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65. How to Forecast Sales with Time Series in Python (pandas and sklearn)

65.7 MAE, MAPE and Plot Past vs Forecast

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Why. “Looks okay on a chart” is not enough. MAE and MAPE give numbers you can put on WhatsApp to a manager.

What.

  • MAE — mean absolute error in the same units (₹). Easy to read.
  • MAPE — mean absolute percentage error. Good to compare scales.

How.

Score and plot

  1. Compute MAE = mean(|actual − pred|).
  2. Compute MAPE = mean(|actual − pred| / actual) * 100.
  3. Build one scoreboard for naive, seasonal naive, MA3, lag+LR.
  4. Plot actual line + forecast line; mark the split.

Worked example A — Scoreboard (Mauli May–Oct 2026).

Model MAE (₹) MAPE (%)
Naive last-value 93,583 11.87
Seasonal naive 103,867 14.58
MA(3) flat 123,416 15.85
Lag + LinearRegression 7,258 0.97
Holt-Winters (optional) 21,162 2.79

What it means. On this fictional series, lag + LR wins. Always re-check on your data.

Worked example B — MAPE in code.

import numpy as np

def mape(y, p):
    y = np.asarray(y, float)
    p = np.asarray(p, float)
    return float(np.mean(np.abs((y - p) / y)) * 100)

actual = [674800, 620700, 602500, 694700, 799900, 878700]
lr_pred = [664259, 623235, 606439, 697050, 807966, 862580]
print("MAPE %:", round(mape(actual, lr_pred), 2))

Output you should see.

MAPE %: 0.97

Worked example C — Plot.

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression

df = pd.read_csv("mauli_monthly_sales.csv", parse_dates=["month"]).sort_values("month")
# ... build pred for test months as in 65.5 ...
# plt.plot(df["month"], df["sales_inr"], label="Actual")
# plt.plot(test["month"], pred, label="Lag + LR")
# plt.axvline(pd.Timestamp("2026-05-01"), ls="--", label="Split")
# plt.legend(); plt.show()

The chapter figure ch65-forecast-plot.png shows actual vs lag+LR and Holt-Winters with the train/test line.

Mauli Kirana fictional monthly sales versus lag LinearRegression and Holt-Winters forecast

Ravindra Bagale's Tip

MAE = error in ₹. MAPE = error in %. Give managers both. The chart builds trust.