Forecasting a cumulative variable in time series
<p>I'm trying to build a time series model based on a cumulative variable that never decreases.</p>

<p>I'm interested in knowing when the observable will reach a certain value (i.e., when it will intersect with the blue line in the image below).</p>

<p><a href="https://i.stack.imgur.com/aCAVF.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/aCAVF.png" alt="enter image description here"></a></p>

<p>The orange line is fixed to the last known data point and increases based on the average of the last 5 observables.</p>

<p>The red line is not fixed and represents a linear fit based on the last 5 observables. This seems problematic because in Time Period 108 in the graph, the predicted value is less than the observable in the previous time period, which will never physically happen.</p>

<p>The green line is not fixed and represents a linear fit based on all observables.</p>

<p>I'm wondering if someone can suggest an alternative/better approach to modelling this type of situation.</p>