# Model Selection Criterion for Time Series Data

For the case of time-series data first OLS should be estimated so that all possible post regression diagnostics can be done on the bases of present issues appropriate model can be used.

 Diagnostic Source Model / Solution Time Series Data Non Normal Residuals (JB Test) Too many outliers (Kurtosis >> 3) Use Logarithm Model Dependent is count variable Use Poisson Regression Multicollinearity (VIF) Sample Too small Use single variable regression Variables too many Step-wise regression Indirect independent variables Indexed variables using Principle Factor analysis One independent is catalysis for another Moderator approach Few independent variables Use de-trended variables Hetroskedasticity   (BP Test) Nonlinear variances in high frequency data ARCH / GARCH model Dependent is binomial dummy Logit / probit model Dependent is multinomial dummy Multinomial logit model Mis-Specification Nonlinear form missing Incorporate nonlinear form or Use Logarithm Model Instability Data might have two or more different qualities Use independent dummy variable for quality change or event (structural break) Autocorrelation      (D-W) Some quality is interconnecting the time series residuals ECM / ARDL require unit root test and cointegration Endogeneity Valid Regression is other way around Reverse the regression or use IV / GMM regression Contemporaneous Correlation / simultaneity Regression is two way with same other independent variables VAR / VECM require unit root test and cointegration Two equations are interrelated  with same independent variables VAR / VECM require unit root test and cointegration Two equations are theoretically related with different independent variables. SURE / SEM

These models are based on statistical characteristics of the data, there are other models available too which can be used in special case for time series data.

This table provides tentative model selection criterion, they are open for suggestions.

## 9 thoughts on “Model Selection Criterion for Time Series Data”

1. Sheraz Khan says:

All the said procedure is to be followed once the unit root test is done or we need anything else before the model selection?

1. Noman Arshed says:

no only the models which are followed by auto-correlation need unit root tests.

2. sokophilip47 says:

Which model do I use when I’m faced with a combination of I(1) and I(2) variables?

1. Noman Arshed says:

Use more than one unit root test to confirm I(2) variable. Then after confirmation take first difference of I(2) variable it will become I(1) variable. Then all variables will become I(1).

1. Juliana says:

Is it proper if y is the first difference term but x is not. Because y is stationary at I (1) only if it is first differenced, otherwise, it is stationary at I(2). X is integrated at I(1).

2. Noman Arshed says:

you can do it, only if the first differenced variable is meaningful. Secondly, I(2) variables are highly rare so confirm using more than one unit root tests.

3. sowparnika says:

Different unit root test show different order of integration what should be considered.

1. Juliana says:

Thank you so much. Your blog helps me a lot.