Building Inputs From Earlier Days

A regression model expects rows of inputs and corresponding answers. Botie's demand log is just one sequence. We need to decide which earlier entries belong beside each future target before we can fit anything.

For each target day, take the two preceding days in chronological order. Then slide that window forward by one position. Keeping the dates aligned is the first part of building a forecasting model.

Increase the history window and notice which early days no longer have enough preceding readings. Each surviving row must end before the day it predicts.

Each row will represent one forecast: the readings available when we make it, paired with the later value we want to predict. With two lags here, the older reading goes in column zero and the newer one in column one. We must use that order when predicting too.

The first two dates do not have enough preceding readings for complete rows. We omit them. Filling that unavailable history with zeros would tell the model that measurements existed when they did not.

Series = [4,6,5,9]
X = [[4,6], [6,5]]
y = [5,9]

The target is the entry immediately after each input window.

A trailing mean summarises only the past window. It can reduce sensitivity to a single noisy reading, at the cost of discarding the order within that window.

A centred moving average is different: it can include observations after the position being summarised. That can help retrospective smoothing but can leak future information if used carelessly as a forecasting feature.

First trailing mean = (4 + 6) / 2 = 5
Second trailing mean = (6 + 5) / 2 = 5.5

We calculate each summary from its input row before examining the target.

A weather forecast issued yesterday might be available now, while tomorrow's measured rainfall is not. A record's measurement date alone does not prove it was available when a prediction was made.

Historical backtests should reproduce publication delays, late corrections, and missing readings where they matter. Replacing an old forecast with today's revised record can create an unrealistically easy problem.

Lagging a column is necessary in some tasks, but it is not a complete availability audit.

import numpy as np
readings = np.array([10, 12, 11, 15])
target_position = 2
features = readings[target_position - 2:target_position]
target = readings[target_position]
print(features.tolist())
print(int(target))

[10, 12]
11

Print a few input rows with their target dates. Check the first and last rows manually, including the oldest and newest entries. This often reveals an off-by-one error more clearly than a model score does.

Botie's workshop constructs the past-only rows and averages each row. It is a moving-mean predictor, not an autoregressive model with fitted coefficients.

The next lessons decide what structure to model once the table is aligned.

For a one-day forecast, the label follows the newest feature immediately. For a two-day forecast, an extra day lies between the newest available observation and the target. Shifting the feature window without shifting the target accordingly changes the task.

Print the first and last training rows with their time positions before fitting. This catches off-by-one errors more clearly than inspecting a final model score.

import numpy as np
y = np.array([10.,12.,14.,16.,18.,20.])
rows, targets = [], []
for origin in range(1, len(y)-2):
    rows.append(y[origin-1:origin+1])
    targets.append(y[origin+2])
print(np.array(rows).tolist())
print([float(value) for value in targets])

[[10.0, 12.0], [12.0, 14.0], [14.0, 16.0]]
[16.0, 18.0, 20.0]

Tomorrow's weekday or a scheduled watering event may already be known today. Tomorrow's actual temperature is not. A forecast can use a weather forecast issued today, but training must use comparable historical forecasts rather than the later observed weather.

Record issue times for external inputs. Revised forecasts and backfilled measurements can leak later information into a retrospective feature table even when the target column is shifted correctly.