Wavelet is a newly developed technique in Economics and Finance literature. Previously this technique mostly used for image processing and signal detecting in Physics and engineering research. Recently, wavelet is the most popular approach for measuring the dynamic nature and optimum level of co-movement in global financial markets. Therefore, in the line of progress, wavelet also development many sub tools like Discrete Wavelet Transform (DWT) and Maximum Overlapping Discrete Wavelet Transform (MODWT). In DWT and MODWT techniques, we commonly decomposed data into many scales. Mostly used up to level 8 (mean D1-D8. My question is why not D1-D5, D1-D9, D1-D10 or more?
The attached PDF Wavelets Tutorials may help you: http://disp.ee.ntu.edu.tw/tutorial/WaveletTutorial.pdf
You have to read tutorial , it's related to equations used to derive the filter bank associated with this subject
The decomposition levels are undetermined. You can use different numbers of levels, such as 1, 2, 3, 4, 5, .....etc. It depends on the image size and the resulted coefficients that affect the accuracy rate.
Please explain what do you mean by D1-D8 or D1-D5?
Are they the detailed coefficients?
I think every problem has its own focus and issues. In my case I am extracting echolocation pulses from a recording of a 70 person dolphin school. In that case I want to pick out the higher frequencies and throw away the lower ones. But the echolocation sounds occupy specific frequencies and so I have to adjust depending on the sampling rate of the recordings. So I might pick D1-D1 if my sampling rate is 96Khz but D1-D3 if my sampling rate is > 500KHz. So the choice is very much depending on the context and your problem focus.
The level of decomposition depends on standard business cycles. Generally the prediction is required for hourly or half hourly then data are acquired weekly in 5 minutes interval. Then the samples are decomposed in D1 to D8 scales. If it is required quarterly prediction then according to that the data should be acquired.
Thanks Mr. K.K Gupta, my data is daily stock index time-series data. Study period 2007 to 2018. It is found that most of the researchers decomposed their data up to D8. My question is why not D9, D10 and so on?
Hi, Sahabuddin
You can decomposed it in D9 or D10 levels, but the number of samples in time series should be sufficient to predict the behavior in desired interval. They are using upto D8 because there time series data is calibrated for it.
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