W e d n e s d a y , J u n e 1 9 , 2 0 1 3

ARDL Models - Part II - Bounds Tests [Note: For an important update of this post, relating to EViews 9, see my 2015 post, here.]

Well, I finally got it done! Some of these posts take more time to prepare than you might

think.

The first part of this discussion was covered in a (sort of!) recent post, in which I gave a brief

description of Autoregressive Distributed Lag (ARDL) models, together with some historical

perspective. Now it's time for us to get down to business and see how these models have come

to play a very important role recently in the modelling of non-stationary time-series data.

In particular, we'll see how they're used to implement the so-called "Bounds Tests", to see if

long-run relationships are present when we have a group of time-series, some of which may

be stationary, while others are not. A detailed worked example, using EViews, is included.

First, recall that the basic form of an ARDL regression model is:

yt = β0 + β1yt-1 + .......+ βkyt-p + α0xt + α1xt-1 + α2xt-2 + ......... + αqxt-q + εt , (1)

where εt is a random "disturbance" term, which we'll assume is "well-behaved" in the usual

sense. In particular, it will be serially independent.

We're going to modify this model somewhat for our purposes here. Specifically, we'll work

with a mixture of differences and levels of the data. The reasons for this will become apparent

as we go along.

Let's suppose that we have a set of time-series variables, and we want to model the

relationship between them, taking into account any unit roots and/or cointegration associated

with the data. First, note that there are three straightforward situations that we're going to put

to one side, because they can be dealt with in standard ways:

1. We know that all of the series are I(0), and hence stationary. In this case, we

can simply model the data in their levels, using OLS estimation, for example.

2. We know that all of the series are integrated of the same order (e.g., I(1)), but

they are not cointegrated. In this case, we can just (appropriately) difference each

series, and estimate a standard regression model using OLS.

3. We know that all of the series are integrated of the same order, and they are

cointegrated. In this case, we can estimate two types of models: (i) An OLS regression

model using the levels of the data. This will provide the long-run equilibrating

relationship between the variables. (ii) An error-correction model (ECM), estimated

by OLS. This model will represent the short-run dynamics of the relationship between

the variables.

1. Now, let's return to the more complicated situation mentioned above. Some of

the variables in question may bestationary, some may be I(1) or even fractionally

integrated, and there is also the possibility of cointegration among some of the I(1)

variables. In other words, things just aren't as "clear cut" as in the three situations

noted above.

What do we do in such cases if we want to model the data appropriately and extract both

long-run and short-run relationships? This is where the ARDL model enters the picture.

The ARDL / Bounds Testing methodology of Pesaran and Shin (1999) and Pesaran et al.

(2001) has a number of features that many researchers feel give it some advantages over

conventional cointegration testing. For instance:

It can be used with a mixture of I(0) and I(1) data.

It involves just a single-equation set-up, making it simple to implement and interpret.

Different variables can be assigned different lag-lengths as they enter the model.

We need a road map to help us. Here are the basic steps that we're going to follow (with

details to be added below):

1. Make sure than none of the variables are I(2), as such data will invalidate the

methodology.

2. Formulate an "unrestricted" error-correction model (ECM). This will be a

particular type of ARDL model.

3. Determine the appropriate lag structure for the model in step 2.

4. Make sure that the errors of this model are serially independent.

5. Make sure that the model is "dynamically stable".

6. Perform a "Bounds Test" to see if there is evidence of a long-run relationship

between the variables.

7. If the outcome at step 6 is positive, estimate a long-run "levels model", as well

as a separate "restricted" ECM.

8. Use the results of the models estimated in step 7 to measure short-run dynamic

effects, and the long-run equilibrating relationship between the variables.

We can see from the form of the generic ARDL model given in equation (1) above, that such

models are characterised by having lags of the dependent variable, as well as lags (and

perhaps the current value) of other variables, as the regressors. Let's suppose that there are

three variables that we're interested in modelling: a dependent variable, y, and two other

explanatory variables, x1 and x2. More generally, there will be (k + 1) variables - a dependent

variable, and k other variables.

