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Help me identify, p,d,P,D seasonal and nonseasonal values. consider seasonal lag at 12,24,36 and d=1 and D=1

To identify the appropriate \( p \), \( d \), \( P \), and \( D \) values for an ARIMA model (where \( p \) is the order of the autoregressive part, \( d \) is the order of differencing, \( P \) is the seasonal autoregressive order, and \( D \) is the order of seasonal differencing), we can analyze the provided Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots.

Given the inputs and considering the seasonal lags at 12, 24, 36 and provided \( d = 1 \) and \( D = 1 \), let's proceed with the analysis:

### ACF and PACF Interpretation
1. **Non-seasonal Parameters (p, d)**
   - **d**: Since you've specified \( d = 1 \), this indicates non-seasonal differencing once, which helps to make the series stationary.
   - **p**: Generally determined by where the PACF plot cuts off (the lag after which most PACF bars are within the confidence interval). The PACF plot doesn't show a clear cut-off within the first few lags, suggesting a low \( p \) value, possibly 0 or 1.

2. **Seasonal Parameters (P, D)**
   - **D**: You've specified \( D = 1 \), indicating seasonal differencing once.
   - **P**: Determined by the PACF at seasonal lags. If we look at lags 12, 24, and 36:
     - At lag 12, there is a significant spike in PACF.
     - At lag 24 and 36, the PACF coefficients are not significantly different from zero.
   - This suggests \( P = 1 \) for the seasonal part of the model, given the significant spike at the first seasonal lag (12 months).

### Suggested Model Configuration
- Based on the analysis:
  - \( p = 1 \) (possibly considering the first few lags in PACF),
  - \( d = 1 \),
  - \( P = 1 \) (due to the significant spike at the first seasonal lag),
  - \( D = 1 \).

This setup implies an ARIMA model with orders (1, 1, 0)(1, 1, 0)[12], considering the significant terms and differencing specified.

Do you need further details or have any other questions? Here are a few additional topics you might find useful:
1. What is the significance of each parameter in the ARIMA model?
2. How does differencing help in making a time series stationary?
3. Why might one choose a seasonal ARIMA model for time series analysis?
4. How can over-differencing affect the performance of an ARIMA model?
5. What are alternative methods to identify the best ARIMA parameters?

**Tip:** It's often useful to perform a model diagnostic check, such as examining the residuals of the ARIMA model, to ensure that the model fits the data well without any apparent patterns or heteroscedasticity remaining in the residuals.

Help me identify, p,d,P,D seasonal and nonseasonal values. Consider seasonal lag at 12, 24, 36 and d=1 and D=1

Identify the seasonal (P,D) and nonseasonal (p,d) parameters for an ARIMA model with lags at 12, 24, and 36. Explore how ACF and PACF plots help in the selection of ARIMA orders and the significance of differencing.

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