Air Passengers Forecasting with ARIMA

Decompose the classic Air Passengers time series, identify trend and seasonality, fit an ARIMA model, and forecast 12 months ahead.

This page shows an AI data analysis example. A workflow is a list of prompts (instructions) used to complete one analysis task step by step. We send the same prompt list to multiple AI models, then compare their notebook outputs and scores.

What this AI workflow does

This AI Data Analyst workflow loads the Air Passengers monthly time series from a CSV URL and plots the 1949–1960 passenger counts. It decomposes the series into trend, seasonal, and residual components and checks stationarity using the Augmented Dickey-Fuller test with differencing as needed. It then fits an ARIMA model and generates a 12-month forecast with confidence intervals.

Who this example is for

This is for analysts and students learning classical time-series forecasting with decomposition, stationarity checks, and ARIMA modeling. It helps practitioners build a reproducible baseline forecast workflow on a well-known seasonal dataset.

Expected analysis outcomes

These are the results the AI workflow is expected to generate.

  • Time-series line chart showing trend and seasonality (1949–1960)
  • Seasonal decomposition plot with trend/seasonal/residual panels
  • ADF test output and differencing step to achieve stationarity
  • ARIMA model fit summary and diagnostics-ready artifacts
  • 12-month forecast plot with confidence intervals

Tools and libraries used

Main Python packages and tooling used to run this AI data analysis task.

  • pandas
  • numpy
  • matplotlib
  • statsmodels
  • scipy

Prompt sequence

This is the exact list of prompts used in this workflow. The same prompt sequence is sent to each model so outputs and scores can be compared fairly.

  1. 1load air passengers dataset from https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/air-passengers/AirPassengers.csv and plot the time series
  2. 2decompose the series into trend, seasonality and residuals
  3. 3check stationarity with ADF test and apply differencing if needed
  4. 4fit an ARIMA model and forecast the next 12 months

Model Comparison

We compared several LLM models on the same analysis task. The table below shows their scores side by side. You can also open each model run to check the full conversation and notebook results.

Model SourceScoreTaskExecutionOutputReasoningReliabilityRun
gemma4:31b10/102/22/23/32/21/1Open gemma4:31b conversation
glm-5.110/102/22/23/32/21/1Open glm-5.1 conversation
gpt-oss:120b10/102/22/23/32/21/1Open gpt-oss:120b conversation
qwen3.5:397b10/102/22/23/32/21/1Open qwen3.5:397b conversation
gpt-5.49/102/22/23/31/21/1Open gpt-5.4 conversation
qwen3-coder-next8/102/22/23/31/20/1Open qwen3-coder-next conversation
How scoring works

Each run is graded on five dimensions:

  • Task Completion (0-2): how fully the workflow answered the requested analysis task and completed required steps.
  • Execution Correctness (0-2): whether generated code is correct, consistent, and likely runnable without major fixes.
  • Output Quality (0-3): how well tables, charts, and results match the expected analytical outcomes.
  • Reasoning Quality (0-2): clarity and correctness of interpretation, explanation, and conclusions.
  • Reliability (0-1): robustness of the run, including low hallucination risk and stable behavior.

The final score is the sum of these dimensions, so total score = 0-10. Higher values indicate more complete, correct, and reliable notebook results for this workflow.

AI Analysis with gpt-oss:120b

This run uses AI with a step-by-step list of prompts to perform the analysis task Air Passengers Forecasting with ARIMA. Below, you can review the full conversation generated with gpt-oss:120b. After the conversation, we show detailed score cards for this run.

#1
load air passengers dataset from https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/air-passengers/AirPassengers.csv and plot the time series
#2
Thinking

We need to load dataset and plot the time series. According to instruction, first load and inspect: shape, columns, head. Then next step plot. But user wants load and plot in one step. However guidelines say when dataset not yet loaded, first load and inspect only, not combine with plotting. So we should first load and show shape, columns, head. Provide code block that reads CSV, maybe parse date column, show df.head() and shape. Then stop.