Before we start, let's recall what a conventional ECM for cointegrated data looks like. It

would be of the form:

Δyt = β0 + Σ βiΔyt-i + ΣγjΔx1t-j + ΣδkΔx2t-k + φzt-1 + et ; (2)

Here, z, the "error-correction term", is the OLS residuals series from the long-run

"cointegrating regression",

yt = α0 + α1x1t + α2x2t + vt ; (3)

The ranges of summation in (2) are from 1 to p, 0 to q1, and 0 to q2 respectively.

Now, back to our own analysis-

Step 1:

We can use the ADF and KPSS tests to check that none of the series we're working with are

I(2).

Step 2:

Formulate the following model:

Δyt = β0 + Σ βiΔyt-i + ΣγjΔx1t-j + ΣδkΔx2t-k + θ0yt-1 + θ1x1t-1 + θ2 x2t-1 + et ; (4)

Notice that this is almost like a traditional ECM. The difference is that we've now replaced

the error-correction term, zt-1 with the terms yt-1, x1t-1, and x2t-1. From (3), we can see that the

lagged residuals series would be zt-1 = (yt-1 - a0 - a1x1t-1 - a2x2t-1), where the a's are the OLS

estimates of the α's. So, what we're doing in equation (4) is including the same lagged levels

as we do in a regular ECM, but we're not restricting their coefficients.

This is why we might call equation (4) an "unrestricted ECM", or an "unconstrained ECM".

Pesaran et al. (2001) call this a "conditional ECM".

Step 3:

The ranges of summation in the various terms in (4) are from 1 to p, 0 to q1, and 0 to

q2 respectively.We need to select the appropriate values for the maximum lags, p, q1, and q2.

Also, note that the "zero lags" on Δx1 and Δx2 may not necessarily be needed. Usually, these

maximum lags are determined by using one or more of the "information criteria" - AIC, SC

(BIC), HQ, etc. These criteria are based on a high log-likelihood value, with a "penalty" for

including more lags to achieve this. The form of the penalty varies from one criterion to

another. Each criterion starts with -2log(L), and then penalizes, so the smaller the value of an

information criterion the better the result.

I generally use the Schwarz (Bayes) criterion (SC), as it's a consistent model-selector. Some

care has to be taken not to "over-select" the maximum lags, and I usually also pay some

attention to the (apparent) significance of the coefficients in the model.

Step 4:

A key assumption in the ARDL / Bounds Testing methodology of Pesaran et al. (2001) is that

the errors of equation (4) must be serially independent. As those authors note (p.308), this

requirement may also be influential in our final choice of the maximum lags for the variables

in the model.

Once an apparently suitable version of (4) has been estimated, we should use the LM test to

test the null hypothesis that the errors are serially independent, against the alternative

hypothesis that the errors are (either) AR(m) or MA(m), for m = 1, 2, 3,...., etc.

Step 5:

We have a model with an autoregressive structure, so we have to be sure that the model is

"dynamically stable". For full details of what this means, see my recent post, When is an

Autoregressive Model Dynamically Stable? What we need to do is to check that all of the

inverse roots of the characteristic equation associated with our model lie strictly inside the

unit circle. That recent post of mine showed how to trick EViews into giving us the

information we want in order to check that this condition is satisfied. I won't repeat that here.

Step 6:

Now we're ready to perform the "Bounds Testing"!

Here's equation (4), again:

Δyt = β0 + Σ βiΔyt-i + ΣγjΔx1t-j + ΣδkΔx2t-k + θ0yt-1 + θ1x1t-1 + θ2 x2t-1 + et ; (4)

All that we're going to do is preform an "F-test" of the hypothesis, H0: θ0 = θ1 = θ2 = 0 ;

against the alternative that H0 is not true. Simple enough - but why are we doing this?

As in conventional cointegration testing, we're testing for the absence of a long-run

equilibrium relationship between the variables. This absence coincides with zero coefficients

for yt-1, x1t-1 and x2t-1 in equation (4). A rejection of H0 implies that we have a long-run

relationship.

