Sample size calculation formula,

http://www.statisticssolutions.com/sample-size-formula/

Thanks a lot.

Thanks a lot.

Dear Sampurno,

The question is not so clear, but it is important to recognise that the minimum number of data points for fractal or chaotic analysis can be different for various time series. Smith (1988) suggested using 42^m for a reliable estimation of the dimension of an attractor where m is the smallest integer above the dimension of the attractor. However, by considering this equation, the number of minimum daily data with an embedding dimension of 4, would be about 8350 years. Nerenberg and Essex (1990) indicated that data requirement may not be so extreme and proposed to use 10^(2+0.4m) for the estimation of dimension. Further, several studies showed that the dimension of a theoretical attractor such as Mackey-Glass equation could be approximated by only using 200 data points with an insignificant overestimation (about 11%). Critical issues for the calculation of dimension estimate that you can consider (1) obtaining a reliable scaling region with the employed dataset mainly for the correlation integral method, (2) noise can be more significant than the length of data (Sivakumar 2000), (3) employing and verifying different methods for obtaining the dimension of the dataset. Please see Sivakumar (2000), Labat et al. (2016), Sivakumar (2009) and Ng et al. (2007) for more details.

Best regards,

Hakan

References

Labat D, Sivakumar B, Mangin A (2016) Evidence for deterministic chaos in long-term high-resolution karstic streamflow time series. Stochastic Environmental Research and Risk Assessment 30(8):2189-2196. doi: 10.1007/s00477-015-1175-5

Nerenberg M, Essex C (1990) Correlation dimension and systematic geometric effects. Physical Review A 42(12):7065.

Ng WW, Panu US, Lennox WC (2007) Chaos based analytical techniques for daily extreme hydrological observations. Journal of Hydrology 342(17-41.

Sivakumar B (2000) Chaos theory in hydrology: important issues and interpretations. Journal of Hydrology 227(1-4):1-20.

Sivakumar B (2009) Nonlinear dynamics and chaos in hydrologic systems: Latest developments and a look forward. Stochastic Environ Res Risk Assess 23(1027.

Smith LA (1988) Intrinsic limits on dimension calculations. Physics Letters A 133(6):283-288.

Dear Hakan,

Thanks a lot. it is really helpful.

Best regards,