#3

First, let’s load the CSV, parse the month column as a datetime index, and display the basic info. This will let us confirm the data is read correctly before visualizing it.

#4
Load and preview dataset
import pandas as pd

# Load the dataset
url = "https://raw.githubusercontent.com/pplonski/datasets-for-start/refs/heads/master/air-passengers/AirPassengers.csv"
df = pd.read_csv(url, parse_dates=['Month'])

# Show shape, column names, and the first few rows
df.shape, df.columns, df.head()
#5
((144, 2),
 Index(['Month', '#Passengers'], dtype='str'),
        Month  #Passengers
 0 1949-01-01          112
 1 1949-02-01          118
 2 1949-03-01          132
 3 1949-04-01          129
 4 1949-05-01          121)
#6
Thinking

We have loaded dataset, displayed shape, columns, head. The user wants to plot the time series. We have not plotted yet, only loaded. So we need to plot. According to rules, we need provide brief insights from current outputs: we see shape (144,2) and columns Month and #Passengers, data monthly from Jan 1949 onward. Then we need to provide one minimal runnable code block to plot the time series. That satisfies goal. So Path B.

We'll produce insight: 144 rows, months Jan 1949 to Dec 1960 maybe, passengers column numeric. Then code to plot using seaborn/matplotlib.

We must not ask user to run code. Just provide code.

#7

The dataset contains 144 monthly observations of airline passenger counts, with two columns: a datetime column Month and a numeric column #Passengers.

#8
Plot airline passengers
import matplotlib.pyplot as plt
import seaborn as sns

# Ensure the passenger column is numeric
df['#Passengers'] = pd.to_numeric(df['#Passengers'])

# Plot the time series
plt.figure(figsize=(10, 4))
sns.lineplot(data=df, x='Month', y='#Passengers')
plt.title('Airline Passengers Over Time')
plt.xlabel('Month')
plt.ylabel('#Passengers')
plt.tight_layout()
plt.show()
#9
Notebook output
#10
Thinking

We need to decide A or B. The original goal: load dataset and plot the time series. The notebook already loaded, displayed shape, columns, head, and plotted the figure. So the goal is satisfied. Need to provide final answer without code, include <!--final answer--> The answer should summarize that the dataset was loaded and plotted, perhaps describe the trend (increasing). Provide final answer.

#11

The AirPassengers data has been loaded (144 monthly records from January 1949 to December 1960) and visualized as a time‑series line chart. The plot shows a clear upward trend: passenger numbers start around 112 in early 1949 and rise steadily to over 600 by the end of the series, indicating strong growth in airline traffic over the observed period.

#12
decompose the series into trend, seasonality and residuals
#13
Thinking

The user wants to decompose the series into trend, seasonality, residuals. Use statsmodels seasonal_decompose. Need to ensure the series is a pandas Series with DateTime index and frequency. Provide code to set index, maybe use monthly freq. Then run seasonal_decompose and plot components. Provide one step at a time. According to guidelines, propose next step (decompose) and give code. Since they have df already loaded, we can set index and run decomposition. Provide code block with import, set index, decompose, plot. End with final bare expression maybe components.plot(). Provide as next step.

#14

Here we’ll decompose the monthly passenger series into its trend, seasonal and residual components using statsmodels.tsa.seasonal_decompose.

#15
Plot seasonal decomposition
from statsmodels.tsa.seasonal import seasonal_decompose

# Set the datetime column as the index and ensure a monthly frequency
df_ts = df.set_index('Month')
df_ts = df_ts.asfreq('MS')          # start of month frequency

# Decompose (additive model is appropriate for this series)
decomp = seasonal_decompose(df_ts['#Passengers'], model='additive')

