ARIMA Model Calculator

Fit ARIMA(p,d,q) models to time series data. Estimate parameters, evaluate model fit with AIC/BIC, generate forecasts, and export Python statsmodels code.

Data & Orders

Time Series (comma-separated)

p (AR)

d (Diff)

q (MA)

Forecast Periods: 6

Model: ARIMA(1,1,0)

1.96

MAE

2.24

RMSE

39.5

AIC

41.7

BIC

Coefficients

Intercept2.5626

AR(1)-0.4967

Forecast

t+1: 141.1t+2: 143.1t+3: 144.7t+4: 146.4t+5: 148.1t+6: 149.9

Forecast Chart

Python Code

import pandas as pd
import numpy as np
from statsmodels.tsa.arima.model import ARIMA
from statsmodels.tsa.stattools import adfuller
import matplotlib.pyplot as plt

# Data
data = pd.Series([100, 102, 105, 103, 107, 110, 108, 112, 115, 113, 117, 120, 118, 122, 125, 123, 127, 130, 128, 132, 135, 133, 137, 140])

# ADF test for stationarity
adf_result = adfuller(data)
print(f"ADF Statistic: {adf_result[0]:.4f}")
print(f"p-value: {adf_result[1]:.4f}")
print(f"Stationary: {'Yes' if adf_result[1] < 0.05 else 'No (consider differencing)'}")

# Fit ARIMA(1,1,0)
model = ARIMA(data, order=(1, 1, 0))
fitted = model.fit()

print(f"\nARIMA(1,1,0) Results:")
print(fitted.summary())

# Forecast
forecast = fitted.forecast(steps=6)
conf_int = fitted.get_forecast(steps=6).conf_int()

print(f"\nForecast (6 periods):")
for i, (fc, lo, hi) in enumerate(zip(forecast, conf_int.iloc[:, 0], conf_int.iloc[:, 1])):
    print(f"  t+{i+1}: {fc:.2f} [{lo:.2f}, {hi:.2f}]")

# Diagnostics
print(f"\nAIC: {fitted.aic:.2f}")
print(f"BIC: {fitted.bic:.2f}")

# Plot
fig, axes = plt.subplots(2, 1, figsize=(12, 8))

# Forecast plot
axes[0].plot(data.index, data, 'ko-', label='Actual', alpha=0.6, markersize=4)
axes[0].plot(data.index, fitted.fittedvalues, 'b-', label='Fitted', linewidth=2)
fc_idx = range(len(data), len(data) + 6)
axes[0].plot(fc_idx, forecast, 'r--', label='Forecast', linewidth=2)
axes[0].fill_between(fc_idx, conf_int.iloc[:, 0], conf_int.iloc[:, 1], alpha=0.2, color='red')
axes[0].legend()
axes[0].set_title('ARIMA(1,1,0) Forecast')
axes[0].grid(True, alpha=0.3)

# Residuals
axes[1].plot(fitted.resid, 'g-', alpha=0.7)
axes[1].axhline(y=0, color='k', linestyle='--')
axes[1].set_title('Residuals')
axes[1].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

# Auto ARIMA (requires pmdarima)
# from pmdarima import auto_arima
# auto_model = auto_arima(data, seasonal=False, trace=True)
# print(auto_model.summary())

Frequently Asked Questions

What do the p, d, q parameters mean?

p = AR order (number of autoregressive lags), d = differencing order (times to difference for stationarity), q = MA order (number of moving average lags). ARIMA(1,1,0) means: 1 AR lag, 1 differencing, no MA. Use ACF/PACF plots to identify p and q; use ADF test for d.

How do I know if my data needs differencing (d)?

Run the Augmented Dickey-Fuller (ADF) test. If p-value > 0.05, the series is non-stationary - apply first differencing (d=1). After differencing, test again. Most economic/business time series need d=1. Rarely is d=2 needed.

What is the difference between AIC and BIC?

Both measure model fit vs complexity. AIC = n·ln(σ²) + 2k, BIC = n·ln(σ²) + k·ln(n). BIC penalizes complexity more, preferring simpler models. Use AIC for prediction accuracy, BIC for identifying the true model. Lower values = better model.

What is auto_arima?

auto_arima (from pmdarima) automatically searches for the best ARIMA(p,d,q) by trying multiple combinations and selecting the one with lowest AIC/BIC. It also handles stationarity tests and seasonal models. Great for quick modeling without manual ACF/PACF analysis.

When should I use SARIMA instead of ARIMA?

Use SARIMA (Seasonal ARIMA) when your data has seasonal patterns. SARIMA adds seasonal AR, differencing, and MA parameters: SARIMA(p,d,q)(P,D,Q)m where m is the seasonal period. Use when ACF shows spikes at seasonal lags (e.g., lag 12 for monthly data).

Related Tools

Autocorrelation

ACF & PACF correlograms

Exponential Smoothing

SES, Holt & Holt-Winters

Moving Average

SMA, EMA & WMA smoothing

import pandas as pd import numpy as np from statsmodels.tsa.arima.model import ARIMA from statsmodels.tsa.stattools import adfuller import matplotlib.pyplot as plt # Data data = pd.Series([100, 102, 105, 103, 107, 110, 108, 112, 115, 113, 117, 120, 118, 122, 125, 123, 127, 130, 128, 132, 135, 133, 137, 140]) # ADF test for stationarity adf_result = adfuller(data) print(f"ADF Statistic: {adf_result[0]:.4f}") print(f"p-value: {adf_result[1]:.4f}") print(f"Stationary: {'Yes' if adf_result[1] < 0.05 else 'No (consider differencing)'}") # Fit ARIMA(1,1,0) model = ARIMA(data, order=(1, 1, 0)) fitted = model.fit() print(f"\nARIMA(1,1,0) Results:") print(fitted.summary()) # Forecast forecast = fitted.forecast(steps=6) conf_int = fitted.get_forecast(steps=6).conf_int() print(f"\nForecast (6 periods):") for i, (fc, lo, hi) in enumerate(zip(forecast, conf_int.iloc[:, 0], conf_int.iloc[:, 1])): print(f" t+{i+1}: {fc:.2f} [{lo:.2f}, {hi:.2f}]") # Diagnostics print(f"\nAIC: {fitted.aic:.2f}") print(f"BIC: {fitted.bic:.2f}") # Plot fig, axes = plt.subplots(2, 1, figsize=(12, 8)) # Forecast plot axes[0].plot(data.index, data, 'ko-', label='Actual', alpha=0.6, markersize=4) axes[0].plot(data.index, fitted.fittedvalues, 'b-', label='Fitted', linewidth=2) fc_idx = range(len(data), len(data) + 6) axes[0].plot(fc_idx, forecast, 'r--', label='Forecast', linewidth=2) axes[0].fill_between(fc_idx, conf_int.iloc[:, 0], conf_int.iloc[:, 1], alpha=0.2, color='red') axes[0].legend() axes[0].set_title('ARIMA(1,1,0) Forecast') axes[0].grid(True, alpha=0.3) # Residuals axes[1].plot(fitted.resid, 'g-', alpha=0.7) axes[1].axhline(y=0, color='k', linestyle='--') axes[1].set_title('Residuals') axes[1].grid(True, alpha=0.3) plt.tight_layout() plt.show() # Auto ARIMA (requires pmdarima) # from pmdarima import auto_arima # auto_model = auto_arima(data, seasonal=False, trace=True) # print(auto_model.summary())