Advanced Econometrics Time Series Analysis Final Project Report

Abstract

This assignment investigates the relationship between AI-hype, proxied by NVIDIA (NVDA) stock returns, and electricity demand in the PJM Interconnection region of the United States. Using daily data from November 30, 2022 (the release date of ChatGPT) to December 31, 2025, we estimate a Vector Autoregression (VAR) model and conduct Granger causality tests. At the daily frequency, we find no statistically significant causal relationship between NVDA returns and electricity load changes (see Section 6.1). However, aggregating the data to longer time horizons reveals a striking pattern: the correlation between cumulative NVDA returns and cumulative PJM load changes increases monotonically from near zero at the daily level to 23% monthly, 36% quarterly, and 51% semi-annually (see Section 6.2). Notably, as we increase the time span, the p-values also increase significantly due to reduced sample sizes, yet the correlation magnitude strengthens. We also evaluate out-of-sample forecasting performance (see Section 6.4).

1. Motivation

The causal chain we investigate is the following:

AI Hype → Data Center Investment → Electricity Demand

If this chain operates quickly, we would expect NVDA stock movements to “Granger-cause” changes in electricity load. If the chain operates slowly (due to construction lead times), we would expect the relationship to strengthen at longer time horizons.

2. Data Description

2.1 Data Sources

We use two primary data sources:

• NVIDIA Stock Price (NVDA): Daily adjusted closing prices obtained from Yahoo Finance via the yfinance Python library. NVDA is the primary indicator of AI-hype, as NVIDIA dominates the market for GPUs used for AI training and inference.
• PJM Electricity Load: Daily electricity demand (in GWh) for the PJM Interconnection, obtained from the U.S. Energy Information Administration’s EIA-930 dataset. PJM operates the largest competitive wholesale electricity market in the world, serving 65 million people across 13 states and the District of Columbia.

2.2 Sample Period

The sample spans from November 30, 2022 (the release date of ChatGPT) to December 31, 2025. After merging on trading days (excluding weekends and holidays when the stock market is closed), the final dataset contains 773 daily observations.

2.3 Transformations

Raw data are trending, meaning it’s non-stationary. This violates the requirements for VAR estimation. Thus, we transform as follows in order to obtain stationarity:

• NVDA: r_t = ln(P_t / P_t−1)
• PJM: Δl_t = ln(L_t / L_t−1)

By Augmented Dickey-Fuller (ADF) tests, the stationarity of data sets are confirmed.

Both p-values are well below 0.05, therefore we reject the null hypothesis and conclude that the processed series are stationary.

3. Exploratory Visualization

The chart below shows the NVDA stock price growth over time (from 2022/11/30 to 2025/12/31) alongside daily PJM electricity load, which shows clear seasonal peaks in summer and winter, and a seemingly very weak upward trend.

4. Modeling Approach

4.1 Vector Autoregression (VAR)

The VAR(p) model used is as follows:

where:

• r_t: NVDA log returns
• Δl_t: PJM log differences
• p: lag order

4.2 Lag Order Selection

Using the AIC, the optimal lag order was found to be p = . This corresponds to roughly one trading week of history, suggesting that the relevant information for forecasting spans approximately one week.

4.3 Granger Causality

To test whether NVDA returns have predictive power for PJM load changes beyond the information already contained in PJM’s own history, we conduct Granger causality tests. The null hypothesis is:

If rejected, we conclude that NVDA “Granger-causes” PJM load—i.e., past NVDA returns help predict future electricity demand.

4.4 Impulse Response Functions

The chart below displays the full system of Impulse Response Functions (IRFs) over a 10-day horizon.

5. Estimation

5.1 VAR Model Results

The estimation of the VAR(7) model using OLS is displayed in Table 2.

The coefficients on the lagged PJM variables (L2 through L7) are highly significant (p < 0.001), confirming the strong autocorrelation and weekly seasonality inherent in electricity demand. In contrast, most NVDA lag coefficients are statistically insignificant, with the exception of the 7th lag (p = 0.050). This marginal significance at the 7-day mark hints at a potential weekly cycle in how market information might transmit to load, but it is not strong enough to drive a significant result in the joint Granger causality test.

5.2 Granger Causality Test Results

In both hypotheses, p-value > 0.05. Therefore we fail to reject the null hypothesis in both cases. This indicates that neither of the variables have statistically significant predictive power over the other.

6. Results and Interpretation

6.1 Daily Analysis: No Short-Term Causality

The Granger causality test results confirm that there is no statistically significant relationship at the daily frequency. The impulse response function (Figure 2) shows this finding: a shock to NVDA returns produces negligible and statistically insignificant responses in PJM load changes over the 10-day horizon.

This result at the daily level is no surprise, since it is likely to take months or years between the processes in the model presented in the first section (AI Hype → Data Center Investment → Electricity Demand), meaning that there should be substantial time lags.

