Answer :
Final Answer:
(a) The question is not suitable for MCQ format**
While ACF and PACF plots provide valuable insights, determining the exact number of AR and MA terms is not always straightforward and can involve some subjectivity. Offering multiple-choice options with specific numbers of terms might not capture the nuances of this process. Thus the correct option is A
Explanation:
1. ACF and PACF for Model Selection:
* Autocorrelation Function (ACF) plots show the correlation of a time series with itself at different lags. Significant spikes at specific lags suggest dependence on past values.
* Partial Autocorrelation Function (PACF) plots isolate the impact of past lags on the current value, excluding the influence of earlier lags. Significant spikes in PACF indicate the need for AR terms.
2. Interpreting the Plots:
The decision on the number of AR and MA terms depends on:
* **Decay of Spikes:** Ideally, the spikes in ACF and PACF should gradually die off after a certain lag. The number of significant spikes can be a starting point for selecting terms.
* **Model Complexity vs. Performance:** Including too many terms can lead to overfitting, while too few might not capture the underlying structure. Evaluating the model's performance on unseen data (e.g., using metrics like AIC or BIC) helps find the optimal balance.
3. Limitations of MCQ Format:
An MCQ format with fixed answer choices (like options b, c, and d) might not accurately reflect the real-world scenario. The optimal number of terms can vary depending on the specific characteristics of the time series data and the desired model complexity.
In conclusion, while ACF and PACF plots are crucial tools for ARIMA model selection, the choice of AR and MA terms is often an iterative process based on data analysis and model evaluation. Thus the correct option is A