There is a practical difficulty that has to be addressed when we conduct the F-test. The

distribution of the test statistic is totally non-standard (and also depends on a "nuisance

parameter", the cointegrating rank of the system) even in the asymptotic case where we have

an infinitely large sample size. (This is somewhat akin to the situation with the Wald test

when we test for Granger non-causality in the presence of non-stationary data. In that case,

the problem is resolved by using the Toda-Yamamoto (1995) procedure, to ensure that the

Wald test statistic is asymptotically chi-square, as discussed here.)

Exact critical values for the F-test aren't available for an arbitrary mix of I(0) and I(1)

variables. However, Pesaran et al. (2001) supply bounds on the critical values for

the asymptotic distribution of the F-statistic. For various situations (e.g., different numbers of

variables, (k + 1)), they give lower and upper bounds on the critical values. In each case, the

lower bound is based on the assumption that all of the variables are I(0), and the upper bound

is based on the assumption that all of the variables are I(1). In fact, the truth may be

somewhere in between these two polar extremes.

If the computed F-statistic falls below the lower bound we would conclude that the variables

are I(0), so no cointegration is possible, by definition. If the F-statistic exceeds the upper

bound, we conclude that we have cointegration. Finally, if the F-statistic falls between the

bounds, the test is inconclusive.

Does this remind you of the old Durbin-Watson test for serial independence? It should!

As a cross-check, we should also perform a "Bounds t-test" of H0 : θ0 = 0, against H1 : θ0 < 0.

If the t-statistic for yt-1 in equation (4) is greater than the "I(1) bound" tabulated by Pesaran et

al. (2001; pp.303-304), this would support the conclusion that there is a long-run relationship

between the variables. If the t-statistic is less than the "I(0) bound", we'd conclude that the

data are all stationary.

Step 7:

Assuming that the bounds test leads to the conclusion of cointegration, we can meaningfully

estimate the long-run equilibrium relationship between the variables:

yt = α0 + α1x1t + α2x2t + vt ; (5)

as well as the usual ECM:

Δyt = β0 + Σ βiΔyt-i + ΣγjΔx1t-j + ΣδkΔx2t-k + φzt-1 + et ; (6)

where zt-1 = (yt-1 -a0 - a1x1t-1 - a2x2t-1), and the a's are the OLS estimates of the α's in (5).

Step 8:

We can "extract" long-run effects from the unrestricted ECM. Looking back at equation (4),

and noting that at a long-run equilibrium, Δyt = 0, Δx1t = Δx2t = 0, we see that the long-run

coefficients for x1 and x2 are -(θ1/ θ0) and -(θ2/ θ0) respectively.

An Example:

Now we're ready to look at a very simple empirical example. I'm going to use the data for

U.S. and European natural gas prices that I made available as a second example in my

post, Testing for Granger Causality. I didn't go through the details of testing for Granger

causality with that set of data, but I mentioned near the end of the post, and the EViews file

(which included a "read_me" object with comments about the results) is there on

the code page for this blog (dated 29 April, 2011).

If you look back at that earlier file, you'll find that I used the Toda-Yamamoto (1995) testing

procedure to determine that there is Granger causality running from the U.S. series to the

European series, but not vice versa.

A new EViews file that uses the same data for our ARDL modelling is available on

the code page, under the date for the current post. The data for the two time-series we'll be

using are also available on the data page for this blog. The data are monthly, from 1995(01)

to 2011(03). In terms of the notation that was introduced earlier, we have (k + 1) = 2

variables, so k = 1 when it comes to the bounds testing.

Here's a plot of the data we'll be using (remember that you can enlarge most of these inserts

by clicking on them):

To complete Step 1, we need to check that neither of our time-series are I(2). Applying the

ADF test to the levels of EUR and US, the p-values are 0.53 and 0.10 respectively. Applying

the test to the first-differences of the series, the p-values are both 0.00. (The lag-lengths for

the ADF regressions were chosen using the Schwarz criterion, SC.) Clearly, neither series is

I(2).

