ARIMA model basics in ML Python - Model Metrics & Evaluation

Metrics & Evaluation - ARIMA model basics

Which metric matters for ARIMA and WHY

For ARIMA models, we focus on error metrics that show how close the model's predictions are to actual values. Common metrics are Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). These metrics measure the size of prediction mistakes in simple terms, helping us understand if the model predicts well over time.

Confusion matrix or equivalent visualization

ARIMA is for continuous values, so confusion matrix does not apply. Instead, we use error tables or plots. For example, a table of actual vs predicted values or a line plot showing both series helps visualize prediction quality.

Time | Actual | Predicted | Error
-----|--------|-----------|-------
t1   | 100    | 98        | 2
t2   | 105    | 107       | -2
t3   | 102    | 101       | 1
    

Tradeoff: Bias vs Variance in ARIMA

ARIMA models balance between being too simple (high bias) and too complex (high variance). A simple model may miss patterns (high error), while a complex model may fit noise (overfit). Choosing the right order (p,d,q) controls this tradeoff. Good error metrics help find this balance.

What "good" vs "bad" metric values look like for ARIMA

Good ARIMA models have low MAE, MSE, and RMSE, meaning predictions are close to actual values. For example, an RMSE of 1.5 on a scale of 100 is good, but 20 is bad. Always compare errors to the scale of your data to judge quality.

Common pitfalls in ARIMA metrics

• Ignoring stationarity: ARIMA assumes data is stationary; if not, errors can be misleading.
• Overfitting: Too many parameters can fit noise, lowering training error but hurting future predictions.
• Using accuracy metrics from classification: ARIMA needs error metrics, not accuracy or precision.
• Not checking residuals: Residuals should look like random noise; patterns mean model issues.

Self-check question

Your ARIMA model has an RMSE of 15 on daily sales data where average sales are around 1000 units. Is this good? Why or why not?

Answer: An RMSE of 15 means the average prediction error is 15 units, which is about 1.5% of average sales. This is quite good because errors are small compared to the scale of data. So, the model predicts well.

Key Result

ARIMA model quality is best judged by error metrics like RMSE, which measure how close predictions are to actual values over time.

Practice

1. What does the d parameter in an ARIMA model represent?

easy

A. The number of times the data is differenced to make it stationary

B. The number of lag observations included in the model

C. The number of moving average terms

D. The total number of data points used for training

Solution

1. Step 1: Understand ARIMA parameters

   ARIMA has three parameters: p (lags), d (differencing), and q (moving average terms).

2. Step 2: Identify the role of d

   The d parameter controls how many times the data is differenced to remove trends and make it stationary.

3. Final Answer:

   The number of times the data is differenced to make it stationary -> Option A

4. Quick Check:

   d = differencing count [OK]

Hint: Remember: d = differencing steps to remove trend [OK]

Common Mistakes:

• Confusing d with p or q parameters
• Thinking d is the number of lag observations
• Assuming d relates to error terms

2. Which of the following is the correct way to import the ARIMA model from the statsmodels library in Python?

easy

A. import ARIMA from statsmodels.tsa

B. import ARIMA from statsmodels.arima

C. from statsmodels.arima_model import ARIMA

D. from statsmodels.tsa.arima.model import ARIMA

Solution

1. Step 1: Recall the correct import path

   The current and recommended import for ARIMA is from statsmodels.tsa.arima.model.

2. Step 2: Check each option

   from statsmodels.tsa.arima.model import ARIMA matches the correct import. Options B, C, and D use outdated or incorrect paths.

3. Final Answer:

   from statsmodels.tsa.arima.model import ARIMA -> Option D

4. Quick Check:

   Correct import path = from statsmodels.tsa.arima.model import ARIMA [OK]

Hint: Use statsmodels.tsa.arima.model for ARIMA import [OK]

Common Mistakes:

• Using deprecated import paths
• Incorrect module names
• Confusing ARIMA with other models

3. Given the following Python code, what will be the output of print(model_fit.aic)?

from statsmodels.tsa.arima.model import ARIMA
import numpy as np
np.random.seed(0)
data = np.random.randn(100)
model = ARIMA(data, order=(1,0,1))
model_fit = model.fit()
print(round(model_fit.aic, 2))

medium

A. Approximately 280.00

B. Approximately -280.00

C. Approximately 0.00

D. Raises an error because of missing differencing

Solution

1. Step 1: Understand the code and model

   The code fits an ARIMA(1,0,1) model on 100 random normal values. The model fit will compute the AIC (Akaike Information Criterion).

2. Step 2: Interpret the AIC output

   Since data is random noise, AIC will be a positive number around 280. Negative or zero values are unlikely here.

3. Final Answer:

   Approximately 280.00 -> Option A

4. Quick Check:

   AIC positive and around 280 for random data [OK]

Hint: AIC is positive and near 280 for random normal data [OK]

Common Mistakes:

• Expecting negative AIC values
• Thinking differencing is mandatory for ARIMA
• Confusing AIC with accuracy

4. Identify the error in the following ARIMA model fitting code:

from statsmodels.tsa.arima.model import ARIMA
data = [1, 2, 3, 4, 5]
model = ARIMA(data, order=(1,1))
model_fit = model.fit()

medium

A. Data must be a numpy array, not a list

B. ARIMA cannot be used with differencing (d > 0)

C. The order tuple must have three values (p, d, q)

D. The fit() method is not available for ARIMA

Solution

1. Step 1: Check the ARIMA order parameter

   The order parameter must be a tuple of three integers: (p, d, q). Here, only two values are given.

2. Step 2: Validate other parts

   Data as list is acceptable. Differencing is allowed. The fit() method exists.

3. Final Answer:

   The order tuple must have three values (p, d, q) -> Option C

4. Quick Check:

   Order needs 3 values (p,d,q) [OK]

Hint: ARIMA order always needs three numbers (p,d,q) [OK]

Common Mistakes:

• Using two values instead of three in order
• Thinking data type must be numpy array
• Believing fit() is unavailable

5. You have a time series with a strong upward trend and seasonal patterns. Which ARIMA order would be the best starting point to model this data?

hard

A. (1, 2, 1) to over-difference the data and reduce noise

B. (1, 1, 1) to handle trend with differencing and simple AR and MA terms

C. (2, 0, 2) to avoid differencing and capture seasonality directly

D. (0, 0, 0) since no differencing or lags are needed

Solution

1. Step 1: Understand the data characteristics

   The data has a strong upward trend and seasonality, so differencing is needed to remove trend.

2. Step 2: Choose ARIMA order

   Order (1,1,1) applies one differencing step (d=1) and includes AR and MA terms to model patterns. Over-differencing (d=2) risks losing information. (0,0,0) ignores trend and seasonality. (2,0,2) misses differencing for trend.

3. Final Answer:

   (1, 1, 1) to handle trend with differencing and simple AR and MA terms -> Option B

4. Quick Check:

   Use d=1 for trend, p and q for patterns [OK]

Hint: Use d=1 for trend, p and q for patterns [OK]

Common Mistakes:

• Skipping differencing for trending data
• Over-differencing causing data loss
• Ignoring seasonality in ARIMA order