Autoregressive Distributed Lag (ARDL)

this is taro be at Purdue University Northwest and this presentation shows how to estimate the autoregressive distributed lags model using eviews I'm also going to provide some interpretations of the results and so the server begins when we have a group of time series some i0 others I want but to be sure there are no ITU's in such a case we're going to use the AR dl bounds test to investigate the short run and long run dynamics i've summarized the process for doing so here so we're going to begin by defining the error dl model and then determine the optimal lag structure and ensure the errors of the model are serially uncorrelated as well as ensure that the model itself is dynamically stable and having verified those were then going to proceed and perform the bounce test and if long run relationship exists we can then estimate the long run levels model obtain the residuals on the model and then estimate the error correction model all right so without further ado I present the AR DL model right here quick specifies both the short run and long run components of the model and in comparison to the error correction model which I brought up here we find that the error correction term the ZT is replaced in the air our DL model with the one period lag values of all the variables in the system so what we're doing in effect with the AR DL model is including the same lag terms as we would do in the error correction model which you see here is the error correction terms without risks but without restricting their coefficients and so the arrow DL model may actually be viewed as a form of unrestricted error correct model so let's go ahead and go to eviews and demo this and the two variables I'm going to use in this bivariate analysis are going to be the X which is the Chicago Board Options Exchange Volatility Index which I found to be a zero in that it is stationary at level and crude oil futures price which I found to be stationary only after first differencing so we have a group of a 0 and a 1 variable some other position VIX as my target variable so let's go to eviews so here are the variables oil and VIX alright and the first step here is to determine the optimal number of lags so for that I'm going to go to quick and then estimate var right there and make sure to check unrestricted var if it's not already checked and then I'm going to enter D VIX that's my endogenous variable and then the oil skip a space after the constant as my X a genus variable you can type in uppercase lowercase doesn't matter alright then click OK so now in this window we can then go ahead and identify the optimal lag structure by going to view lag structure and move it to the right and go to lead length criteria right here and you can leave it at us 8 or you can type a number larger than that just click OK expand this and as you can see all the elect selection criteria that you see here defined right at the bottom here settle for one lag all right as you see right here right they'll settle for one lag so that's what I'm going to use in the analysis let's shrink this back up all right so now the next thing I want to do is to estimate the AR DL model to do so I'm going to go to quick estimate equation and here's my error DL equation so d6 this is my target variable alright D is the change Delta C is constant and then the right side of the equation I have C is a constant and then D VIX and open parenthesis minus 1 so that's fixed lag one period close the parenthesis there space and then the oil I only need one lag D all open parenthesis minus one double close it there and then so these are the short run coefficients right there then introduce a long run sorry the short run terms and then for the long run terms Vic's minus 1 and then all lag one and just look at it again make sure it all looks good yeah looks good the parenthesis or where they belong and then okay so here we have it all right and so we have our output here we can see the short term coefficients right here we can see they these are the short run coefficients and we can see the long run coefficients but before we get carried away we got to do model Diagnostics all right so first off we want to check for serial correlation so we go to view residual Diagnostics and then go to serial correlation LM test click on it and we want to make sure that this is 1 because we're using one leg okay and as you can see here the p value associated with the chi-square statistic here is more than five percent away more than five percent so we cannot reject the null hypothesis the results show that there is no evidence of zero correlation so we're quite happy with that next up we're going to check for model stability and for that we bring this work okay click view and then go to stability Diagnostics right there and then we want to choose recursive estimate right here or less only click on it and let's select custom test and okay and insofar as the blue trendline here so to speak lies within the boundary we're quite fine so we conclude that this is largely the model is largely stable right so we're quite happy with that as well so having made those verifications when I'm going to go ahead and perform the bounce test to do so we click on we let's click on estimate to bring it back up and then you know here are the codes a terms that we entered before so we click okay to look at our results once again so again the coefficients are as follows one two three four five so we have five coefficients of which these last two here are the long-run coefficients alright so this is going to be C 4 and C 5 all right this is C 1 C 2 C 3 C 4 and C 5 these are our two long-run coefficients now we want to test them jointly to see if in fact it they are statistically significant so for that we go to view we go to coefficients Diagnostics and then we're going to go to wall test click on it and then we type our null hypothesis our null hypothesis is C 4 equal C 5 equals zero all right that's what we want right there and then we click OK now that's lovely right there because we have our results that's our F statistic all right and that caution based statistical