Smoothed Derived Indicators

Here the smoothed versions of the derived indicators are described.

Introduction

Smoothed versions of a base indicator offer a less jagged curve. This can be useful, for instance, to avoid whipsaw signals. They help focus on the real trend of the indicator, disregarding minor and faster fluctuations. They are commonly used to identify upturns and downturns, too, by looking at the crossings of the indicator with its smoothed version.

Smoothed Versions of the Base Indicator

Four different versions are available for each base indicator:

EMA of indicator
MA of indicator
Two EMAs of indicator
Two MAs of indicator

Moving Average

All smoothing versions are derived by applying a Moving Average (MA) to the output of a base indicator:

  smoothed = moving average (base indicator)

MA Of an Indicator

Kinds of Moving Average

Different kinds of Moving Averages (MA) exist. For all indicators denoted as

  MA of indicator name    [1]

  MA of ATR

Trading Conceiver lets you choose which moving average to apply to the indicator in order to smooth it. The selection is made in the Indicators tab. You can select between the following moving averages:

SMA (Simple Moving Average)
EMA (Exponential Moving Average)
LWMA (Linear Weighted Moving Average)
Wilder's Moving Average

For instance, if you selected the Linear Weighted Moving Average (LWMA), all indicators denoted as in [1] would be built by applying the LWMA to the output of indicator:

  LWMA (indicator)

This is a very powerful feature, letting you customize how the indicators are averaged according to the formula of your choice. This smoothed version is even more important because it is used by other composed indicators, like the ones implementing the concept of derivative, as explained in the relevant section.

Interpretation and Signals

The interpretation and the signals of the moving average of a base indicator corresponds exactly to those of the base indicator itself. They are basically the same thing.

Input Parameters Order

The input parameter for the MA, which is a lookback period, comes before the input parameters of the indicator it is applied to. For instance, in the case of the ATR indicator:

  MA lookback     (5)
  ATR lookback   (14)

Output Series

The rationale about whether plotting, on charts, only the derived smoothed indicator or even the base indicator in the same graph, is to keep the charts readable, which implies avoid cluttering the charts with too many curves. Hence, the general criterion is to plot the base indicator together with its smoothed version only for indicators, but not for overlays. Indeed, each indicator has its own chart, while all the overlays are drawn in the same chart, together with price. This is why, for example, there are two output series for

  EMA of ATR

but just one output series for

  EMA of SMA

Formulae

Given the sequence of values x(i), the following formulae hold for the average at n.

SMA

            x(n-lookback+1) + ... + x(n)
  SMA(n) = ──────────────────────────────
                     lookback

EMA


  EMA(n) = EMA(n-1) + (x(n) - EMA(n-1)) · smoothing factor
where:
                           2
  smoothing factor = ──────────────
                      lookback + 1

LWMA

             x(n-lookback+1)·1 + ... + x(n)·lookback
  LWMA(n) = ─────────────────────────────────────────
               1 + ... + (lookback-1) + lookback

Wilder's Moving Average


  Wilder(n) = Wilder(n-1) + (x(n) - Wilder(n-1)) · smoothing factor
where:
                        1
  smoothing factor = ────────
                     lookback

MA lookback = 1

Note that, for all types of MA, by selecting

  MA lookback = 1

you get exactly the input data. So:

  MA (indicator) = indicator    MA lookback = 1

EMA of an indicator

As a particular case of the MA of an indicator, the EMA of an indicator is particularly important. For indicators like:

Negative Volume Index (NVI)
Positive Volume Index (PVI)

the most important signals are given by the crossing of the indicator with its EMA. So it is essential to visualize a plot where an indicator and its EMA are drawn together. For this reason the

  EMA of indicator

has been added to the more general

  MA of indicator

It is compulsory in some cases to have the EMA available, but, simultaneously, you might want to opt for other types of MA in general. This way, you have the maximum flexibility.

Two MAs of Indicator

This is similar to the MA of an indicator explained above, but two different Moving Averages (MAs) are plotted together, a fast one and a slow one.

Input Parameters Order

In the order of the input parameters, the fast lookback comes before the slow lookback. For instance, in the case of the ATR indicator:

  Fast MA lookback     (12)
  Slow MA lookback     (26)
  ATR lookback         (14)

Two EMAs of Indicator

Again, as a particular case of two Moving Averages, having two EMAs of an indicator is particularly important. Some indicators are defined through two EMAs. For instance, given the Accumulation Distribution (AD) indicator, the Chaikin Oscillator is defined as:

  Chaikin Oscillator =
    = fast EMA(AD) - slow EMA(AD)

So it is necessary to plot the Accumulation Distribution (AD) indicator together with two of its EMAs. Moreover, in some trading algorithms it is important to watch for EMA crossing. For this reason the

  Two EMAs of indicator

has been added to the more general

  Two MAs of indicator

It is compulsory in some cases to have the two EMAs version available, but, simultaneously, you might want to opt for other types of MA in general. This way, you have the maximum flexibility.