RYUSEIYAMAKI.COM

AI Hype and Electricity Demand: A Time Series Analysis

Ryusei Yamaki · Final project for my time series analysis class at Waseda university

Abstract

This analysis 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. 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. We also evaluate out-of-sample forecasting performance.

1. Motivation

The causal chain we investigate is:

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

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.

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.

Transformations

Raw data are trending, meaning they are non-stationary. This violates the requirements for VAR estimation. We transform as follows to obtain stationarity:

  • NVDA: rt = ln(Pt / Pt-1)
  • PJM: Δlt = ln(Lt / Lt-1)
Transformed Series: NVDA Log Returns and PJM Log Differences
Figure 1: Transformed Series — NVDA Log Returns and PJM Log Differences

By Augmented Dickey-Fuller (ADF) tests, the stationarity of both series is confirmed:

Variable ADF Statistic p-value
NVDA Log Returns -17.15 < 0.001
PJM Log Differences -14.86 < 0.001

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

NVDA Close Price
Figure 2: NVDA Close Price (Nov 2022 – Dec 2025)
PJM Daily Electricity Load
Figure 3: PJM Daily Electricity Load (GWh)

The NVDA stock price shows dramatic growth over the sample period. PJM electricity load shows clear seasonal peaks in summer and winter, and a seemingly very weak upward trend.

4. Modeling Approach

Vector Autoregression (VAR)

The VAR(p) model used is:

rt = α1 + Σi=1..p β1i rt-i + Σi=1..p γ1i Δlt-i + ε1t
Δlt = α2 + Σi=1..p β2i rt-i + Σi=1..p γ2i Δlt-i + ε2t

where rt denotes NVDA log returns, Δlt denotes PJM log differences, and p is the lag order.

Lag Order Selection

Using the AIC, the optimal lag order was found to be p = 7. This corresponds to roughly one trading week of history, suggesting that the relevant information for forecasting spans approximately one week.

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 that all lagged NVDA coefficients in the PJM equation are jointly zero. If rejected, we conclude that NVDA "Granger-causes" PJM load.

Impulse Response Functions

System Impulse Response Functions
Figure 4: System Impulse Response Functions (10-day horizon)

5. Estimation

VAR Model Results

Variable Coefficient Std. Error p-value
Constant -0.0007 0.0019 0.705
L1.NVDA_Log_Return 0.0774 0.0598 0.195
L7.NVDA_Log_Return 0.1165 0.0594 0.050
L2.PJM_Log_Diff -0.2147 0.0365 < 0.001
L3.PJM_Log_Diff -0.1532 0.0369 < 0.001
L4.PJM_Log_Diff -0.1593 0.0369 < 0.001
L5.PJM_Log_Diff -0.1387 0.0371 < 0.001
L7.PJM_Log_Diff -0.1235 0.0367 0.001

Table 2: Selected VAR(7) Coefficients for PJM Log Diff Equation

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.

Granger Causality Test Results

Null Hypothesis p-value Decision
NVDA does not Granger-cause PJM 0.3003 Fail to reject H0
PJM does not Granger-cause NVDA 0.2031 Fail to reject H0

Table 3: Granger Causality Test Results (7 lags)

In both cases, p-value > 0.05. Therefore we fail to reject the null hypothesis in both directions. This indicates that neither variable has statistically significant predictive power over the other at the daily frequency.

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 shows this clearly: a shock to NVDA returns produces negligible and statistically insignificant responses in PJM load changes over the 10-day horizon.

IRF: Shock to NVDA Returns to PJM Load Changes
Figure 5: Impulse Response Function — Shock to NVDA Returns → PJM Load Changes

This result at the daily level is unsurprising. It is likely to take months or years between the processes in the causal chain (AI Hype → Data Center Investment → Electricity Demand), meaning there should be substantial time lags.

6.2 Long-Term Analysis: Emerging Correlation

While the daily relationship was negligible and statistically insignificant, aggregating the variables to monthly, quarterly, semi-annual, and annual frequencies reveals a different story.

Correlation by Aggregation Frequency
Figure 6: Correlation by Aggregation Frequency

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.

6.3 Interpretation

The results suggest that while daily movements are not correlated, cumulative movements are associated with each other. This is consistent with data center investment reality: investment decisions take a longer period of time for 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, consistent with the finding of no short-term Granger causality.

Forecast Comparison: VAR vs AR
Figure 7: Out-of-Sample Forecast Comparison (VAR vs AR Benchmark)

7. Limitations and Possible Extensions

Limitations

  1. Proxy validity: NVDA stock price reflects AI-hype market sentiment well, but more direct measures such as announced data center construction projects would be preferable. However, such data are difficult to obtain at high frequency and are likely private.
  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 (Oregon, Texas, Ireland) not captured in our analysis.
  3. Confounding factors: Electricity demand is driven by many factors (weather, economic activity, population growth, etc.) not controlled for in this model. The observed long-horizon correlations could be spurious.
  4. Short sample at low frequencies: While the daily sample is large, it shrinks significantly when aggregated. This affects the statistical power of inference at longer horizons.

Possible Extensions

  1. Additional proxies: Combine other AI-related tickers (AMD, GOOG, MSFT) to reduce idiosyncratic noise in NVDA.
  2. Control variables: Incorporate temperature, GDP growth, etc. 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 analysis investigates the relationship between AI-hype (using NVDA) and electricity demand (measured by PJM Interconnection) in the period following the release of ChatGPT. Using a VAR model and Granger causality test, 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 the daily level to over 50% at the 6-month level. This pattern is consistent with the reality of data center investment: physical infrastructure takes time to build, so the effects on electricity consumption take a long time to emerge.

These findings imply a long-term rise in electricity demand: as AI adoption continues to accelerate, electricity demand goes up. Since there is no short-term causality, daily stock market fluctuations won't work as a predictive instrument for daily electricity demand. However, the strong long-horizon correlation indicates 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 in Joules. The quantitative relationship between expansion of AI and energy will be increasingly prominent in the coming years.

References