significance of this F value of 8.17 is not based on it's not going to be based on this p value that you see there all right and this is where percerin comes in because he shows that the exact critical values for this F test car's not available for an arbitrary mix of a 0 and a 1 variables we have here but fortunately we have the pasaron table which provide us bounds on the critical values of the asymptotic distribution of the F statistic right here so let's go to that table right there all right and this is a reference rather so in the table we have lower bound values under I 0 and upper bound values on the right one for different levels of significance 10% 5% 2.5% 1% all right now they'll be careful to identify the portion of the table appropriate for your study the first one here is no intercept and no trend second one is restricted intercept and no trend third one here is unrestricted in assets and no trend continuing we have unrestricted innocent and restricted trend and then finally we have unrestricted in assets and unrestricted a trend the third one applies to us right here which is unrestricted intercept and no trend because in my unit root test I settle for intercept with no trend so with that going for a 5% level and my K is 1 meaning one explanatory variable which is all in this case so this is my line right here alright this is my line right here but under 5% this is what I want right here right so I find here that the lower bound is four point ninety four upper bound is five point seven three so if my calculated F test is below four point ninety four then I cannot reject the null hypothesis I would conclude that there is no long-run relationship if it is above 5.73 five point seven three five use percent it's not if it's about it then I'll say yeah I reject my h0 and conclude that there is in fact a long-run equilibrium relationship among the variables between these two numbers so that's indeterminate and as you can see right here Oh actually want to go here so you can see right here our calculated value of 8.7 8.7 teen exceeds let's go back here exceeds this upper bound and so we conclude that the model is significant in that we do have a long-run relationship between the variables six and all price so we're quite happy with that so we can now proceed an estimated error correction model but what we're going to do first is to obtain the residuals from the long-run model so to do so quick estimate equation and I'm going to have to tie the long-run model there where VIX is position is target variables C is constant and all is the explanatory variable right just click OK until a bit so that's the long-run model output so we're not going to derive the residuals of this of this long run model so actually we already have the residuals right here all right so it just spits it out automatically so what I'm going to do to use a more conventional name I'm going to copy this data set here copy and then right-click to pay and I'm going to name it ECT for error correction term something more conventional on north in earlier right there so so actually this ECT and this Raziel or the same thing if I right click this ECT and open it you're going to see the first values one point eight seven three or in going down similarly right here same thing all right in any event this is what I'm going to use in the analysis all right so now we can go ahead and estimate the error correction model and to do so I'm going to go to quick I'm going to go to estimate equation and right here I will define my ECF so it's going to be defects I'm going to second defects right there constant and then D fix lag one period make sure you double close that parentheses and then the OL lag one period that will close it to be sure and then as you know in the error correction model we need the error correction term alright and lag one period right just single parenthesis close so look at it again make sure we did well in the use of our parentheses all right that's it and so we click OK and yes and there you have it so as you can see right here in this output we have the this is our error correction model right here this is the Arabic full error correction our model with a concern the constants the coefficients of the short-term variables and importantly the coefficients of the error correction term which here is negative point 1168 this value that you see here again is our speed of adjustment toward long-run equilibrium again remember it should be negative and statistically significant because negative means that if the system is moving out of equilibrium in one direction it's going to pull it back to equilibrium and so what this is telling us is that about eleven point seven percent of departures from long-run equilibrium are corrected each period so that's quite interesting I will find that this is statistically significant right there so then we are pretty much done final check model Diagnostics do we have zero correlation in this final model so let's know hypothesis is no zero correlation so view and residual Diagnostics and again zero correlation LM test writer and don't forget we're using one lag in this example so okay and as you can see there is no evidence of zero correlation because p-value is more than five percent so we cannot reject the null hypothesis of non zero correlation and if you find that you have zero correlation in your model you could play along and and change the lags using your model to see whether by altering the lags or including additional ones reducing and including additional ones would fix the problem so and then finally we do a final model Diagnostics and check for model stability and so view and stability Diagnostics right down here and then we're going to go to recursive estimates or less only and choose custom tests again okay and we like what we see because this blue line lives within the boundary line so we conclude that the model is stable we're quite happy with this model alright and this is a wrap

Channel: Pat Obi

Views: 48,303

Rating: 4.8839049 out of 5

Keywords: ARDL, VECM, Pesaran

Id: 2t3i9UFzWks

Length: 17min 36sec (1056 seconds)

Published: Tue Aug 08 2017