Performing time series regression Stata - YouTube

In today's video tutorial we'll discuss  how can we perform time series regression  

using the software Stata. Let's take an example.  Here you can see this is Stata software and let's  

go to the data file. We have three variables  inflation, which is our dependent variable  

and we have two independent variables one is  import and another one is exchange rate, so we  

want to see the impact of import and exchange rate  on inflation. As this is time series data we have  

the last 80 years data we have started from  

1940 and this ended 2019, so last eight years  data. So it is a time series that you can see,  

right. Now first you need to declare your data set  to be time series, so to do this you need to type  

'tsset' and you can see this is the time variable  which we have decoded as a year so I put it there  

and since this is the yearly data so you  can write yearly, press enter so it says  

it is a time series data so it's from 1940  to 2019 and the change is one year. Our next  

job is to check whether this data, this  time is stationary or not, so we'll  

start by having a graphical analysis of the static  variables. So to do this you need to write 'line'  

and your dependent variable, that is inflation  and two independents, import, exchange rate  

and we'd like to put our time variables as  it is here, so here comma and then 'legend'  

and do not keep any space between legend  and this first bracket, so it will  

come just after this first bracket,  will come just after legend, so legend,  

first bracket and then 'size' and  then you can first bracket 'medsmall'

close up this bracket and press enter. Now  we can see the graphical presentation of this  

three time series data, so it denotes which,  indicates on this, you know one is the inflation,  

exchange rate, so this actually denotes  which variable and you can see here that  

these lines are actually trending upward  and almost constant from 1940 to 2020.  

So this means during specifying  our stationarity test that is  

Augmented Dickey-Fuller test that we will use  here. We have to include constant and trend  

so we will now perform Augmented  Dickey-Fuller test and this is actually called  

in abbreviation ADF test. So let's see what  happened to our variables at each level. So  

to do this we just you can take any of this  variable, so you can you need to do this  

one by one variable, so I'm just  taking one variable as an example,  

so you need to write 'dfuller' and then for  example I'm just taking import and trend because  

we need to use trend that we have seen this  from this graphical presentation just before,  

and 'lag0', so this is actually at level. Press  enter. Now you can see the p value it is not  

statistically significant, that means these  variables, this data, actually not stationary  

at level, so if it is not stationary at level,  so we need to then perform the same analysis  

but including lag length so the fuller import  trend lag, so I'm now including first lag. So now  

you can see this time it is statistically  significant right, so as it is less than one  

percent, so this is statistically significant.  That means our data is first order integrated.  

So if it is not first order integrated, then you  again need to run this same formula but adding  

more lag length here. So in this way we can check  for each of these variables and say whether they  

are stationary at level or stationary at the  first difference, or at the second difference.

So if our variable are first order integrated  or variables are stationary in first difference  

we need to perform co-integration test  to establish long-run relationship.  

Here we'll perform Johansen co-integration test.  

Our our null hypothesis is no co-integration  equation, against the alternative hypothesis  

there is co-integration relationship. However,  we need to select our determined appropriate lag  

length before running Johansen co-integration  test. So to do this we need to use this command  

'varbasic' it is actually two-step command,  so this is the first step, varbasic and our  

variable dependent variable inflation  and two independent variable  

and I can check this up to for example lag  length four you can take like length five,  

six whatever but I think it's good to  check up to five or four, so one by four.

Press enter, you will get some result here

and after this command the second step  you need to type 'varsoc' now you will get  

the selection order criteria, so these  are different criteria, so this indicates  

what appropriate lag length you need  to select. You can see here that FPE,  

AIC, HQIC and SBIC this all four actually  indicates this actually stars, stars, stars,  

stars so this all four actually indicates  appropriate lag length is 2, although LR,  

this criteria is saying that appropriate lag  length is 4, but it's the only one criteria that's  

saying this, but you say the maximum of these  these four they are actually indicating two. So  

if you see the maximum criteria, which indicates  the appropriate length you need to select that  

one ,so that is actually in this case two, so  our appropriate lag length should be two. Now  

we know our appropriate lag length, so we now can  perform Johansen co-integration test. To do this  

we need to type 'vecrank' and then our variable  so inflation is dependent on import, exchange rate

and lags and these lags that we have just  identified, it is actually two, so you need to  

write '2' and 'trend'

'(constant)' and 'levela' 'max'. So this  command you need to use this to perform  

this Johansen co-integration test. So you can see  the result of Johansen test for co-integration.

Now, the decision criteria is that,  

if your trace statistic, if it is greater  than your critical value then you will

reject the null hypothesis. So in that case,  if this trace statistic is greater than  

our maximum eigen statistic, it is greater  than critical value, in that case I can say  

that there is a co-integration equation,  a cointegration relationship exists.  

So I can see here that this 39 is greater than 29  so yeah there is one co-integration relationship,  

however this one is actually less than 15 and  this one also less than this critical value,  

similarly if you take that maximum again  test statistic, you can see here that 28 is  

greater than 20 so it also indicates that  at least one co-integration relationship,  

however these are less than the critical  value. Since both test statistics and max  

eigen statistics both are indicating that  at least one co-integration relationship  

exists, so we can perform our regression  which is in our cases it is actually,

we call it vector auto regression model. Now to  perform vector auto regression model you need to  

write our formula that is 'var' that is actually  vector auto regression model and then you need to

if you find your dependent inflation  and import, exchange rate, these two are  

independent variables and 'lags' and we previously  defined one by obviously defined that our  

appropriate length is two or  two and a bracket and enter.

So we get this vector auto regression result,  right. So this table is a little bit tricky but  

no matter to worry because, you need  to see this this actually inflation and  

this is the dependent variable and this  shows the relationship with this one.  

So if inflation is the dependent variable  and I would like to see the relationship  

with the import, so there is no significant  impact of import on inflation because it  

is not statistically significant. However  we can see here that exchange rate at the  

second order, you can see here, it is  actually statistically significant right.  

So exchange rate positively actually  affect our inflation at the second order  

and it is statistically significant. Last stage  of our analysis is the Granger causality test,  

so to perform Granger causality test, the first  step you need to type this formula so you need to  

perform vector auto regression that we already  have done here. So if you previously not and  

not do this, then you first need to run  this command and then you need to run this  

Granger causality test command. So already we  have performed this, so we got this result.  

So just after this you need to type the command  for the Granger causality which is very easy,  

just var and granger, so you can  see this is the command and press  

enter. Now you can get this result here. Now,  import and so this actually the causality  

actually runs from this one to that one, this  one to that one, this one with that one, so

you need to see this significance value, a p value  and you can see here import, this actually does  

not- Granger cause inflation because it is not  statistically significant and if you consider  

significance level of 10 percent in that case  you can say yeah exchange rate- Granger cause  

inflation and this all means this all together  does not Granger cause inflation. However,  

from here you can see that in inflation and  Granger cause import, exchange rate Granger  

cause import and these two variables together  Granger cause import, so in this way we can um  

explain the result of Granger causality thank you.