Moving averages

See computation details in the associated notebook.

To identify a bullish/bearish trend, one can look whether the price is above/below the moving average. Using a larger window allows to detect more persistent moves.

Note: the below draw is a visual memo to remember how to detect trends with the relationship price/MA.

• prices above the MA => bullish trend

• price below the MA => bearish trend

Simple moving average

Using only a SMA is not ideal to detect persistent moves. One can use a confirmation lag to make sure the trend is here since some time.

Exponential moving average

The EMA is more sensitive than the SMA (= it reverses faster). It can be compared with a SMA with a shorter window in the sense that an EMA with a long window can achieve the same sensitivity. However, the EMA is in general better because it relies on more data (bigger window). \

As a reminder:

See Time Series (chapter in /Stats) to have more details.

With confirmation lag:

SMA crossover

Using a MA crossover can be seen as a variation of using a MA with a confirmation lag: instead of comparing all values in the lag with the long MA, we compare only one aggregated value (= average in the case of a SMA) with the long MA.

EMA crossover (= MACD)

MACD = Moving Average Convergence Divergence.

where:

• $EMA_{ST}$ is the short-term exponential moving average of the price –> moves fast

• $EMA_{LT}$ is the long-term exponential moving average of the price –> moves slow

As a reminder:

See Time Series (chapter in /Stats) to have more details.

Advantages of the MACD over a simple moving average:

• It oscillates around 0, hence it can easily be combined with other indicators to find signals.

• It shows the difference between moving averages of 2 different delays, hence, intuitively, we can better spot timing changes (e.g. a strong reversal). In other words, it responds quicker to price changes.

In the below graph, the MACD (red) is also represented by the gray areas.

The MACD crossover is a strategy that consists in using the MACD to detect buy and sell orders.

In addition to the MACD, the strategy involves another curve: the signal line.

The signal line is thus a lagged version of the MACD. When the MACD crosses the signal and end above it, it is a good indication to buy.

In the below, we use shift() to find first and lag price of a range.

lag = 3 is used to allow the crossover to happen on a range of observations to get more signals.

# MACD crossover (vectorized)

lag = 3
short_ema = df[column_price].ewm(span=12, min_periods=12).mean()
long_ema = df[column_price].ewm(span=26, min_periods=26).mean()
df['macd'] = short_ema - long_ema
df['signal_line'] = df['macd'].ewm(span=9, min_periods=9).mean()
df['signal_line_shifted'] = df['signal_line'].shift(lag)
df['macd_shifted'] = df['macd'].shift(lag)
df.loc[(df['macd']>df['signal_line']) & (df['macd_shifted']<df['signal_line_shifted']), 'is_macd_crossover_bullish_{}'.format(lag)] = True
df.loc[(df['macd']<df['signal_line']) & (df['macd_shifted']>df['signal_line_shifted']), 'is_macd_crossover_bullish_{}'.format(lag)] = True

Note: it is recommended to combine this indicator with a long term moving average (e.g. $EMA_{200}$).