Applying the KPSS test we reject the null of stationarity, even at the 1% significance level,

for both EUR and US, but cannot reject the null of I(1) against I(2). The p-value of 10% for

the ADF test of I(1) vs. I(0) for the EUR series may leave us wondering if that series is

stationary, or not. You'll know that apparent "conflicts" between the outcomes of tests such as

these are very common in practice.

This is a great illustration of how the ARDL / Bounds Testing methodology can help us. In

order for standard cointegration testing (such as that of Engle and Granger, or Johansen) to

make any sense, we must be really sure that all of the series are integrated of the same order.

In this instance, you might not be feeling totally sure that this is the case.

Step 2 is straightforward. Given that the Granger causality testing associated with my earlier

post suggested that there is causality from US to EUR (but not vice versa), ΔEUR is going to

be the dependent variable in my unrestricted ECM:

ΔEURt = β0 + Σ βiΔEURt-i + ΣγjΔUSt-j + θ0EURt-1 + θ1USt-1 + et ; (5)

That's Step 2 out of the way!

To implement the information criteria for selecting the lag-lengths in an time-efficient way, I

"tricked" EViews into providing lots of them at once by doing the following. I estimated a 1-

equation VAR model for ΔEURt and I supplied the intercept, EURt-1, USt-1, and a fixed

number of lags of ΔUSt as exogenous regressors. For example, when the fixed number of lags

on ΔUSt was zero, here's how I specified the VAR:

After estimating this model, I then chose VIEW, LAG STRUCTURE, LAG LENGTH

CRITERIA:

I then repeated this by adding ΔUSt-1 to the list of exogenous variables, and got the following

results:

I proceeded in this manner with additional lags of ΔUSt in the "exogenous" list. I also

considered cases such as:

which resulted in the following information criteria values:

Looking at the SC values in these three tables of results, we see that a maximum lag of 4 is

suggested for ΔEURt. (The AIC values suggest that 8 lags of ΔEURt may be appropriate, but

some experimentation with this was not fruitful.)

There is virtually no difference between the SC values for the case where the model includes

just USt as a regressor (0.8714), and the case where just ΔUSt-1 is included (0.8718). To get

some dynamics into the model, I'm going to go with the latter case.

With Step 3 completed, and with this lag specification in mind, let's now look at the estimated

unrestricted ECM:

Step 4 involves checking that the errors of this model are serially independent. Selecting

VIEW, RESIDUAL DIAGNOSTICS, SERIAL CORRELATION LM TEST, I get the

following results:

m LM p-value

1 0.079 0.779

2 2.878 0.237

3 5.380 0.146

4 11.753 0.019

O.K., we have a problem with serial correlation! To deal with it, I experimented with one or

two additional lags of the dependent variable as regressors, and ended up with the following

specification for the unrestricted ECM:

The serial independence results now look much more satisfactory:

m LM p-value

1 0.013 0.911

2 3.337 0.189

3 5.183 0.159

4 7.989 0.092

5 8.473 0.132

6 11.023 0.088

7 12.270 0.092

8 12.334 0.137

Next, Step 5 involves checking the dynamic stability of this ARDL model. Here are the

inverse roots of the associated characteristic equation:

All seems to be well - these roots are all inside the unit circle.

Before proceeding to the Bounds Testing, let's take a look at the "fit" of our unrestricted

ECM. The "Actual / Fitted / Residuals" plot looks like this:

When we "unscramble" these results, and look at the fit of the model in terms of explaining

the level of EUR itself, rather than ΔEUR, things look pretty good:

We're now ready for Step 6 - the Bounds Test itself. We want to test if the coefficients

of both EUR(-1) and US(-1) are zero in our estimated model (repeated below):

The associated F-test is obtained as follows:

With the result:

The value of our F-statistic is 5.827, and we have (k + 1) = 2 variables (EUR and US) in our

model. So, when we go to the Bounds Test tables of critical values, we have k = 1.

