A Bitcoin price prediction model assuming oscillatory growth and lengthening cycles

Figures & data

Figure 1. Assuming no oscillation amplitude $\alpha =0$, the empirical price $p_E$, logistic growth $p_L$, Gompertz growth $p_G$, charged capacitor growth $p_C$, combined logistic and charged capacitor growth $p_{LC}$ and $p_{LC\lambda }$, and combined Gompertz and charged capacitor growth $p_{GC}$ and $p_{GC\lambda }$, for 23 July 2010–21 June 2021 (panels a and c) and until 1 January 2100 (panels b and d), $K=\mathrm{\$}476,190$. Panels a and b apply the least squares method. Panels c and d apply the weighted least squares method.

Figure 2. Assuming no oscillation amplitude $\alpha =0$, the empirical price $p_E$, logistic growth $p_L$, Gompertz growth $p_G$, charged capacitor growth $p_C$, combined logistic and charged capacitor growth $p_{LC}$ and $p_{LC\lambda }$, and combined Gompertz and charged capacitor growth $p_{GC}$ and $p_{GC\lambda }$, for 23 July 2010–21 June 2021 (panels a and c) and until 1 January 2100 (panels b and d), $K=\mathrm{\$}23,809,524$. Panels a and b apply the least squares method. Panels c and d apply the weighted least squares method.

Figure 3. Assuming oscillation amplitude $\alpha \ge 0$, the empirical price $p_E$, logistic growth $p_L$, Gompertz growth $p_G$, charged capacitor growth $p_C$, combined logistic and charged capacitor growth $p_{LC}$ and $p_{LC\lambda }$, and combined Gompertz and charged capacitor growth $p_{GC}$ and $p_{GC\lambda }$, for 23 July 2010–21 June 2021 (panels a and c) and until 1 January 2040 (panels b and d), $K=\mathrm{\$}476,190$. Panels a and b apply the least squares method. Panels c and d apply the weighted least squares method.

Figure 4. Assuming oscillations $\alpha \ge 0$, the empirical price $p_E$, logistic growth $p_L$, Gompertz growth $p_G$, charged capacitor growth $p_C$, combined logistic and charged capacitor growth $p_{LC}$ and $p_{LC\lambda }$, and combined Gompertz and charged capacitor growth $p_{GC}$ and $p_{GC\lambda }$, for 23 July 2010–21 June 2021 (panels a and c) and until 1 January 2040 (panels b and d), $K=\mathrm{\$}23,809,524$. Panels a and b apply the least squares method. Panels c and d apply the weighted least squares method.

Table 1. Dates and magnitudes of bull market local maxima 4,5,6,7,8 when $K=\mathrm{\$}476,190$ and $K=\mathrm{\$}23,809,524$, predicted until year 2050

