1Demonstration 1 of 4
Period and amplitude, not the path
What do the two fit statistics say about the record, the model and the holdout window?
The statistics ignore phase, so the model is not rewarded for landing peaks on the record's peaks. On the window it was fitted to, both errors are small. On the earlier window the period misses by a wide margin.
Utilization is percent. The series is detrended by a straight line. The period is a lag in months, the amplitude a range in percentage points, and the autocorrelation is unitless.
Predict first. Run on the earlier window, will the fitted model's period come close to the record's 64 months?
Choose an example
Constructed example on the committed public record: the windows are the chapter's fit and holdout windows, and the model is fitted to the first.
Calculated values
- Window
- 1990 to 2019
- Series
- record
- Dominant period
- 90 months
- Amplitude (points)
- 17.96
- Mean utilization (points)
- 77.5
Amplitude = largest minus smallest value of the straight-line-detrended series = 17.96 points, and the period is the lag of the first local peak of the autocorrelation after it first crosses zero: 90 months. The raw range is 84.7 - 63.5 = 21.2 points, wider because the record drifts down. The autocorrelation at the period is a weak return, and the statistic is a first-return measure.
Use the idea
Fit a cycle on its period and amplitude, and report the holdout window beside the fit window.
Where the conclusion applies
A straight-line trend, a first-return period statistic, and an amplitude that one spike can set. The period statistic fails when the autocorrelation bumps twice before the real return.
Check your understanding: If a model cycles at 88 months where the record cycles at 64, what is the period error?
Chapter 38 source: section "How the fit was scored". Demonstration C38-D01.
2Demonstration 2 of 4
Sensible at every step, and still a cycle
Which investment rule cycles, and does that depend on where demand sits?
Build when margins are good responds to a margin that is six months old and lands plants eighteen months later, so the response arrives after the signal has gone. A dead band or a response to current utilization removes part of that lag.
Utilization is percent of capacity. Demand is held constant, 80 or 84 in these states. The period is in months and the amplitude in percentage points.
Predict first. At a demand of 80 does the dead band rule cycle, and at a demand of 84?
Choose an example
Constructed example on the committed public record: the structure is fitted to it, the rules are the chapter's constructed rules, and the demand of 84 is a constructed value.
Calculated values
- Rule
- Build when margins are good (fitted)
- Demand (held constant)
- 80
- Period
- 93 months
- Amplitude (points)
- 18.1
- Mean utilization
- 72.8
- Highest and lowest
- 81.9 and 64.5
- Mean bound (at least 74)
- breaks
- Amplitude bound (at most 17.96)
- breaks
Highest minus lowest = 81.9 - 64.5 = 17.4 points, and the detrended amplitude is 18.1. Mean utilization 72.8 against the record's 77.5 is (-4.7) points, and against the mean bound of 74 it breaks that bound (72.8 - 74 = (-1.2)). The cycle comes from the delays in the loop, with demand held fixed. Demand is a constructed setting, and the rules are run on the fitted structure.
Use the idea
Test a rule at the demand levels it may face, not only at the one it was tuned on.
Where the conclusion applies
Constant demand, a fifteen-year lifetime, and no entry or bankruptcy. A rule that damps at one demand level may cycle at another, as the dead band does here.
Check your understanding: A path peaks at 81.9 and troughs at 64.5. What is the raw range?
Chapter 38 source: section "Why building when margins are good is the rule that makes the cycle". Demonstration C38-D02.
3Demonstration 3 of 4
The construction delay carries the period
How far does the model's period move as the construction delay changes?
A longer delay holds more plants in progress when the margin turns, so the swing takes longer to reverse. The gain changes how hard the loop pushes against that delay.
The construction delay is in months. The investment gain is capacity growth per month per unit of excess margin. The period is a lag in months.
Predict first. If the construction delay doubles from 18 to 36 months, does the period roughly double?
Choose an example
Constructed example on the committed public record: the sweep is the chapter's, and a gain of 0.15 is a constructed value beside the fitted 0.25.
Calculated values
- Construction delay
- 18 months
- Investment gain
- 0.25
- Model period
- 93 months
- Model amplitude (points)
- 18.1
- Record period
- 90 months
Period error = |93 - 90| / 90 = 3.3 percent, inside the 20 percent tolerance. Only the delay and the gain differ between the points, the rest held at the fitted values. The fitted delay of 18 months is a property of an aggregate and the fit, not the time to build a plant, and the gain of 0.25 is the fitted value.
Use the idea
Measure a delay before fitting it, since a fitted delay of an aggregate is not a build time.
Where the conclusion applies
The perception delay, lifetime and margin sensitivity stay at the fitted values. The record cannot tell this loop from a driven one.
Check your understanding: If the model period is 105 months and the record's is 90, what is the period error?
Chapter 38 source: section "Which parameter decides it". Demonstration C38-D03.
4Demonstration 4 of 4
A period is not a date
How far does the next trough move if only the starting point in the cycle changes?
The same loop started at a different point in its cycle puts its first trough in a different year, because the pipeline of plants already ordered differs.
The start is utilization in percent at month 0. Demand is 80, so starting capacity is 100 x 80 / start in index units. Months count from the start.
Predict first. Do the first troughs of a start at 70 and a start at 86 fall within ten months of each other?
Choose an example
Constructed example on the committed public record: the structure is fitted to it, and the starting utilizations are constructed values.
Calculated values
- Start utilization
- 78
- Starting capacity (index)
- 102.6
- First trough (month)
- 29
Starting capacity = 100 x 80 / 78 = 102.6, so demand of 80 meets a utilization of 78 percent at month 0. The first trough falls at month 29. Switch to all five starts to see how far the same structure's trough date moves. The starting points are constructed settings, not records.
Use the idea
To forecast a date you need the state of the pipeline, not a better fit.
Where the conclusion applies
Only the starting capacity changes. The pipeline of plants ordered is not measured in the record, and the starts are constructed.
Check your understanding: If the earliest first trough is at month 29 and the latest at month 78, what is the spread?
Chapter 38 source: section "The phase-uncertainty envelope". Demonstration C38-D04.