Table CI (iii) on p.300 of Pesaran et al. (2001) is the relevant table for us to use here. We

haven't constrained the intercept of our model, and there is no linear trend term included in

the ECM. The lower and upper bounds for the F-test statistic at the 10%, 5%, and 1%

significance levels are [4.04 , 4.78], [4.94 , 5.73], and [6.84 , 7.84] respectively.

As the value of our F-statistic exceeds the upper bound at the 5% significance level, we can

conclude that there is evidence of a long-run relationship between the two time-series (at this

level of significance or greater).

In addition, the t-statistic on EUR(-1) is -2.926. When we look at Table CII (iii) on p.303

of Pesaran et al. (2001), we find that the I(0) and I(1) bounds for the t-statistic at the 10%,

5%, and 1% significance levels are [-2.57 , -2.91], [-2.86 , -3.22], and [-3.43 , -3.82]

respectively. At least at the 10% significance level, this result reinforces our conclusion that

there is a long-run relationship between EUR and US.

So, here we are at Step 7 and Step 8.

Recalling our preferred unrestricted ECM:

we see that the long-run multiplier between US and EUR is -(0.047134 / (-0.030804)) = 1.53.

In the long run, an increase of 1 unit in US will lead to an increase of 1.53 units in EUR.

If we estimate the levels model,

EURt = α0 + α1USt + vt ,

by OLS, and construct the residuals series, {zt}, we can fit a regular (restricted) ECM:

Notice that the coefficient of the error-correction term, zt-1, is negative and very significant.

This is what we'd expect if there is cointegration between EUR and US. The magnitude of this

coefficient implies that nearly 3% of any disequilibrium between EUR and US is corrected

within one period (one month).

This final ECM is dynamically stable:

As none of the roots lie on the X (real) axis, it's clear that we have three complex conjugate

pairs of roots. Accordingly, the short-run dynamics associated with the model are quite

complicated. This can be seen if we consider the impulse response function associated with a

"shock" of one (sample) standard deviation:

Finally, the within-sample fit (in terms of the levels of EUR) is exceptionally good:

In fact, the simple correlations between EUR and the "fitted" EUR series from the unrestricted

and regular ECM's are each 0.994, and the correlation between the two fitted series is 0.9999.

So, there we have it - bounds testing with an ARDL model.

[Note: For an important update of this post, relating to EViews 9, see my 2015 post, here.]

References

Pesaran, M. H. and Y. Shin, 1999. An autoregressive distributed lag modelling approach to

cointegration analysis. Chapter 11 in S. Strom (ed.), Econometrics and Economic Theory in

the 20th Century: The Ragnar Frisch Centennial Symposium. Cambridge University Press,

Cambridge. (Discussion Paper version.)

Pesaran, M. H., Shin, Y. and Smith, R. J., 2001. Bounds testing approaches to the analysis

of level relationships. Journal of Applied Econometrics, 16, 289–326.

Pesaran, M. H. and R. P. Smith, 1998. Structural analysis of cointegrating VARs. Journal

of Economic Surveys, 12, 471-505.

Toda, H. Y and T. Yamamoto (1995). Statistical inferences in vector autoregressions with

possibly integrated processes. Journal of Econometrics, 66, 225-250.

© 2013, David E. Giles

F r i d a y , J a n u a r y 9 , 2 0 1 5

ARDL Modelling in EViews 9 My previous posts relating to ARDL models (here and here) have drawn a lot of hits. So, it's

great to see that EViews 9 (now in Beta release - see the details here) incorporates an ARDL

modelling option, together with the associated "bounds testing".

This is a great feature, and I just know that it's going to be a "winner" for EViews.

It certainly deserves a post, so here goes!

First, it's important to note that although there was previously an EViews "add-in" for ARDL

models (see here and here), this was quite limited in its capabilities. What's now available is

a full-blown ARDL estimation option, together with bounds testing and an analysis of the

long-run relationship between the variables being modelled.