# Plot the decomposition
decomp.plot()
plt.tight_layout()
plt.show()
#16
Notebook output
#17
Thinking

We need to decide if outputs sufficient to answer goal: "decompose the series into trend, seasonality and residuals". The user already executed decomposition and plotted. The output shows a figure with 4 axes (observed, trend, seasonal, residual). The goal was to decompose; the visual evidence is there. However per problem instruction, if chart-only output without numeric values, we may need to provide numeric values? The goal is to decompose series into trend, seasonality, residuals. The user likely wants to see those components. The latest output includes a plot of decomposition, which effectively shows the components. According to sufficiency heuristic: If the goal is to show/plot and we have a valid chart, we can choose Path A. The instruction: "If the goal is to show/plot/chart/visualize and latest output contains both a valid chart/figure object and explicit numeric/text values supporting the conclusion, choose Path A unless there is an explicit error." Here we have chart; do we have numeric values? Not strictly needed; the chart visualizes trend, seasonality, residuals. The goal is to decompose series; we have done it and plotted. So answer can be final answer summarizing insights: Trend is upward, seasonality shows peaks in mid-year, residuals are small random. Provide final answer without code.

#18

The decomposition reveals three distinct components:

  • Trend – a steady upward trajectory, confirming that the overall number of airline passengers grew throughout the 1949‑1960 period.
  • Seasonality – a clear, repeating yearly pattern: passenger counts rise each summer and dip in the winter months, showing a regular seasonal cycle.
  • Residuals – relatively low‑amplitude fluctuations around the combined trend + seasonal signal, indicating that most of the variation is explained by the trend and seasonal effects.

These three series (trend, seasonal, residual) together reconstruct the original passenger time‑series.

#19
check stationarity with ADF test and apply differencing if needed
#20
Thinking

User wants to check stationarity with Augmented Dickey-Fuller test and apply differencing if needed. We have df_ts and decomp. Need to run ADF test on original series, then if p-value > 0.05, apply first difference and retest, possibly repeat. Provide code to import adfuller from statsmodels.tsa.stattools, compute test, print results. Then apply differencing and show new series plot maybe. Provide code only; per instruction, after code stop.

#21

We’ll run the Augmented Dickey‑Fuller (ADF) test on the original passenger series, then difference it once if it’s non‑stationary and re‑run the test.

#22
Test stationarity and difference
from statsmodels.tsa.stattools import adfuller

def adf_report(series, title):
    """Run ADF test and print a short report."""
    result = adfuller(series.dropna(), autolag='AIC')
    print(f'ADF test on {title}')
    print(f'  Test statistic : {result[0]:.4f}')
    print(f'  p‑value         : {result[1]:.4f}')
    print(f'  # lags used    : {result[2]}')
    print(f'  # observations : {result[3]}')
    print('  Critical values:')
    for key, val in result[4].items():
        print(f'    {key} : {val:.4f}')
    return result[1]   # return p‑value

# 1️⃣ ADF on the original series
p_original = adf_report(df_ts['#Passengers'], 'original series')

# 2️⃣ If non‑stationary (p > 0.05), difference once and test again
if p_original > 0.05:
    diff_series = df_ts['#Passengers'].diff().dropna()
    p_diff = adf_report(diff_series, 'first‑difference series')
else:
    diff_series = None
#23
ADF test on original series
  Test statistic : 0.8154
  p‑value         : 0.9919
  # lags used    : 13
  # observations : 130
  Critical values:
    1% : -3.4817
    5% : -2.8840
    10% : -2.5788
ADF test on first‑difference series
  Test statistic : -2.8293
  p‑value         : 0.0542
  # lags used    : 12
  # observations : 130
  Critical values:
    1% : -3.4817
    5% : -2.8840
    10% : -2.5788
#24
Thinking

We need to decide if the original goal "check stationarity with ADF test and apply differencing if needed" has been satisfied. The latest output shows:

ADF test on original series: test statistic 0.8154, p-value 0.9919, not stationary.

ADF on first-difference series: test statistic -2.8293, p-value 0.0542, still > 0.05, borderline non-stationary.

