[EquisMetaStock Group] Indeed, zero-lag trend indicators

[formulaprimer <no_reply@xxxxxxxxxxxxxxx>]

Momentum,

MS calculates momentum as (close / ref( close, -12 )) * 100

"but a liquid tradable asset has a continuous price curve. The magnitude of the price changes over a fixed look-back period, or its slope, is called Momentum of the price.
Momentum = Close(0) ? Close (-n), where n is the look back period
In our physical world, momentum is analogous to the speed of a moving car. It foretells the change in the distance traveled by the moving car. Higher the speed, the farther the car travels per fixed time intervals. Similarly, higher momentum readings indicate faster price changes. As a price curve is rising, we observe that the momentum is positive. As prices increase at a slower pace, the momentum stays positive but falls in magnitude. As the prices peak, momentum is zero since prices are neither rising nor falling, i.e., the slope of the price curve is zero(flat). After the prices peak, momentum becomes negative since slope is negative. The value of a negative momentum suggests the quality of the price decline. As the decline in prices wanes, momentum stays negative but its magnitude begins to rise. At the bottom of the decline, momentum is again zero(flat) as is the slope. Again, prices are neither falling nor rising.
Smoothing of Momentum
The problem with momentum is that it can make noisy prices even nosier. Thus we need to smooth - or even double-smooth the momentum -- to get a better read on the quality of
the price changes. The most popular smoothing method used is applying a moving average to a price curve. Moving averages of price using a short look-back periods, while introducing small lag, do not give us a smooth trending indicator. On the other hand, moving averages with long-look back periods introduce considerable lag. In contrast, in the case of the moving average of the momentum of the price curve, the longer the look back period, the lower the lag is. How come? First-year college calculus teaches us that, in the limit, a long moving average of momentum (1st derivative of the price curve) has the exact shape of the price curve. Why? The mathematical integration of the first derivative, equates to the original curve minus a constant of integration, regardless of the type of moving average applied, i.e., simple, exponential, or weighted."

To summarize, anything is possible with math even solving the lag problem...







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