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What Path For SPX? With the entire world a bit shaken by everything in it including the S&P 500 Index now would be a good time to see how the market has previously turned the corner after being clipped by a “Black Swan”. I’ll start with the monthly chart which will update monthly, weekly, daily, etc. Technical Indicators I enjoy using include moving averages, Williams Alligator, Gaussian Channels and occasionally the VSRS. I might also use ADX and RSI, occasionally. This chart includes a reversed Fibonacci Retracement Scale along with both Elliott Impulse and Correction Waves retracements of the SPX going back to August of 1982 to help us keep a calm and level mind going forward. If you take notice you will see the market is still well above the blue 100 EMA however you can observe the market has been below it several times in the history of the SPX as well as the red 200 EMA. You might also recognize the Elliot characteristics in the Elliott Impulse Wave from Aug 2009 up to the past ATH of 3393. Notice point 2 does not drop below point 0 at (c), that leg 3 is the longest, that leg 1 and 5 closely match in length and that it is also the start of the Elliott Correction Phase. Is there anything that could substantiate that? There is. The Elliot Correction Phase has undeniably begun. The low for March was a measly 162 points above being a full 50% Fib Retracement. That same low also dove below the last Elliott Impulse Wave 5. The refreshing thing I think is the Elliott Correction Wave is a simple path to follow. Hope to see all of you as we progress forward. Remember. This is not trading advice. Please engage the like button and add your comments below, Follow me if you wish, share it if you want.
TVC:SPXEducation
by Flatratepete
Why A Cascading SMA Approximate A Gaussian Filter ?Introduction The gaussian filter don't see many uses in technical analysis and financial data smoothing in general, however it possess really interesting properties and a really close relationship with the simple moving average. The gaussian filter is a filter which possess a function approximately gaussian (bell shaped curve) as : impulse response, step response and frequency response. This characteristic is pretty cool actually, the gaussian function is always mysterious. Now why do I talk about sma and estimation ? Well it is true, you can estimate a gaussian filter by applying an sma to another sma and so on such as : sma(...sma()) But why ? Just why is that so ? Well there are a lot of explanations, some of them involving the central limit theorem which would lead to a statistical explanation but I'll give a simpler explanation of this case by using signal processing. Understanding Impulses Responses The impulse response of a filter is the filter output using an impulse function as input or more simply : filter(impulse) The impulse function is a simple function equal to 1 at a certain point in time, for example we can use : impulse = 1 if t = 10 else 0, where t = 1,2,3...inf The impulse response of a filter tell us how to actually make the filter, for example : a = filter(impulse) b = sum(input*a) = filter(input) This process is called convolution, and is simply the sum of the product of two functions, the input function and the kernel function, a kernel is just a way to say filter coefficients. The Explanation Now that you know that, let's explain why sma(...sma()) approximate a gaussian filter. To do so let's take an impulse function and let's start applying an sma to it such as sma(impulse) (the sma period doesn't matter here) Only one sma give a constant, let's use two sma's such as sma(sma(impulse)) This give us a triangular function, this is why sma(sma()) is often called triangular moving average, now let's repeat the process and add more sma's. Do you see ? We are approximating a gaussian curve, if we do it many times the approximation will be even more correct. Now let's recall : The impulse response of a gaussian filter is a gaussian function f The impulse response of many sma's give a function f' who approximate a gaussian function, therefore f ≈ f' So sum(input*f') ≈ sum(input*f) and therefore sma(...sma(input)) ≈ gaussfilter(input) Note : the process of applying a filter several time is called cascading Conclusion Simple isn't it ? The simple moving average is always fun to use and posses many properties, now you don't want to use such method because it's mega inefficient. But maybe that you want to know about an efficient gaussian filter implementation ? I can work on it. Thanks for reading !
Education
by alexgrover
14