Is there an AI bubble? Robust date-stamping for periods of exuberance

Figure 1.  Nasdaq index together with the stock prices of Tesla, Broadcom, and Nvidia over the past ten years. The pronounced run-ups in these stocks during 2020–2025 are suggestive of speculative bubble dynamics. Data source: Yahoo Finance [59].

Figure 2.  Stock prices for Broadcom and Nvidia over 2022-2026 exhibit pronounced heteroskedasticity. Volatility is calculated using a rolling window of the previous 8 weeks. The visual evidence supports a specification that allows for persistent variation in scale.

Figure 3.  Proposed SV-ADF procedure identified speculative explosive bubble behaviour in individual stocks. The dotted red vertical lines mark bubble origination, the dotted green lines signify collapse. Speculative intervals: Nvidia (Jan' 2024 – Aug' 2024), Tesla (June 2020 – March 2021).

Figure 4.  Misdating of Bitcoin and Nvidia bubble episodes under PWY approach. PWY date-stamps: Oct' 2020 – Dec' 2020 for Bitcoin, May 2023 – Nov' 2023 for Nvidia. This discrepancy reflects the reliance on homoskedastic thresholds in an environment where volatility is strongly time-varying. SV-ADF procedure delivers more economically plausible bubble date-stamps aligned with major market news: late Dec' 2020 – June 2021 for Bitcoin, Jan' 2024 – Aug' 2024 for Nvidia.

Figure 5.  Daily adjusted close prices of the "Magnificent-Seven" and the six largest semiconductor/AI-infrastructure firms by market capitalization over the past 10 years. Panels are arranged in descending market-cap order, with the first six showing tech firms and the next six for the rest. The vertical line at January 2020 marks the onset of the surge emphasized in our analysis. Source: Yahoo Finance [59].

Figure 6.  Stock-price volatility for Nvidia over 2022–2025 causes misdating through PWY. Since volatility exhibits pronounced peaks and troughs, PWY signals a spurious bubble window in one such high-volatility episode (June–November 2023). SV-ADF procedure identifies the most persistent and quantitatively pronounced episode of explosiveness (January–August 2024), rather than short-lived price spikes induced by volatility fluctuations.

Figure 7.  Recursive SV-ADF statistic (blue) and daily stock price (red) for the six largest technology firms by market capitalization, along with their bubble origination and collapse date-stamps. Plotting both series provides visual inspection on whether threshold crossings in the recursive statistic coincide with meaningful price movements. The orange line denotes the 90% upper critical value under $ H_0 $ used for bubble origination, while the brown line denotes the 10% lower critical value under $ H_1 $ used for bubble collapse. Green and violet vertical lines respectively mark the estimated origination and collapse dates from the SV-ADF procedure. The sample period is 2022–2026, except for Tesla, 2018–2022. No bubble detected for Apple, Microsoft, and Amazon. Tesla had price exuberance during 2020–21, while Alphabet is currently in a bubble.

Figure 8.  Recursive SV-ADF Statistic (blue) and daily stock price (red) for the six largest semiconductor/AI-infrastructure firms by market capitalization. The sample period is 2022–2026, except ASML July 2018–2026. The color scheme is the same as Figure 7. Every semiconductor equities exhibited speculative behavior during some interval in this AI boom.

Figure 9.  Date-stamping bubble behaviour in Nasdaq index. Time period for upper panel: 2020–2026, no exuberance detected. Time period for lower panel: 1982–2012, significant exuberance detected in 1995-2000. SV-ADF identifies bubble origination in early April 1995, two months before the June 1995 PWY date. This earlier signal suggests that volatility-robust inference can detect the onset of exuberance sooner without altering the economically accepted collapse window. The color scheme is the same as Figure 7.

Figure 10.  Recursive SV-ADF test suggests significant bubble in Bitcoin and Ethereum during December 2020–June 2021. PWY misdates Bitcoin bubble completely and suggests October 2020 - December 2020. Similar cryptocoins during this era exhibited pronounced exuberance (see Appendix A.7). The color scheme is the same as Figure 7.

Figure 11.  Estimated autoregressive coefficients, growth rates, and their 95% C.I for the 12 stocks over 2022–2026. For most firms, unity lies within the interval for the AR coefficient, consistent with near-unit-root behavior.

Figure 12.  One time series path (black) and recursive SV-ADF statistic (blue). Red and brown vertical lines denote true bubble origination $ r_e = 0.3, $ collapse $ r_f = 0.6 $ respectively, while the blue and green mark the estimated $ \widehat r_e = 0.308, \widehat r_f = 0.652 $. The orange horizontal line is the origination threshold ($ \log(ns)/10 $), purple line is collapse threshold ($ \log(ns)/2 $). [43] considered a uniform threshold for both origination and collapse.

Figure 13.  Conclusive evidence: $ X_{\tau_f}-X_{\tau_e} \neq O_p(1) $. The panels report the average value of $ X_{\tau_f}-X_{\tau_e} $ on a logarithmic scale under homoskedasticity (left) and stochastic volatility (right). In both panels, $ r_e = 0.4 $, $ r_f = 0.6 $, $ c = 1 $, and $ \alpha = 0.5 $. The sample size ranges from $ n = 50,100, \ldots, 500 $, while the number of Monte Carlo replications is fixed at $ B = 500 $. The visual evidence indicates that this difference grows exponentially with the sample size, which stands in sharp contradiction to the PWY maintained assumption.

Figure 14.  Bubble detection in some more crypto-coins. The recursive SV-ADF test indicates a pronounced bubble episode in Cardano and Solana during 2021. By contrast, Binance Coin exhibited only weak and short-lived exuberance, while Dogecoin showed no evidence of a bubble.

Figure 15.  The same threshold plots as in Table 6 under $ H_0 $ in red and $ H_1 $ in blue.