Improve forecast with step changes #2466
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tveasey
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Nov 2, 2023
We model the level of a time series which we've observed having step discontinuities via a Markov process for forecasting. Specifically, we estimate the historical step size distribution and the distribution of the steps in time and as a function of the time series value. For this second part we use an online naive Bayes model to estimate the probability that at any given point in a roll out for forecasting we will get a step. This approach generally works well unless we're in the tails of the distribution values we've observed for the time series historically when we roll out. In this case, our prediction probability are very sensitive to the tail behaviour of the distributions we fit to the time series values where we saw a step and sometimes we predict far too many steps as a result. We can detect this case: when we're in the tails of time series value distribution. This change does this and stops predicting changes in such cases, which avoids pathologies. This fixes #2466.
tveasey
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Nov 3, 2023
We model the level of a time series which we've observed having step discontinuities via a Markov process for forecasting. Specifically, we estimate the historical step size distribution and the distribution of the steps in time and as a function of the time series value. For this second part we use an online naive Bayes model to estimate the probability that at any given point in a roll out for forecasting we will get a step. This approach generally works well unless we're in the tails of the distribution values we've observed for the time series historically when we roll out. In this case, our prediction probability are very sensitive to the tail behaviour of the distributions we fit to the time series values where we saw a step and sometimes we predict far too many steps as a result. We can detect this case: when we're in the tails of time series value distribution. This change does this and stops predicting changes in such cases, which avoids pathologies. This fixes #2466.
tveasey
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Dec 7, 2023
We model the level of a time series which we've observed having step discontinuities via a Markov process for forecasting. Specifically, we estimate the historical step size distribution and the distribution of the steps in time and as a function of the time series value. For this second part we use an online naive Bayes model to estimate the probability that at any given point in a roll out for forecasting we will get a step. This approach generally works well unless we're in the tails of the distribution values we've observed for the time series historically when we roll out. In this case, our prediction probability are very sensitive to the tail behaviour of the distributions we fit to the time series values where we saw a step and sometimes we predict far too many steps as a result. We can detect this case: when we're in the tails of time series value distribution. This change does this and stops predicting changes in such cases, which avoids pathologies. This fixes #2466.
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When creating forecasts for time series which have step changes we create a model of conditions under which we expect the time series to step, specifically the values at and interval between steps, based on historical data. This is a probabilistic model so we run a number of roll outs to estimate an expected value and distribution. We have seen this misbehaving when the forecast time series value is too far from the values for which we have a reasonable characterisation of this distribution. It would be more appropriate to be cautious in such cases: at the moment the behaviour depends on the choice of characterisation of distribution tail values. This issue covers the work to detect and avoid stepping the time series in such cases.
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