Report esame Statistics for experiments and forecasts in the field of technology

University of Florence management engineering

“Analysis of Net Electricity Generation by type of fuel: Geothermal”

Name: Guido
Surname: Nannini
Identification Number: 7176619
Email: guido.nannini1@edu.unifi.it
Date of Delivery: April 1, 2026

Net electricity generation: Geothermal

University of Florence — Management Engineering

1 Introduction

This report presents a complete time series analysis of the Net Electricity Generation from Geothermal sources in Italy, sourced from ESTAT (Eurostat). Geothermal energy represents a significant component of Italy’s renewable energy mix, as the country is among the leading European producers of geothermal electricity, particularly concentrated in the Tuscan region (Larderello area). Monitoring this indicator is crucial for understanding the evolution of the national energy transition, evaluating the stability of renewable baseload capacity, and supporting energy policy decisions.

Unlike other renewable sources such as wind and solar, geothermal generation is characterized by high continuity and relatively low seasonal variability, making it a particularly interesting candidate for time series modelling.

Data characteristics

• Data Source: ESTAT (Eurostat)
• Dataset: Net electricity generation by type of fuel: Geothermal
• Last Updated: 04/06/2025 =
• Time Frequency: Monthly (S 12)
• Territory: Italy
• Indicator: Net Electricity Generation — Geothermal
• Unit of Measure: Gigawatt-hour (GWh)
• Time Frame: January 2008 – February 2025
• Total Observations: 206

The analysis is conducted following the Box-Jenkins methodology, which provides a rigorous and systematic framework for identifying, estimating, and validating Seasonal ARIMA models. This approach allows for the modelling of the temporal dynamics of the series through autoregressive, integrated, and moving average components, both at the non-seasonal and seasonal levels, enabling reliable short-term forecasting based on the historical structure of the data.

2 Preliminary analysis

The dataset is imported from a CSV file using semicolon as delimiter, with missing values encoded as dots replaced by NA. Date strings in year-month format (YYYY-MM) are converted to proper Date objects by appending the first day of each month. The data are then structured as a monthly time series object with frequency 12, starting from January 2008, using R’s native class to enable time-aware analysis and ts() modelling.

The time series plot reveals a series oscillating around a mean of approximately 450 GWh, with no clear persistent long-term trend. A mild upward movement is observed from 2008 to approximately 2016–2017, followed by a gradual decline toward 2025, suggesting a weak form of stationarity with long-run mean-reversion tendencies rather than a structural trend. Regular annual oscillations are clearly visible throughout = the entire sample period, providing strong visual evidence of a seasonal component with period 12. This S pattern is consistent with the known production cycle of Italian geothermal plants, whose output exhibits modest but systematic intra-year variation.

Figure 1: Time Series Plot 1

Net Electricity Generation: Geothermal University of Florence — Management Engineering

The Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) of the original series are examined to identify the orders of the ARIMA model, following the Box-Jenkins identification rules.

The ACF displays significant spikes across many lags with slow exponential decay, suggesting short-term = autoregressive dependence with 1. The slow decay without an abrupt cutoff is also consistent with a p = = process requiring 0, though the persistence of significant lags leaves open the possibility of 1, which d d will be evaluated during the estimation phase. A prominent spike at lag 12 confirms seasonal dependence = = with 12, motivating 1. S Q

The PACF shows a dominant spike at lag 1 (≈ 0.65), rapidly decaying thereafter, consistent with an AR(1) non-seasonal component. Crucially, a large positive spike at lag 12 (≈ 0.45) followed by a sharp negative −0.45) spike at lag 13 (≈ is visible. According to theory, this alternating pattern at seasonal lags is a signal = of potential non-stationarity at the seasonal level, suggesting that 1 may be required. However, as a D = = conservative starting point and to allow the data to guide the specification, 0 and 1 are adopted for D PM1, with seasonal differencing reconsidered if the diagnostics indicate residual seasonal structure.

These considerations lead to the specification of ARIMA(1, 0, 1)(1, 0, 1)[12] as the starting model M1.

Figure 2: ACF and PACF of the original time series × (P,

3 ARIMA(p, d, q) specification D, Q)S

The model specification phase follows the iterative logic of the Box-Jenkins procedure: starting from a null benchmark, candidate models are progressively refined based on the analysis of estimated coefficients, information criteria, and residual diagnostics. Each model is evaluated against its predecessor, and the transition to a new specification is always motivated by specific statistical signals rather than arbitrary trial and error. The goal is to identify the most parsimonious model that adequately captures the temporal structure of the series, as measured by the lowest AIC/BIC values and by the absence of autocorrelation in the residuals.

M0 — ARIMA(0,0,0) with non-zero mean (Null Model)

The null model serves as the minimum performance benchmark. It contains no autoregressive or moving average components and predicts the sample mean for all time periods. While clearly inadequate as a forecasting model, it provides a reference point for the information criteria and error measures against which all subsequent models are compared. The strong ACF1 of the residuals (0.612) confirms that substantial temporal structure remains unexplained, as expected. Any model that fails to outperform this benchmark would be considered uninformative.

M1 — ARIMA(1,0,1)(1,0,1)[12]

The first candidate model is specified directly from the ACF and PACF of the original series, as described in the preliminary analysis. A non-zero mean is included given the apparent stationarity of the series. The model achieves a substantial improvement over M0, with AIC dropping from 1937.35 to 1542.19 and MASE ≈ falling below 1. However, two critical signals emerge from the estimated coefficients: 0.962 and φ̂1 ≈ 0.9999, both dangerously close to 1, suggesting the possible need for non-seasonal and seasonal Φ̂ 1 differencing respectively.

2Net Electricity Generation: Geothermal University of Florence — Management Engineering

Figure 3: ACF and PACF of M1

Both the ACF and PACF of the residuals show all spikes well within the confidence bands across all 60 lags, with no evidence of remaining seasonal or non-seasonal autocorrelation structure at the graphical level. This visual evidence is encouraging; however, the formal Ljung-Box test at lag 24 returns a p-value of 0.021, which falls below the 5% significance threshold, indicating that a statistically significant residual = autocorrelation structure remains, particularly at shorter lags. The test at lag 48 passes with 0.134. This p discrepancy between the graphical and formal evidence, combined with the near-unit-root signals in and φ̂1, confirms that M1 does not fully satisfy the white noise requirement and motivates the transition to M2. Φ̂ 1

M2 — ARIMA(1,0,1)(0,1,1)[12]

Motivated by 1 in M1, seasonal differencing 1 is introduced in M2. The SAR component D Φ̂1 is removed, as it is absorbed by the differencing operator, and the constant is set to standard False, = practice when 1 is applied. This reduces the model to three parameters while improving both AIC D ≈ (1433.59) and RMSE. However, two problems persist: 0.968 remains close to 1, suggesting that