Looking at different type of trend models is important to mix up signals and provide better insights on market direction. A problem with traditional trend models is that they are often simplistic and followed by many traders. A single model is problematic because it may have issues with capturing turning points and with crowdedness.
Trend-followers will often use two moving averages or a combination of trend models to diversify signals. The ensemble approach has benefits; however, there are additional benefits if the ensemble includes two very different models which are dynamically weighted.
An approach that is starting to get more traction with forecasters is the theta model which has performed well in forecasting tests using the M3-competition data set. The theta model focuses on the second differences on a price series. Through measuring the second differences with some different scaling factors (thetas), we can decompose prices between different theta models. In a two model case, there can be a linear model (zero theta) to capture long-term trend and an exponential approach to capture curvature. The decomposition of any price series can be a weighted bundle of two models to form a ensemble forecast.
Theta measures the curvature or second derivative of the price series. If theta is zero, there is no curvature because the second derivative does not exist. Hence, it is a linear forecast. As theta increases, there is more weight on curvature. A theta of one will represent the original series. If the theta is less than one, there is a deflation of the series, but it captures turning points. If the theta value is above 1 then the forecast series is inflated with more emphasis on curvature.
We can create any number of theta models from one that is linear (theta = 0) to one that has a high theta value (theta>1) that places a high value on curvature. The idea of a theta approach is to weight two models, a linear time model which is forecasting the long-term linear movement and an exponential model that captures the turning points. Assume you want to combine two forecasts. An optimizer can be used to find the weight for each theta model that will minimize the forecast error of the combination.
What is really going on is that the trend-follower is forming an ensemble model between a linear trend and exponential model that is focused on getting the turning points, second derivatives. It will provide different insights on price movements.
See:
Grzegorz Dudek — Short-term load forecasting using Theta method
Rob J. Hyndman, Baki Billah — Unmasking the Theta method
V. Assimakopoulos, K. Nikolopoulos — The theta model: a decomposition approach to forecasting
K. Nikolopoulos, V. Assimakopoulos, N. Bougioukos, A. Litsa — The Theta Model: An Essential Forecasting Tool for Supply Chain Planning
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