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Figure 6.  Lag of a 5-bar EMA.

The discussion of the responses of FIR and IIR filters were just precursors to the discussion of the hybrid FIR-IIR filters I propose.  This is because we must understand the components before we can appreciate the benefits of the hybrid.  Recalling the equation for an EMA, there is no reason we cannot modify it to be

Hybrid = *WMA + (1-)*Hybrid[1]

This simple change constitutes one of our hybrid filters.  All we did was insert the WMA for Price in the EMA equation.  If we insert a 4-bar WMA in a 5-bar EMA we get the frequency response shown in Figure 7.  Its lag is shown in Figure 8.  Wow!  We get a ton of additional smoothing for the minor price of only one additional bar of low frequency lag, compared to standard EMA.

Figure 7.  Frequency Response of Hybrid 4-bar WMA and 5-bar EMA filter.

Figure 8.  Lag of Hybrid 4-bar WMA and 5-bar EMA filter.

While it’s well and good that we can get additional smoothing from our Hybrid filter, let’s return to the original premise that the filter lag can be reduced.  One way of reducing lag is adding the slope of prices to the current price.  This is like making a prediction of future prices if the rate of change continues.  If we add a 1-bar momentum to the current price, this is like making a 1-bar prediction.  The equation looks like

Filt = Price + (Price – Price[1])
       = 2*Price – Price[1]

This is a kind of FIR filter, and this filter has a 1-bar lead instead of a lag.  The frequency response of this FIR filter is shown in Figure 9.  Whoa!  Not only do we not have smoothing, but the higher frequency components are actually amplified.  A 2-bar cycle is amplified by nearly 10 dB.  This amplification is why predictive filters are seldom successful – the amplified high frequency components make the prediction so erratic that the prediction is useless.