My research has the dependent variable that cannot have data prior to 1995 as the existence of the variable commences since that year only. So I now have 22 annual time series data. I am testing for the determinants against 6 other variables which are strongly related to the dependent variable. My test results indicate the following:
Unit root test (DF-GLS) - stationary
ARDL F-bounds test - Cointegration exists at a 1 per cent significance level
ARDL long-run cointegration - All explanatory variables are statistically significant
ECM - Cointegration across all variables shows statistical significance
Diagnostics tests - The results validate the null hypothesis assumptions of no autocorrelation (Serial Correlation LM Test - Breusch-Godfrey), the existence of homoscedasticity (Heteroscedasticity Test: Breusch-Pagan-Godfrey), normal distribution of the residuals (Normality Test: Jarque-Bera), and a correct model specification (Ramsey RESET).
Parameter stability - CUSUM and CUSUMSQ plots are within the critical lines of 5 per cent.
Can I go ahead with this econometric analysis or is there still a possibility of a spurious regression with such data? Please share your thoughts and suggestions. Are there are any studies on similar lines i.e. small sample data for ARDL estimation that I can refer to?
I would apply Mann-Kendall test first to check if there are any trends in your variables in order to avoid spurious results.
Also perhaps you'll need to transform your data so that variance becomes more stable, but you need to first start with visual analysis.
Please let me recommend this work with visual analysis tools for your dataset:
Poster A Visual Framework for Longitudinal and Panel Studies (with ...
So the first step is to assess data quality. Then visually check if data is stationary and if any transformations are needed. Then the tools you mentioned should be applicable.
Paresh Narayan tabulated small sample critical values for the ARDL bounds testing approach. It is available as a discussion paper at Monash University.
Article Reformulating Critical Values for the Bounds F- statistics A...
The critical values were also included in the following paper:
Narayan, P.K., (2005), “The saving and investment nexus for China: evidence from cointegration tests”, Applied Economics, 37, 1979–1990.
I believe the data set with 22 observations is too small to carry out the ARDL bounds testing estimations. See the excerpt from Paresh's paper below:
"As an additional contribution to the literature, critical values for sample sizes ranging from 30–80 observations are calculated and reported in the Appendix".
Thanks so much for the inputs. I hope to get some direction from the paper.
Please ensure that the value of F-Bounds test exceeds the 5% upper bound value. Cointegration value should be negative and significant.
For classic frequentist analysis (i.e, panel model & time series); depends on the hypothesis.
There is no rules of thumbs casted on stone, that a certain number of independent variables should be the minimum in exploring the links between dependent variables and independent variables. But having 22 observations are enough and have high degree of freedom to conduct the study. However, avoid including too many variables in the same model (i.e 7 variables) may cause multicollinearity.
You can also use Bayesian estimate, in which the small samples sizes can be simulated to larger sample by MCMC....
- Badges
- Science topic
- Similar topics
- Statistics
- Time Series