1. Continuous Wavelet of SSE (Shanghai Composite)[Daubechies 6 to Level 5]
2. SSE De-Noised with Haar wavelet and Adaptive Thresholding to Level 5
3. Residuals of SSE, Histogram, Autocorrelation and Spectrum
4. Continuous wavelet of STI (Straits Times Index)[Daubechies 6 to Level 5]
5. De-Noised STI with Haar wavelet using Adaptive Thresholding to Level 5
6. Residuals of STI, Histogram, Autocorrelation and Spectrum
Contrary to popular opinion, a market that is less-fundamentally driven [by which I mean it is more technically driven] is easier to predict. This can be illustrated with the example of the SSE versus the STI. The SSE is wilder in its swings and speculation plays a greater part. It is also more insular and less affected by international events and other international markets. The STI on the other hand is very open, and like Singapore's economy is easily rocked by international events and other markets. Trying to predict the direction and magnitude of change for tomorrow's close of the STI is nigh impossible. On the other hand, using technical analysis and other non-linear tools, it is possible to for a short period grasp the mathematical properties of the SSE for prediction purpose.Image 1 and image 4 compare a continuous wavelet (CWT) of the SSE and the STI. A CWT can capture the fractal self-simlar patterns of a time series, and looking at the SSE and the STI we see that the patterns are less defined for the STI. As an afterthought and to show you something that is even less predictable than the STI, I put the CWT of the XLF which is the iShares ETF of the US Finance Sector right at the top.In image 2 and image 4, I used a Haar wavelet to denoise the SSE and STI. The original and de-noised signals can be seen as an overlay. Unlike a moving average, wavelets have no lag. And if we were to for example put a +1 % upper band and a -1% lower band to the de-noised signal, we could use it as a Buy/Sell signal. You would be able to ignore the small moves, ride the big upswings and cut loss on the big downswings. Images 3 and 6 show that the noise removal has been quite effective. The residuals are random, the histogram is Gaussian (normal) the autocorrelations drop nicely from zero, and spectrums indicate that signal energy has been retained for the lower (significant) frequency approximations.
