var models in stata

VAR-models in Stata

Anton ParlowLab session Econ710

UWM Econ Department

03/12/2010

Anton Parlow Lab session Econ710 UWM Econ Department ()VAR-models in Stata 03/12/2010 1 / 13

Our plan

Introduction to VAR

How to import data into Stata

Unit root tests

First differencing a time series

VAR-estimation

VAR and optimal lag length

VAR again

VAR stability

VAR forecasting

Exercises


Introduction to VAR models

A vector-autoregressive (VAR) model is a multi-variate way of modeling time series. Imagineyou have two series and want to explain these two with own past realizations and pastrealizations of the other series

e.g. GDP and defense spending help explaining each others current values

Let a simple bivariate VAR(2)-process be the following (meaning two series and two lags of theregressive terms)

yt = c1 + 11yt1 + 12yt2 + 13dst1 + 14dst2 + 1t

dt = c2 + 21dst1 + 22dst2 + 23yt1 + 24yt2 + 2t

where yt = log of real GDP and dst = log of defense spending

In general a VAR(p)-process would be:

yt = c + 1yt1 + 2yt2 . . . pytp + t where t iid N(0,)

where p is the lag length, c a vector of constants, the variance-covariance matrix of the errorterm and yt a vector containing the different time series.


Introduction to VAR models continued

To estimate a VAR-model properly, we need stationary data. Taking a look at quarterly defensespending and real GDP from 1947 to 2008 shows us a non-stationary time series having a trendalready.

As usual a series of unit-root test will help us confirming it but first let us import some data.


Importing data into Stata

Imagine someone gives you a txt-file containing defense spending and another txt-file containingreal GDP.

The easiest way is copying both files to Excel to have it in one file. Use the first row for thenames of the variables.

Then save it as csv and let it be comma-separated.

Go to Stata:

1. File Import Ascii Data created by a spreadsheet browse for the csv-file on yourcomputer

2. Ignore the options and let Stata determine which format (automatically determine delimiter,works most of the time) and click okay

3. You should see 2 new variables and have a data-set in the data-browser

4. Save it as var.dta

5. start a log-file: File Log Begin save it as .log


Unit root tests

We know the Dickey Fuller test is sensible to different options, as well the Philips Perron test and of course the proper lag lengthhas to be chosen!

Furthermore for a VAR-model both series have to be stationary.

This implies following testing strategy and imagine Schwerts rule of thumb tells you 15 lags have to be included:

dfuller lds, lags(15)

dfuller lds, lags(15) noconstant

dfuller lds, lags(15) trend

for defense spendings and for real GDP

dfuller lrgdp, lags(15)

dfuller lrgdp, lags(15) noconstant

dfuller lrgdp, lags(15) trend

and similarly you can do the same 6 tests for the Philips Perron test

pperron lrgdp, lags(15)

and so on

If we are lucky most of them tell us, these two series are non-stationary. And we get a very nice table for a term paper. Now

imagine you split the sample e.g. Cold war vs. entire period because then you have to the tests again (and another table!)


First differencing a time series

To generate a first differenced version of defense spending and real GDP, do the following:

gen flds=D.lds

gen flrgp=D.lrgdp

and save the data-set

Now its time for a VAR-estimation. We will use the standard command without any optionsand determine the lag-length after the estimation


Var estimation

The command is

var variable1 variable2

in our example it will be

var flrgdp flds

and Stata assume two lags without any option. Now we can determine the optimal lag-lengthusing information criteria like AIC, BIC and SIC. Stata will do it for us.

You can find the output attached! You should care about the significance of the lags explainingyour dependent variables. Remember Stata use L for lag e.g flrgdpL1 is the first lag of realGDP.

We will use varsoc for determining the lag-length.


Var and optimal lag-length

After estimating the bivariate VAR(2) we can use following command for figuring out theoptimal lag-length. Let us include 10 lags for testing it

varsoc, lags(10)

See output. Maybe 2 or 5 lags. The stars tell us what lag-length is picked by the criteria

If we do the same test for 5 lags

varsoc, lags(5)

Most of the stars point at 5 lags for our VAR-model. Note: Information criteria have to beminimized, thats the reason why you see the stars at certain values.


Var-estimation continued

We will estimate the bivariate VAR for 5 lags (suggested by lag-length criteria)

var flrgdp flds, lag(1 2 3 4 5)

or

var flrgdp flds, lag(1/5)

A very nice table including 5 lags for each variable e.g. defense spending are explained by pastrealizations of defense spendings and real GDP and real GDP is explained by past realizations ofreal GDP and defense spendings.

Look at the significance and the sign of the lags. Its more important than the actual magnitude(doesnt tell too much in a VAR). Because the story is more about the lag and the sign but notthe magnitude. Or we just describe these two series. The magnitudes would get more meaningin a structural VAR.


VAR stability

For a stable VAR-model we want to eigenvalues to be less than one. This can be tested afterthe estimation using following command:

varstable

gives you a table with the eigenvalues for the estimated VAR. All lie inside the unit circle andthats good.

If you use the option varstable, graph you get graph of the unit circle additional to theoutput table.

What else could be done. We could test for remaining autocorrelation in the error-terms (thereshould be none) but most of the time nobody is really doing this anymore. I guess its not toobig of a problem. So let us do a simple dynamic out of sample forecast (apparently the only onebuilt in in Stata 10..). Eviews is still more flexible and powerful in forecasting than Stata.


VAR forecasting

Stata uses two commands for forecasting after a VAR, SVAR and ECM estimation.

First you need to compute the forecast:

fcast compute m1_, step(24)

fcast compute is the command, m1_ gives a suffix to the auxiliary estimations for defensespending and real GDP. You will find the forecast for defense spending as a new variablem1_flds for example. step(24) is an option telling Stata to forecast 24 quarters out of sample.

Second you can graph the dynamic forecast for defense spending and real GDP usingfcast graph

e.g.

fcast graph m1_flrgdp m1_flds

and you get kind of nice forecast graphs.


Exercises

Do the same as above but for different sub samples. We did it for the entire period 1947 to2008. Try the Cold war period from 1947 to 1991

Just use the command for specifying the time span:

var flrgdp flds tin(1947q1,1991q4)

for the VAR-system without any lags.

And one example of a unit-root test:

dfuller lrgdp if tin(1947q1,1991q4)

Very nice command tin


Introduction to VARImporting data into StataUnit root testsFirst differencingVar estimationIntroductionOptimal lag lengthVAR estimation continuedStabilityForecasting

Exercises

var models in stata

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