution.

The preceding formulas are for the basic Dickey-Fuller test. The dicky fuller test was invented by D.A Dickey and W.A Fuller, they produced the dickey-fuller distribution relating number of test samples and the value of to a probability of a unit root.

Further reading can be found at Dickey Fuller Test – Wikipedia. THE PRESENCE OF NONSTATIONARY VOLATILITY. By. Giuseppe Cavaliere, Peter C.B. Phillips, the augmented Dickey-Fuller [ADF] test regression which is a deterministic function of the sample size.

In practice, however, applied researchers usually base their analysis on an ADF in the presence of nonstationary volatility: standard information. Furthermore, Augmented Dickey-Fuller Test in Excel incorporates a deterministic trend (and trend squared), so it allows a trend-stationary process to occur.

The main difference between the ADFTest and a normal Dickey Fuller test is that ADFTest allows for higher-order autoregressive processes. The Johansen test can be seen as a multivariate generalization of the augmented Dickey-Fuller test.

The generalization is the examination of linear combinations of variables for unit roots. The Johansen test and estimation strategy { maximum likelihood { makes it. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site.

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Dickey Fuller interpretation - Statalist