As an additional diagnostic, the Forecast Error Variance Decomposition (FEVD) below shows the share of PJM load forecast variance attributable to NVDA shocks across the 10-day horizon. The NVDA contribution remains near zero, consistent with the IRF and Granger causality findings.

6.2 Long-Term Analysis: Emerging Correlation

Daily relationship was negligible and statistically insignificant. However, to investigate the relationship over longer horizons, we aggregate the variables to monthly, quarterly, semi-annual, and annual frequencies. The chart below shows the 90-day rolling correlation between the two processed series, illustrating how the short-horizon correlation evolves through the sample.

The correlation increases as we increase the time horizon, rising from near 0.10 at the daily level to over 0.50 at the semi-annual level. This suggests that aggregation acts as a filter, removing high-frequency noise and revealing the underlying structural link between capital investment and energy consumption.

However, we observe a sharp drop in correlation at the annual frequency (0.06). This anomaly is likely due to the extremely small sample size at this level (N = 4 years), rendering the statistic unreliable compared to the robust trend observed up to the semi-annual horizon. Although the p-values increase with aggregation (indicating lower statistical significance due to smaller N), the magnitude of the relationship clearly strengthens as the time window expands.

6.3 Interpretation

The results suggest that while daily movements are not correlated, cumulative movements are associated with each other. This is consistent with the situation of data center investment: investment decisions take longer period of time for the implementation.

6.4 Out-of-Sample Forecasting

We compare the out-of-sample forecasting performance of the VAR model against a univariate AR benchmark. Using a rolling window of 252 days (approximately one trading year), we generate 514 one-step-ahead forecasts for PJM load changes.

The results show that the VAR model RMSE (0.0536) and the AR benchmark RMSE (0.0531) are nearly identical (difference < 1.1%). This confirms that adding NVDA returns does not improve short-term electricity demand forecasts, which is consistent with our finding of no short-term Granger causality.

7. Limitations and Possible Extensions

7.1 Limitations

1. Proxy validity: NVDA stock price embodies “AI-hype” perfectly, reflecting the market sentiment. However, more direct measures, such as announced data center construction projects, would be preferable, but it is difficult to obtain at high frequency, and these data are highly likely to be private and near impossible to obtain.
2. Geographic mismatch: PJM covers only the eastern United States, while AI-related electricity demand is distributed globally. Major data center clusters exist in other regions (e.g., Oregon, Texas, Ireland) that are not captured in our analysis.
3. Confounding factors: Electricity demand is driven by many factors such as weather, economic activity, population growth, etc. These are not controlled in the model used in here. The observed long-horizon correlations could be spurious, explaining the low p-values.
4. Short sample at low frequencies: While the daily sample number is large, it shrinks down significantly when the data set gets aggregated. This also explains the low p-values, since this affects the statistical power of inference.

7.2 Possible Extensions

1. Additional proxies: Combine other AI-related tickers (AMD, GOOG, MSFT) and reduce idiosyncratic noise in NVDA.
2. Control variables: Incorporate other variables such as temperature, GDP growth to isolate the AI-specific effect on electricity demand.
3. Longer horizon: As more post-ChatGPT data becomes available, re-estimate the models to test whether the correlations strengthen over time.

8. Conclusion

This assignment investigates the relationship between AI-hype (using NVDA) and electricity demand (measured by PJM interconnection) in the period following the most pivotal moment in the history of LLM, the release of ChatGPT (known as ChatGPT moment). Using a VAR model and Granger causality test on the data period, we find no evidence of short-term causality between the variables.

However, aggregating the data to longer time horizons reveals a different picture. The correlation between the variables increases from near zero at daily level to over 50% at the 6-months level. This pattern is consistent with the reality around data center investment: physical data center infrastructure takes time to implement, so the effects of the investment on electricity consumption takes a long time to emerge.

These findings implies the long term rise in the electricity demand: as AI adoption continues to accelerate, the electricity demand goes up. Since there is no short-term causality among the variables, daily stock market fluctuations won’t work as a predictive instrument for the daily electricity demand. However, the strong long-horizon correlation indicate that tracking AI investment trends may be valuable for long-term electricity capacity planning.

In the current state of artificial intelligence, it is becoming apparent that computational power is more abundant than energy, and I believe that in the future, intelligence will be measured by Joules. This topic, the quantitative relationship between expansion of AI and energy will be increasingly more prominent in the coming years.

9. References and Appendix

9.1 Data Resources

• yfinance (GitHub) – Python library for Yahoo Finance data
• EIA Electricity Grid Monitor – Source for PJM hourly load data (EIA-930)
• View full original LaTeX Report (PDF)
• Full Python analysis pipeline (scripts + README) – 1_modeling through 5_forecasting, reproducible end-to-end

9.2 AI Assistance

This assignment utilized AI assistance (Claude, Grok) for the following tasks:

• Dependency Management: Identifying and listing required packages for the Python environment.
• Documentation: Assistance in drafting and formatting the README.md file.
• LaTeX Support: Troubleshooting syntax and formatting for tables and figures.