In the last portion of our three-part series, we will be reviewing some of the code behind the Simple Moving Average (SMA) and Exponential Moving Average (EMA) predictive indicators that we have developed. Specifically, we will spend a little bit of time looking at the EMA Projection and the EMA Projection Trend indicators, since these have seemed to be the most useful ones thus far.

Before we get into it, I would like to introduce you to the Huddle, a place where we can crowd around, look at quantitative analytics code, and share ideas. Think of it as a community of ideas and concrete code in a format that is a bit less formal than a traditional code repository might be.

EMA Projection

First up, we have the EMA Projection, which is just our standard EMA, except for the current T0, we gross slope of our line as

m = dx / dy
dx = EMA_at_T_minus_1 - EMA_at_T_minus_period_minus_1
dy = Period - 1  # because the difference in the
                 # number of bars necessarily
                 # reduces dy by 1

Specifically, the code that matters looks more like this in the real deal:

Specifically, ema is an EMA object that calculates our exponential moving average for us already. We do not have to perform all of that work again.

Period is a property that is passed into the object at runtime, and Projection is a time-series plot added to the object at runtime. By default, Period is 14.

As you can see, there’s nothing complicated about this code. The entire algorithm is really only a couple lines if you were to “golf” that code, but let’s leave it as it is for readability.

The key to this code is that it calculates the gross slope of the line. It does not compute the derivative, which would give us the true slope. Perhaps we can fix that another time, but so far, calculating the slope using the most recent T-1 data with the T-N data has proved effective enough.

EMA Projection Trend

Building on the code from the EMA Projection, we have the EMA Projection Trend. It is a simple extension to the EMA Projection, but it provides a much clearer view of momentum. Specifically, it shows the changes in the slope of our EMA Projection as a proxy of momentum, which is a proxy of volatility, where larger bars indicate more change in the trend.

Altogether, this indicator seems to respond well to trend changes and can let us catch rides after it confirms other leading indicators. At least I have enjoyed using it.

Without further delay, here is the entire algorithm:

As one can tell, it uses our EMA Projection. It performs a simple comparison of the T0 projection to the most recent prior projection at T-1. This shows us the trend and lets us see the momentum of our projection as it progresses.

The reason for TrendUp and TrendDown calculations being separate is because they are actually two different time-series plots. This allows us to choose distinct colors and is how we can show both green and red bars efficiently.

That’s All!

And with that, that’s all we have for today. This series is really supposed to be a three-part series, but having written what I have, I believe there is the possibility of some more talk on using moving averages as leading indicators.

In the first part of our story, we discussed the Simple Moving Average (SMA) Projection line that showcased the SMA and a projection of the SMA in the next time step. From this, we could determine a little bit about volatility and also where the projections look like the current price action should be going.

I concluded my analysis of the SMA Projection as saying that I would not rely on it, but I think that I had spoken too soon. I performed more research on the idea and came up with another concept called the SMA Projection Trend, which is the same data, except it is instead represented as the difference between the current T0 projection and the most recent T-1 projection.

However, this will not be about the SMA Projection and SMA Projection Trend indicators. Instead, I have found more utility in the EMA Projection and Exponential Moving Average (EMA) Projection Trend indicators. The EMA is more responsive to immediate events and exponentially decays the more historic data to give a an average that is more biased towards recent data, which is important for traders that care about current price action.

Whether talking about the SMA or EMA Projection Trends, they both measure momentum, which also takes into account volatility. For example, looking at the next chart, you can see captured momentum soon after the RSI crossed into overbought territory.

To get a clearer picture, I have zoomed into the area of interest. For a 30 minute period, the RSI crossed into overbought territory before returning to normal. That was our first signal that we should begin paying attention for a good entrance, but we did not receive confirmation until three hours later that momentum was finally beginning to move downward.

Patience is key. The more confirmation signals you have, the more reliable your entrance.

In my opinion, we would have actually entered a short position three and a half hours after the RSI overbought signal, because we would have wanted to confirm that the close of the first downward momentum bar we saw actually closed down. Remember, patience is key, and before entering any position based on technical or fundamental data, acquiring a lot of confirming signals adds fuel to the fire for your entrance.

Use a critical eye. Nothing is guaranteed.

