The Directional Probability Index — Estimating the Direction of the Market.

Creating a Simple Measure that Shows the Next Likely Direction.

This article discusses a simple indicator used to detect the current regime and to give contrarian signals. It is important to understand how to use indicators and how they are calculated in order to tweak them and know their limitations.

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Creating the Directional Probability Index Step-By-Step

The index is a simple calculation that will be transformed into a two-in-one indicator which has the following goals:

• Regime detection.
• Inflection point detection.

The first step is to calculate the percentage of times when the close price was higher than the open and divide it by a lookback period which is by default 13.

This gives us a sort of probability of the current regime. As simplistic as it may be, some times these types of methods help us find good opportunities.

def adder(Data, times):
    
    for i in range(1, times + 1):
    
        new = np.zeros((len(Data), 1), dtype = float)
        Data = np.append(Data, new, axis = 1)

    return Data

def deleter(Data, index, times):
    
    for i in range(1, times + 1):
    
        Data = np.delete(Data, index, axis = 1)

    return Data

def directional_probability_index(Data, lookback, open_column, close_column, where):
    
    # Adding a few columns
    Data = adder(Data, 3)
    
    # Calculating the DPI
    for i in range(len(Data)):
        
        if Data[i, close_column] > Data[i, open_column]:
            
            Data[i, where] = 1
            
    for i in range(len(Data)):
        
        Data[i, where + 1] = Data[i - lookback + 1:i + 1, where].sum()
        
    Data[:, where + 2] = (Data[:, where + 1] / lookback) * 100
    
    Data = deleter(Data, where, 2)
    
    return Data

Whenever the DPI is showing a value greater than 50%, we can consider the market to be in a bullish regime and whenever it is showing a value lower than 50%, we can consider the market to be in a bearish regime. One more utility, is that we can also use it as a reversal indicator through the concept of statistical extremes. Whenever the DPI approaches 80%, we like to think that the bullish stance is overheating and might correct and whenever the DPI approaches 20%, we can expect that the bearish stance is at its extreme and might correct with a bullish reaction.

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Using the Directional Probability Index

Having discussed the two ways of using the DPI, we will now proceed into applying them. We will understand at each time step, what the current regime is and whether we expect a reaction or not. Let us first code the signal function for the reactions:

• A long (Buy) signal is generated whenever the 13-period DPI is at 20% or lower.
• A short (Sell) signal is generated whenever the 13-period DPI is at 80% or higher.

def signal(Data, indicator_column, buy, sell):
    
    Data = adder(Data, 10)
        
    for i in range(len(Data)):
            
        if Data[i, indicator_column] < 20 and Data[i - 1, indicator_column] > 20 and Data[i - 2, indicator_column] > 20: 
               
               Data[i, buy] = 1

        elif Data[i, indicator_column] > 80 and Data[i - 1, indicator_column] < 80  and Data[i - 2, indicator_column] < 80: 
               
               Data[i, sell] = -1
               
    return Data

my_data = directional_probability_index(my_data, 13, 0, 3, 4)        
my_data = signal(my_data, 4, 6, 7)

Now, we will color-code the charts following these rules:

• The bar is colored in blue if the current 13-period DPI is showing a reading above 50%.
• The bar is colored in brown if the current 13-period DPI is showing a reading below 50%.

def ohlc_plot_candles(Data, window):
      
    Chosen = Data[-window:, ]
    
    for i in range(len(Chosen)):
        
        plt.vlines(x = i, ymin = Chosen[i, 2], ymax = Chosen[i, 1], color = 'black', linewidth = 1)  
        
        if Chosen[i, 4] > 50:
            color_chosen = 'blue'
            plt.vlines(x = i, ymin = Chosen[i, 0], ymax = Chosen[i, 3], color = color_chosen, linewidth = 3)

        if Chosen[i, 4] < 50:
            color_chosen = 'brown'
            plt.vlines(x = i, ymin = Chosen[i, 3], ymax = Chosen[i, 0], color = color_chosen, linewidth = 3)  
            
    plt.grid()

def signal_chart(Data, close, what_bull, what_bear, window = 500):   
     
    Plottable = Data[-window:, ]
    
    fig, ax = plt.subplots(figsize = (10, 5))
    
    ohlc_plot_candles(Data, window)

    for i in range(len(Plottable)):
        
        if Plottable[i, what_bull] == 1:
            
            x = i
            y = Plottable[i, close]
        
            ax.annotate(' ', xy = (x, y), 
                        arrowprops = dict(width = 9, headlength = 11, headwidth = 11, facecolor = 'green', color = 'green'))
        
        elif Plottable[i, what_bear] == -1:
            
            x = i
            y = Plottable[i, close]
        
            ax.annotate(' ', xy = (x, y), 
                        arrowprops = dict(width = 9, headlength = -11, headwidth = -11, facecolor = 'red', color = 'red'))

The above chart shows the indicator applied to a clean chart. The bars in blue indicate a bullish regime and when we encounter a red arrow, it means that we expect a reaction to the downside. The bars in brown indicate a bearish regime and when we encounter a green arrow, it means that we expect a reaction to the upside.

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Conclusion

Remember to always do your back-tests. You should always believe that other people are wrong. My indicators and style of trading may work for me but maybe not for you.

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