# Which Statistical Test To use?

#### pmangueira

##### New Member
HI,

I'm struggling to find out which statistical test is most appropriate to analyze the impact of negative interest rates on profitability;

Data collected:

Sample - 30 Banks
Yearly data for each variable from year end 2007 to year end 2017 - 10 years

Variables I'm considering are:

Independent - Interest Rate
Dependent - Assets; ROA; ROE; Net Interest Income; Non Interest Income; Loans/assets; Deposit/Assets; NPLs. Based on this, I believe I do not need variables on the liabilities side, but not sure of that?

Should I use Z-score/ T-student or a correlation analysis for this? Or any other test should be more appropriate for this?

Thanks
Regards

PM

#### pmangueira

##### New Member
Thanks for your reply. What do you mean? I want to assess to what extent are the variables influenced by the interest rate changes? Is there any significant statistical relationship between them? I'm not sure, i'm a bit lost actually.

#### staassis

##### Active Member
For each dependent variable, you can estimate ARMAX time series models. Before entering the dependent variable (e.g. Net Interest Income) and the independent variable (Interest Rate) into a particular model, you have to transform them to make them stationary. In other words, if a given variable is not weakly stationary, you can check whether differencing, log-differencing or something similar makes it weakly stationary. Weak stationarity can be tested using the augmented Dickey-Fuller test, among other methods.

Once a particular ARMAX model has been estimated, statistical significance of each term can be determined using a likelihood ratio test.

#### pmangueira

##### New Member
Yes, variables are not stationary, i'll start by doing that. I'm not familiar with the ARMAX time series. I'm conducting research for an executive master thesis, just for you to know that i'm not actually a "black belt in statistics" sorry for that. Why is Autoregressive Moving Average eXogenous the most appropriate? I also never used the likelihood ratio test, but as long as it suits best, i'll go read about it. I will be using STATA to perform the analysis, not sure if this restricts anything, but i believe STATA performs them all, right?