Combined with some other indicators, such as the ATR, RSI and perhaps the Bollinger bands if it suits you, the Projection Trend seems to be a pretty reliable detector. As a word of caution, however, you must look at the charts and these indicators with a critical eye, because unforeseen events can occur that lead them to lie to you. Therefore, always ensure you are paying attention to as much general information as you can.

To aid in preventing these pitfalls of unforeseen challenges, I recommend setting appropriate trailing stops. You can choose these to suit your own risk levels, but I would think the ATR can help you do this by looking at the total level of volatility over the last several bars of information. Perhaps you would want to do 2x ATR, or perhaps you would want to calculate the volatility through the Black-Scholes equation and use that to determine potential price movements. However you do it is an exercise left to the reader, but these are just some ideas.

Come back again as one more part to this series will be released that links to Happiness Enterprises’ github repo with these models in it. If you have Ninja Trader 8, you will be able to use them directly, and if not, well, you can at least translate the code to your own platform of choice.

Everyone is likely familiar with the simple moving average (SMA). In trading, it is a lagging indicator used to visualize the average trend of price action over windows of time. Below is a chart with the SMA(14) plotted on it. Each data point corresponds with the average closing price of the 14 closing prices preceding it.

As you can see, the SMA(14) follows the general trend of the chart, but one thing is clear: it’s always lagging behind the actual price movement:

Visually, it appears that the SMA is shifted right of the price bars. In essence, they are, because the SMA lags. Also, since the SMA is an average of the previous prices, the curve is smoother and seems to travel somewhere close to the middle of the price action. Averages being averages, however, this will not always be the case.

So what can we do?

If moving averages are lagging, is there any way we can use them to predict the next value? Actually, there is.

Going back to geometry class, one might remember computing the slope of a line: y = dy / dx. The concept is simple enough: compute the difference in price from the T-1 time to the T-Tx time. In our case, since we are assuming 14 time periods, then it would be T-14 time periods. The difference in time would then be 13, because there are only 13 time periods separating time period T-1 to time period T-14.

Analysis

Given the above formula, let’s look at something we shall call the “SMA Projection”, because it can be used to project or predict the next value in the series based on the calculation of average price changes over time.

The color scheme above is a little different than earlier. This time, the goldenrod color is the SMA(14), and the aqua color is our SMA(14) projection.

Following the SMA(14) with the projection, we can consider a couple questions:

• How far away from our projections were we compared to the SMA that was ultimately calculated? The closer we are, the less volatility there is, and the more accurately we have predicted where the average is moving.
• How far away from our projections were we compared to the actual closing price? Again, the closer we are, the less volatility there is, and the more accurately we have predicted where price action is moving.

Can we trade based on this?

Looking closely at the above charts, it is possible to surmise some patterns that could lead to profitable trades:

• If the open is below the prediction but the slope of the prediction is increasing, we could assume that price action is beginning to move upward in the direction of the averages, and we should enter long.
• Conversely, if the open is above the prediction but the slope of the prediction is decreasing, we could assume that price action is beginning to move downward in the direction of the averages, and we should enter short.

Looking at the charts, we can see several possible opportunities like this. We can also see that there are several false positives as well.

Do we use this?

Personally, I would not use this as a very effective predictive measure on its own. Combined with Bollinger bands, it may be more effective, but it is still based on lagging data. The lag can be improved by shortening the time period of the SMA, but then it becomes more like looking at current price action rather than trends. If you want to play with that, however, you can try several, maybe starting with a period length of 5 rather than 14.

Conclusion

The point of this article was to serve as an easy-to-understand introduction to predictive analytics. Most people understand moving averages, and the simple moving average is the easiest of them all to grasp.

So what exactly is happening, and how can we leverage it? Well, predictive analytics basically involves determining the slope of a “line” or some other higher-dimensional surface and then predicting the next value on that surface by following the slope. Even when reaching the level of neural networks, although the math becomes more complicated, a slope is ultimately determined, and we use it to compute which category our next predicted data point is at time T. Although, in the case of neural networks, the opposite question can be asked: given actual input appearing right now, what category is it?

What’s next?

In our next article, we will continue to explore the SMA Projection in code. This will allow readers to become familiar with coding and the basic math involved before we begin moving to more advanced models.