I only have 28 observations for a regression, while the minimum is often said to be 30. Is that ok anyway, and are there any extra security measures I can take, such as more stern application of significance (1% level)? I use an ARDL model.
Eftersom samplets storlek rekommenderas ha ett minimum av 30 observationer så skulle man kunna tänka sig att en nonparametrisk regressionsanalys skulle passa. MEN det står att den kräver ett större sampel än den parametriska så använd en nonparametrisk variansanalys istället: Kruskal-Wallis för oberoende data och Friedmans tvåvägsanalys för beroende data.
Vilken forskningsfråga har Du? Det kan hända att någon annan metod passar bättre.
It depends on the order of the AR process. For AR(1) it should be okay.. David Booth
In addition to what David said, as with any sample size issue, it depends on variance.
In the case of official energy statistics with a simple model, where an annual census might be used for regressor (predictor) data for monthly or weekly sample surveys, with low variance, 10 or fewer points are often enough - sometimes very few, especially with borrowed strength from nearby geographic regions.
The point is that variance matters, as well as the particulars of your model, such as the point David made about autoregression.
Béatrice Marianne Ewalds-Kvist -
The reason a "nonparametric" (distribution-free) test requires a larger sample is because information may be said to be lost. For example, when using a rank test, infinitely many continuous data sets could be represented by the same set of ranks. At any rate, a lone p-value is virtually meaningless without knowledge of effect size. Even then, it can be hard to interpret. If you stick to standard errors, they also change with sample size, but they are better interpreted. For the current case, the question is Standard error of what? One can look at the estimated variance of the prediction error, but that varies for each associated prediction, especially so if there is heteroscedasticity, which naturally occurs with different predicted-yi size. I have used relative standard error of predicted totals at the US Energy Information Administration. Here, some individual cases of the estimated variance of the prediction error may be useful. Sigma for the estimated residuals may often be used, but that assumes homoscedasticity, which is often a very bad leap. There are other measures, but often 'a picture is worth a thousand words,' so a "graphical residual analysis" may be very helpful. That reminds one also, that regardless of any measure, what you are looking at is just your sample, and perhaps a "cross-validation" would be useful.
The above is in response to what you wrote, but all of what I wrote may not be very relevant to the question here. I have mostly worked with finite populations, not time series, and ARDL is not a specialty for me, and I see that ARDL models assume OLS, regardless, so if one can make that work, then maybe sigma may be among the measures one could use here.
Cheers - Jim
You should have more datapoints than parameters. The more, the better.
See examples here:
www.lerenisplezant.be/fitting.htm
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