Comprehensive Time-Series Regression Models Using GRETL -- U.S. GDP and   Government Consumption Expenditures & Gross Investment from 1980 to 2013
  Using Gretl, I apply ARMA, Vector ARMA, VAR, state-space model with a Kalman filter, transfer-function and intervention models, unit root tests, cointegration test, volatility models (ARCH, GARCH, ARCH-M, GARCH-M, Taylor-Schwert GARCH, GJR, TARCH, NARCH, APARCH, EGARCH) to analyze quarterly time series of GDP and Government Consumption Expenditures & Gross Investment (GCEGI) from 1980 to 2013. The article is organized as: (I) Definition; (II) Regression Models; (III) Discussion. Additionally, I discovered a unique interaction between GDP and GCEGI in both the short-run and the long-run and provided policy makers with some suggestions. For example in the short run, GDP responded positively and very significantly (0.00248) to GCEGI, while GCEGI reacted positively but not too significantly (0.08051) to GDP. In the long run, current GDP responded negatively and permanently (0.09229) to a shock in past GCEGI, while current GCEGI reacted negatively yet temporarily (0.29821) to a shock in past GDP. Therefore, policy makers should not adjust current GCEGI based merely on the condition of current and past GDP. Although increasing GCEGI does help GDP in the short-term, significantly abrupt increase in GCEGI might not be good to the long-term health of GDP. Instead, a balanced, sustainable, and economically viable solution is recommended, so that the short-term benefits to the current economy from increasing GCEGI often largely secured by the long-term loan outweigh or at least equal to the negative effect to the future economy from the long-term debt incurred by the loan. Finally, I found that non-normally distributed volatility models generally perform better than normally distributed ones. More specifically, TARCH-GED performs the best in the group of non-normally distributed, while GARCH-M does the best in the group of normally distributed. 
Juehui Shi
econ.GN q-fin.EC stat.AP