Here, I'll take you through another example of ARDL modelling - this one involves the

relationship between the retail price of gasoline, and the price of crude oil. More specifically,

the crude oil price is for Canadian Par at Edmonton; and the gasoline price is that for the

Canadian city of Vancouver. Although crude oil prices are recorded daily, the gasoline prices

are available only weekly. So, the price data that we'll use are weekly (end-of-week), for the 4

January 2000 to 16 July 2013, inclusive.

The oil prices are measured in Candian dollars per cubic meter. The gasoline prices are in

Canadian cents per litre, and they exclude taxes. Here's a plot of the raw data:

The data are available on the data page for this blog. The EViews workfile is on the code

page.

I'm going to work with the logarithms of the data: LOG_CRUDE and LOG_GAS. There's still

a clear structural break in the data for both of these series. Specifically there's a structural

break that occurs over the weeks ended 8 July 2008 to 30 December 2008 inclusive. I've

constructed a dummy variable, BREAK, that takes the value one for these observations, and

zero everywhere else.

The break doesn't occur at just a single point in time. Instead, there's a change in the level and

trend of the data that evolves over several periods. We call this an "innovational outlier", and

in testing the two time series for unit roots, I've taken this into account.

In a recent post I discussed the new "Breakpoint Unit Root Test" options that are available in

EViews 9. They're perfectly suited for our current situation. Here's how I've implemented the

appropriate test of a unit root in the case of the LOG_CRUDE series:

The result is:

We wouldn't reject the hypothesis of a unit root at the 5% significance level, and the result is

marginal at the 10% level. The corresponding result for the LOG_GAS series is:

In this case we'd reject the null hypothesis of a unit root at the 5% significance level, but not

at the 1% level. Overall, the results are somewhat inconclusive, and this is precisely the

situation that ARDL modelling and bounds testing is designed for. Applying the unit root

tests to the first-differences of each series leads to a very clear rejection of the hypothesis that

the data are I(2), which is important for the legitimate application of the bounds test below.

Now, let's go ahead with the specification and estimation of a basic ARDL model that

explains the retail price of gasoline in terms of past values of that price, as well as the current

and past values of the price of crude oil. We can do this in the same way that we'd estimate

any equation in EViews, but we select the "Estimation Method" to be "ARDL" (see below):

Notice that I've set the maximum number of lags for both the dependent variable and the

principal regressor to be 8. This means that 72 different model specifications will be

considered, allowing for the fact that the current value of LOG_CRUDE can be considered as

a regressor. Also, notice that I've included the BREAK dummy variable, as well as an

intercept and linear trend as (fixed) regressors. (That is, they won't be lagged.)

Using the OPTIONS tab, let's select the Schwarz criterion (SC) as the basis for determining

the lag orders for the regressors:

The model which minimizes SC will be chosen. This results in a rather parsimonious model

specification, as you can see:

I mentioned in an earlier post on Information Criteria that SC tends to select a simpler

model specification than some other information criteria. So, instead of SC, I'm going to use

Akaike's Information Criterion (AIC) for selecting the lag structure in the ARDL model.

There's a risk of "over-fitting" the model, but I definitely don't want to under-fit it. Here's

what we get:

It's important that the errors of this model are serially independent - if not, the parameter

estimates won't be consistent (because of the lagged values of the dependent variable that

appear as regressors in the model. To that end, we can use the VIEW tab to choose,

RESIDUAL DIAGNOSTICS; CORRELOGRAM - Q-STATISTICS, and this gives us the

following results:

The p-values are only approximate, but they strongly suggest that there is no evidence of

autocorrelation in the model's residuals. This is good news!

Now, recall that, in total, 72 ARDL model specifications were considered. Although an

ARDL(4,2) was finally selected, we can also see how well some other specifications

performed in terms of minimizing AIC. Selecting the VIEW tab in the regression output, and

then choosing MODEL SELECTION SUMMARY; CRITERIA GRAPH from the drop-

down, we see the "Top Twenty" results:

(You can get the full summary of the AIC, SC, Hannan-Quinn, and adjusted R2 statistics

for all 72 model specifications if you select CRITERIA TABLE, rather than CRITERIA

GRAPH.)

