Forecasting Conditional Variance Alongside a Predicted Mean

Summary

The document considers whether the variance of an outcome should be treated as constant or modeled as changing with context. Its example is predicting NBA fantasy points: a model already estimates the expected score, and the author wants a corresponding variance estimate to use when sampling a normal distribution in a Monte Carlo simulation. The proposed constant-variance baseline is the variance calculated from all past observations.

The question suggests that conditions such as home versus away games, injuries, and opponent quality could affect dispersion as well as the expected score. It asks whether those features can improve forecasts of variance, but supplies no proposed method, results, or validation evidence. For quantitative modeling, the key issue is whether the prediction target is conditional variance: a single historical variance ignores potential changes across situations. The post does not establish that a normal distribution is appropriate, nor does it describe how to estimate or test conditional variance.

Key ideas

• A historical sample variance can serve as a baseline when assuming constant dispersion.
• The author wants to predict variance as well as the expected outcome for Monte Carlo simulation.
• Game context, injuries, and opponent strength are proposed as possible drivers of changing variance.
• The document asks about conditional variance forecasting but provides no method or empirical comparison.
• The assumed normal distribution is not evaluated in the post.

Tags

# Can variance change over time?


# Can variance change over time?












I'm working on a toy project that involves fantasy basketball, I know this is the quantitative finance stackexchange, but it seemed like the best place to ask this question.

My goal is to make predictions about fantasy points totals for different NBA players in upcoming games. I'm considering `fantasy_points_total` a continuous random variable and my goal is to predict both a) an expected mean `E(mean)` and expected variance `E(Var)`. I then want to use those predicted mean and variance to model and sample a normal distribution `N(mean, var)` in a monte carlo simulation.

I'm using a gradient boosted random forest to predict `E(mean)` and I'm satisfied with it's accuracy. I'm running into problems predicting `E(Var)`.

It seems like for a normal random variable with no changes over time one could expect that variance is constant and a decent way to calculate `E(Var)` would be to look at all past data, calculate it's variance and use that past variance as `E(Var)`.

Is it possible to get a more accurate forecast of `E(Var)` when variance might change due to other factors? For example in my case, home vs. away, injuries and opponent quality could all effect the variance of a players fantasy points expectations.

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