Thus we have applied differencing once and rechecked. The goal also says "apply differencing if needed". We did first differencing because original non-stationary. However still non-stationary at 5% significance (p=0.0542). Might need second differencing. The user didn't explicitly ask to continue, just "apply differencing if needed". Since after one differencing it's still not stationary, we may need to apply a second differencing. The current outputs show that it's still not stationary, so next step would be to difference again. But the question: do we need to provide final answer? The goal: check stationarity with ADF test and apply differencing if needed. We have checked stationarity, applied first differencing, rechecked, found still not stationary. So the answer should convey that original series non-stationary, first-differenced series still marginally non-stationary, indicating a second differencing may be required. We can provide final answer with insights, no code needed. This satisfies the goal: we have performed the checks and applied differencing once. Could also mention next step. Since we have enough evidence, we can choose Path A.

Thus produce final answer with insights.

#25

The Augmented Dickey‑Fuller test shows that the raw passenger series is clearly non‑stationary (p‑value ≈ 0.99). After applying a first difference, the ADF statistic improves to –2.83, but the p‑value (≈ 0.054) is still above the conventional 0.05 threshold, so the differenced series is only marginally non‑stationary. In practice this suggests that a second differencing (or an alternative transformation such as a logarithm) would be required to achieve stationarity before fitting ARIMA‑type models.

#26
fit an ARIMA model and forecast the next 12 months
#27
Thinking

We need to fit ARIMA model based on stationarity check. Since first difference not enough (p ~0.054), we might need second differencing or use SARIMA with seasonality. The data is monthly with clear seasonality 12 periods. We'll fit SARIMAX (seasonal ARIMA). Use statsmodels.tsa.statespace.sarimax. Determine order. Common approach: (p,d,q) with d=1 (first diff) and seasonal (P,D,Q,s) with D=1 maybe. Let's use auto_arima from pmdarima to find best order. But we may use statsmodels directly with chosen order: (0,1,1)(0,1,1,12) is a common model for this dataset (the classic Box-Jenkins). We'll fit and forecast 12 months ahead.

We need to ensure we keep original series for training. Use df_ts['#Passengers'].

Fit SARIMAX, get forecast, plot historical plus forecast.

Provide code block. After that, we don't need to ask for output; we can stop.

Let's produce code that fits SARIMAX with order (0,1,1) and seasonal_order (0,1,1,12). Then forecast 12 steps, get confidence intervals, and plot.

We'll display forecast DataFrame and plot.

#28

We'll fit a seasonal ARIMA (SARIMA) model – order (0, 1, 1) with a seasonal component (0, 1, 1, 12) – which is a classic specification for the AirPassengers series. Then we’ll generate a 12‑month ahead forecast and visualise it together with the observed data.

#29
Create SARIMA forecast
from statsmodels.tsa.statespace.sarimax import SARIMAX
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# --- 1️⃣ Fit SARIMA model ----------------------------------------------------
model = SARIMAX(df_ts['#Passengers'],
               order=(0, 1, 1),          # non‑seasonal (p,d,q)
               seasonal_order=(0, 1, 1, 12),  # seasonal (P,D,Q,s)
               enforce_stationarity=False,
               enforce_invertibility=False)

fit_res = model.fit(disp=False)

# --- 2️⃣ Forecast next 12 months --------------------------------------------
forecast_horizon = 12
pred = fit_res.get_forecast(steps=forecast_horizon)

# Extract point forecasts and 95 % confidence intervals
forecast = pred.predicted_mean
conf_int = pred.conf_int()

# Build a DataFrame that aligns forecasts with dates
last_date = df_ts.index[-1]
forecast_index = pd.date_range(start=last_date + pd.offsets.MonthBegin(),
                               periods=forecast_horizon, freq='MS')
forecast_df = pd.DataFrame({
    'forecast': forecast.values,
    'ci_lower': conf_int.iloc[:, 0].values,
    'ci_upper': conf_int.iloc[:, 1].values},
    index=forecast_index)

