Hi Gian

First, please see the time series plot of each of the five variables and then look at the scatter plots between each pair of variables to get some idea of how your variables are behaving during the study period.

What I understood is that a VAR model assumes each variable to be endogenous, that is, it is determined within the system. Thus, the model estimates 5 equations by Ordinary Least Square estimator. Each equation would have one of the variables as the dependent variable and other four variables (along with appropriate lags) as independent variables.

Therefore if some variables are non-stationary it would impact the estimations. The year-on-year difference would take care of the seasonality. But to make the non-stationary variables stationary, you may have to do the first-difference also and see how the coefficients change.

One suggestion: the 'monetary policy rate' variable may be constant for long periods of time with step-wise upward or downward movement. Maybe to capture the interest rate cycle, you could take the 'overnight inter-bank interest rate' as a proxy for the monetary policy rate.

Good Luck.

Arun

Definitely non-stationarity will be a problem for VAR modelling. Stationarity is necessary for modelling because it guarantees statistical properties over time of the variables. Forecasting may be reliably done.

The sample size is 10 years so small to analysis in time series model. So you must increase the sample size at least 50 years.Also I expecte that the number of variables is 5 and number of observations is 10 (# of variable half of # of observations) my be coused another propleme.

Abbas Lafta Kneehr Thank you for your answer. I think there's been a misunderstanding. My data is on a monthly basis (1999 till 09/2019). So I have 350 observations. But I have to say that I divide this period into two samples (Sample 1: 1999 till 09/2008 (117 observations) and Sample 2: 2011 till 09/2019 (105 observations)). That should be fine.

Ette Etuk Thank you for your answer. Yeah, I know that non-stationarity can cause problems but there are authors who assume that their data (e. g. y/y growth rates) are stationary, even though tests for unit roots (e. g. ADF) show the presence of one.

Arun Vishnu Kumar Thanks also to you for the answer. Yeah, exactly I took logarithmized y/y differences for prices, production and exchange rates to eliminate seasonality, but the data of the variables have still an unit root (according to the ADF). So would you differentiate them again?

I took a shadow rate as a proxy for the monetary policy rate to avoid the problem but this rate (like the 10-year government yields) are non-stationary as well.

Gian

1. What I understood from Prof Ette Etuk's reply is that if you are interested in reliable forecasts then stationarity of the variables will be necessary.

2. Another option you have is to check whether Industrial growth rate is Cointegrated with any of the other variables. If so then you could estimate a Vector Error Correction Model (VECM). In VECM, the Long-Run Equation is usually estimated in levels (growth rates here) though they are non-stationary. The Short-Run equation will be the error correction model which would be in first-differences

3. I presume that you are checking the stationarity of the 'shadow rate' and the 10-yr G-Sec yields for the two periods separately. It is likely that interest rates were mostly rising in the first period (up to 2008) and then mostly declining in the second period (from 2008). The non-stationarity may be because of the rising trend in the first period and declining in the 2nd period.

4. Another suggestion I have is that you can model using the entire time series (1999 to 2019) and use a Dummy Variable for structural break at 2008.

I would request Prof Ette Etuk 's for his guidance on the above four points.

Arun

If there is initially an upward trend and then a downward trend there is a trend. Stationarity implies the absence of trend (i.e. the trend is horizontal) and the absence of seasonality. For a stationary series the mean and variance are invariant across time.

Arun Vishnu Kumar Thank you for your suggestions! I have to say that I don't want to forecast. My purpose is to study the interrelationships between the variables and monetary shocks. As you have said, the non-stationarity of yields and interest rates will come about through the trend.

Ette Etuk Thanks also to you. Yes, I see your point. But is this trend of the shadow rates (which I want to use as a monetary policy indicator) a problem since I don't want to forecast? I mean, if I differentiated the variables again, wouldn't the economic interpretation get lost? There are some papers which also study the interrelationships in a SVAR without differencing (non-stationary variables and cointegrated).