One of the main purposes of estimating an ARDL model is to use it as the basis for applying

the "Bounds Test". This test is discussed in detail in one of my earlier posts. The null

hypothesis is that there is no long-run relationship between the variables - in this case,

LOG_CRUDE and LOG_GAS.

In the estimation results, if we select the VIEW tab, and then from the drop-down menu

choose COEFFICIENT DIAGNOSTICS; BOUNDS TEST, this is what we'll get:

We see that the F-statistic for the Bounds Test is 32.38, and this clearly exceeds even the 1%

critical value for the upper bound. Accordingly, we strongly reject the hypothesis of "No

Long-Run Relationship".

The output at this point also shows the modified ARDL model that was used to obtain this

result. The form that this model takes will be familiar if you've read my earlier post on

bounds testing.

In the estimation results for our chosen ARDL model, if we select the VIEW tab, and then

from the drop-down menu choose COEFFICIENT DIAGNOSTICS; COINTEGRATION

AND LONG RUN FORM, this is what we'll see:

The error-correction coefficient is negative (-0.2028), as required, and is very significant.

Importantly, the long-run coefficients from the cointegrating equation are reported, with their

standard errors, t-statistics, and p-values:

So, what do we conclude from all of this?

First, not surprisingly, there's a long-run equilibrium relationship between the price of crude

oil, and the retail price of gasoline.

Second, there is a relatively quick adjustment in the price of gasoline when the price of crude

oil changes. (Recall that the data are observed weekly.)

Third, a 10% change in the price of crude oil will result in a long-run change of 7% in the

price of retail gasoline.

Whether or not these responses are symmetric with respect to price increases and price

decreases is the subject of someon-going work of mine.

© 2015, David E. Giles

Ardl With Cointegrating Bounds Using Eviews 9

Posted on May 2, 2015 by Noman Arshed

Well we can now have ARDL module in EViews 9 which can replicate same results as

compared to what Microfit can do with the advantage that we can have more than two lags

and more than 6 variables which currently available demo version of Microfit does not allow.

You can download your trial version of EViews 9 at following link

http://register1.eviews.com/demo/

In this post I will provide a brief tutorial to how to do ARDL in EViews rest of the details can

be seen from my previous ARDL manual post.

First of all we have to import the data into the EViews 9

After that we select the variables by pressing control button and selecting the dependent

variable first and independent variables after it and right click it and open it as equation. Here

in the drop down menu we can see option of ARDL at bottom

Select it. It will show the options of ARDL model

Here we can fix some particular lag or use automatic selection within the maximum lags of

dependent variable and independent variable. The automatic lag selection criteria can be

changed from default in the option window. press ok to see the ARDL model results in the

following

These are the basic results see here that there are 4 lags used for the dependent and 2 for the

first independent and 3 for the second independent variable using AIC criteria. Now we need

the Bounds F test to see if there is cointegration or not, it can be done by pressing view button

on the top and going in the coefficient diagnostics

This F test will tell if we can proceed further or not

Here we can see that our F test value of 3.5 is not bigger than any of the I1 bound value hence

there is no cointegration among these variables. Since it is a tutorial I will show you further

steps. If the F test value is small then we have to change the variables (add or remove) or try

adding trend variable. and If we find F test value larger then we can go for the Long run

results which can be seen by pressing view button and coefficient diagnostics

It will then show the short run and long run results both

Here we can see that there was no cointegration because all the long run coefficients are

insignificant and the coefficient of cointEq(-1) is also non negative and insignificant which is

with the short run coefficients. These should be significant as they are important. Further

diagnostics like hetroskedasticity, Auto-correlation etc can be done by selecting view and

residuals diagnostics.

This was the brief overview of how ARDL can be operated further details can be seen in the

blog link above.