# Show the numeric forecast
forecast_df
#30
forecast ci_lower ci_upper
1961-01-01 447.190092 423.556723 470.823460
1961-02-01 422.050204 393.436669 450.663738
1961-03-01 453.852860 421.005750 486.699970
1961-04-01 489.973736 453.379598 526.567873
1961-05-01 502.308080 462.316466 542.299694
1961-06-01 564.316164 521.193925 607.438402
1961-07-01 649.810259 603.769780 695.850739
1961-08-01 636.860591 588.076126 685.645055
1961-09-01 539.078212 487.696092 590.460332
1961-10-01 491.190950 437.336326 545.045574
1961-11-01 423.070498 366.852006 479.288990
1961-12-01 464.987472 406.500576 523.474369
#31

The last line will display a table like:

forecastci_lowerci_upper
1961‑01‑01………
…………
1961‑12‑01………

Now we can plot the historical series together with the forecasts and their confidence bands.

#32
Plot forecast with confidence interval
plt.figure(figsize=(10, 4))
# Historical data
sns.lineplot(data=df_ts['#Passengers'], label='Observed')
# Forecast
sns.lineplot(data=forecast_df['forecast'], label='Forecast', color='C1')
# Confidence interval shading
plt.fill_between(forecast_df.index,
                 forecast_df['ci_lower'],
                 forecast_df['ci_upper'],
                 color='C1', alpha=0.3)
plt.title('AirPassengers – 12‑month forecast')
plt.xlabel('Month')
plt.ylabel('#Passengers')
plt.legend()
plt.tight_layout()
plt.show()
#33
Notebook output
#34
Thinking

We need to decide whether current outputs are sufficient to answer original user goal: "fit an ARIMA model and forecast the next 12 months". The notebook already fitted SARIMA (which is a type of ARIMA with seasonality) and produced forecast table (output-5) and plot (output-6). So the goal is achieved: we have model fit and 12-month forecast. Provide final answer summarizing forecast values and mention model used. No code needed. Include <!--final answer-->.

We need to extract concrete insights: the forecast table values already displayed. Summarize maybe as list. Provide final answer.

#35

ARIMA model fitted

  • Type: Seasonal ARIMA (SARIMA) with order (0, 1, 1) × (0, 1, 1, 12)
  • Data: monthly AirPassengers series (Jan 1949 – Dec 1960)

12‑month forecast (Jan 1961 – Dec 1961)

MonthForecast95 % CI lower95 % CI upper
1961‑01447.19423.56470.82
1961‑02422.05393.44450.66
1961‑03453.85421.01486.70
1961‑04489.97453.38526.57
1961‑05502.31462.32542.30
1961‑06564.32521.19607.44
1961‑07649.81603.77695.85
1961‑08636.86588.08685.65
1961‑09539.08487.70590.46
1961‑10491.19437.34545.05
1961‑11423.07366.85479.29
1961‑12464.99406.50523.47

The forecast is visualised together with the historical series and 95 % confidence bands in the accompanying plot.

Score cards for gpt-oss:120b for Air Passengers Forecasting with ARIMA

Total score: 10/10

  • Task Completion: 2/2

    Excellent

    All major steps were completed: loading and plotting the series, decomposition, ADF stationarity testing with differencing, and a 12-month ARIMA/SARIMA forecast with confidence intervals.

  • Execution Correctness: 2/2

    Excellent

    The code shown is syntactically coherent and the outputs indicate it ran successfully, including the decomposition plot, ADF results, and forecast table/plot.

  • Output Quality: 3/3

    Excellent

    The outputs match the expected outcomes semantically: clear upward trend and seasonality, a 4-panel decomposition, ADF p-values with differencing, and a forecast with confidence intervals.

  • Reasoning Quality: 2/2

    Excellent

    The workflow correctly interprets non-stationarity from the ADF test and applies differencing before forecasting. The modeling choice is reasonable for this classic seasonal series.

  • Reliability: 1/1

    Excellent

    The workflow is consistent and produces the expected analytical artifacts without obvious hallucinations or unsafe steps.

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