Parametric vs. Nonprametric estimation in favor of Chaos!!!

Hi everyone.

As I promised I am uploading the results of EWRA 2015 conference (i.e. Scatter plot of models) which I used to model the water elevation in Lake Urmia that have GEV distribution as I mentioned before. The full paper of the conference will be soon uploaded in Research gate and inrested people can refer to it. In  this paper I used 11 month lagged data due to high persistence of the procedure (i.e. almost infinite). Then I used to model the water elevation by 9 different method categorized generally in parametric and non-parametric approaches. For the case of parametric approach I used multi linear regression (MLR), nonlinear regression (NLR) and decision tree (DT) while, ANN models namely radial basis function (RBF), feed forward back propagation (FFBP) and generalized regression neural network (GRN) with Gaussian transfer function were used in favor of non-parametric approach. Figure 1, shows the early results of the models indicating that parametric approaches are more favorable but FFBP still is a good competitor to the parametric results.

Fig 1. Scatter plot of all parametric and non-parametric models

The most fitted model was NLR with multiplicative nature  and this means that the procedure is extremely nonlinear. This results are in favor of some related research like Khatami Mashhadi (2013) whom tracked Chaos in the procedure.

GRN, DT and RBF shares the poorest results and generally speaking could not tracked down the real trend of the procedure.

Sincerely

Babak

Refferences:

• Khatami Mashhadi, S. (2013). Nonlinear Chaotic and Trend Analyses of Water Level at Urmia Lake, Iran.

Some Analytics

Good night.

I decided to put some of my conference paper's results in the weblog. therefore you can see them underneath. First of all, I had separated the time history of water level in lake every 107 years. you can see the results in Fig.1.

Fig.1. Trend Analysis.

you can see the changes in trends here every 107 years. It is obvius that the great changes was occurred in late 90's. Then I decided to fit the best polynomial curve for it. So here is the results (Fig.2).

Fig.2. Polynomial Curve Fitting Results.

Then, I simulated the water level in lake by ANN and MLR techniques (time-lag) and you can see the the results of GRN, MLR and RBF in Fig 3~5.

Fig.3. GRN results

Fig.4. RBF results

Fig.5. MLR results

As you can see here the best fitted model is MLR, so I think the reaction is totally linear (I didn't put the results of FFBP but I tested it, the best result was still in MLR).

Sincerely yours.

Babak Vaheddoost.