Estimating Data Use in Moving Average Crossover Strategies

Summary

The document discusses how moving average choices affect the data consumed by a crossover strategy when estimating degrees of freedom. It compares crossovers using high or low prices and simple or exponential moving averages, applying a definition that subtracts strategy rules and the observations those rules require from the full sample.

The response gives estimates for four configurations. Two simple moving averages with lookbacks of 10 and 20 are said to consume 20 observations, whether both use high prices or both use low prices. Pairing a 10-period simple average with a 20-period exponential average is estimated to consume 54 observations under a conservative approach, but possibly 20 under a liberal one. These estimates are specific to the stated configurations; the source does not explain the derivation of the exponential-average estimate. Total degrees of freedom also depend on other strategy rules, such as entry and exit conditions or filters.

Key ideas

• A moving average crossover consumes observations needed to calculate its averages.
• The stated 10- and 20-period simple moving average pairs consume 20 observations.
• A 20-period exponential average may consume more data under a conservative convention than under a liberal one.
• Additional entry, exit, and filter rules also reduce a strategy's degrees of freedom.

Tags

# Degrees of freedom in moving average crossover strategies with varying parameters


# Degrees of freedom in moving average crossover strategies with varying parameters












How might variables, such as using high price vs low price or Simple moving average (SMA) vs exponential moving average (EMA), influence a determination of degrees of freedom or data points that are consumed by a moving crossover strategy.

How many degrees of freedom are consumed by a moving average crossover strategy in the following 4 cases?

SMA (10, high), SMA (20, high) SMA (10, low), SMA (20, low) SMA (10, high), EMA (20, high) SMA (10, high), EMA (20, low)

As defined by Pardo

> degrees of freedom = whole data sample – rules and conditions – data consumed by rules and conditions

I realize that there might be different answers depending on a more conservative or liberal approach.

## Answer by Content_Quantinsti (score 0)

https://quant.stackexchange.com/a/80960

Defined for both conservative and liberal approach

MA (10, high) vs SMA (20, high): 20 data points (conservative and liberal).

SMA (10, low) vs SMA (20, low): 20 data points (conservative and liberal).

SMA (10, high) vs EMA (20, high): 54 data points (conservative), possibly 20 (liberal).

SMA (10, high) vs EMA (20, low): 54 data points (conservative), possibly 20 (liberal).

In all cases, the exact degrees of freedom also depend on the number of rules and conditions applied to the strategy (e.g., entry/exit conditions, filters).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.