Bull market local maximum	4	5	6	7	8
Logistic growth $p_L$	Asymptotic. 07/06/24; 431,785. Asymptotic. 05/05/24; 3,360,314.	Asymptotic. 01/28/30; 476,153. Asymptotic. 11/18/29; 23,694,323.	Asymptotic. Asymptotic. Asymptotic. 02/06/36; 23,809,485.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.
Gompertz growth $p_G$	05/22/22; 75,506. Asymptotic. 06/29/22; 107,064. Asymptotic.	08/25/27; 221,873. Asymptotic. 10/08/27; 1,032,330. Asymptotic.	08/11/33; 358,456. Asymptotic. 09/29/33; 4,343,140. Asymptotic.	03/21/40; 432,860. Asymptotic. 05/15/40; 10,021,700. Asymptotic.	06/11/47; 462,526. Asymptotic. 08/09/47; 15,732,787. Asymptotic.
Charged capacitor growth $p_C$	08/08/21; 18,032. Asymptotic. 08/15/21; 18,317. Asymptotic.	09/29/26; 24,619. Asymptotic. 10/07/26; 25,173. Asymptotic.	08/05/32; 31,829. Asymptotic. 08/14/32; 32,789. Asymptotic.	02/07/39; 39,587. Asymptotic. 02/17/39; 41,119. Asymptotic.	03/25/46; 47,827. Asymptotic. 04/04/46; 50,127. Asymptotic.
Combined logistic and charged capacitor growth $p_{LC}$	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.
Combined logistic and charged capacitor growth $p_{LC\lambda }$	08/19/22; 113,012. Asymptotic. 09/16/22; 133,710. Asymptotic.	12/05/27; 391,125. Asymptotic. 01/07/28; 1,497,123. Asymptotic.	12/03/33; 470,084. Asymptotic. 01/08/34; 8,753,549. Asymptotic.	07/25/40; 475,908. Asymptotic. 09/03/40; 19,460,471. Asymptotic.	10/26/47; 476,180. Asymptotic. 12/08/47; 23,181,174. Asymptotic.
Combined Gompertz and charged capacitor growth $p_{GC}$	Asymptotic. Asymptotic. 06/26/22; 94,049. 06/27/23; 65,062.	Asymptotic. Asymptotic. 10/05/27; 512,728. 11/27/28; 367,353.	Asymptotic. Asymptotic. 09/25/33; 1,714,019. 01/06/35; 1,286,048.	Asymptotic. Asymptotic. 05/10/40; 4,022,084. 10/06/41; 3,169,232.	Asymptotic. Asymptotic. 08/04/47; 7,301,533. 02/12/49; 6,030,620.
Combined Gompertz and charged capacitor growth $p_{GC\lambda }$	02/12/22; 46,652. Asymptotic. 04/28/22; 68,116. Asymptotic.	05/03/27; 110,018. Asymptotic. 07/29/27; 264,925. Asymptotic.	04/05/33; 191,648. Asymptotic. 07/11/33; 736,127. Asymptotic.	11/02/39; 273,762. Asymptotic. 02/16/40; 1,611,829. Asymptotic.	01/10/47; 342,930. Asymptotic. 05/06/47; 2,960,784. Asymptotic.
Date and local maximum expected value $\pm$ standard deviation	12/12/22 $\pm 314$. 11/29/22 $\pm 397$. 05/18/22 $\pm$ 94. 07/06/24 $\pm 0$. 12/21/22 $\pm$ 288. 07/02/22 $\pm 58$. 11/30/23 $\pm$ 221. 166,739 $\pm$ 178,774. 78,390 $\pm 33,274$. 431,785 $\pm 0$. 638,053 $\pm 1,333,874$. 100,735 $\pm 27,301$. 1,712,688 $\pm 2,330,095.$	04/15/28 $\pm 359$. 03/30/28 $\pm 454$. 08/21/27 $\pm$ 108. 01/28/30 $\pm 0$. 04/25/28 $\pm$ 329. 10/12/27 $\pm 66$. 05/24/29 $\pm$ 252. 299,792 $\pm$ 164,854. 241,005 $\pm 141,527$. 476,153 $\pm 0$. 4,561,464 $\pm 9,384,608$. 826,777 $\pm 549,521$. 12,030,838 $\pm 16,494,659.$	02/07/34 $\pm 327$. 08/06/33 $\pm 121$. 08/06/33 $\pm 121$. Asymptotic. 05/10/34 $\pm 367$. 10/03/33 $\pm 74$. 07/23/35 $\pm 280$. 340,063 $\pm 140,126$. 340,063 $\pm 140,126$. Asymptotic. 6,773,728 $\pm 8,856,776$. 3,886,709 $\pm 3,584,281$. 12,547,767 $\pm 15,926,475.$	06/27/40 $\pm 211$. 03/16/40 $\pm 133$. 03/16/40 $\pm 133$. Asymptotic. 08/28/40 $\pm 237$. 05/19/40 $\pm 82$. 10/06/41 $\pm 0$. 394,177 $\pm 106,480$. 394,177 $\pm 106,480$. Asymptotic. 7,657,063 $\pm 7,328,208$. 8,779,021 $\pm 7,950,571$. 3,169,232 $\pm 0.$	09/25/47 $\pm 228$. 06/06/47 $\pm 145$. 06/06/47 $\pm 145$. Asymptotic. 12/01/47 $\pm 257$. 08/14/47 $\pm 89$. 02/12/49 $\pm 0$. 427,212 $\pm 73,309$. 427,212 $\pm 73,309$. Asymptotic. 11,041,380 $\pm 8,273,060$. 12,294,070 $\pm 8,988,687$. 6,030,620 $\pm 0$.

Each cell has four entries, except in the bottom row. Each entry ends with period ”.”. The dates are in the format month/day/year for the least squares method and the weighted least squares method in entries 1 and 2 when $K=\mathrm{\$}476,190$. Entries 3 and 4 are for the least squares method and the weighted least squares method when $K=\mathrm{\$}23,809,524$. After each date the price follows in $. Asymptotic means that no local maximum exists, but that the Bitcoin price $p$ approaches $K$ asymptotically. In the bottom row each cell has 13 entries. Each entry ends with period ”.”. This gives seven entries with dates and six entries with local maxima expressed as expected value $\pm$ standard deviation in days and $\mathrm{\$}$. Entry 1 gives the date for both methods and both $K=\mathrm{\$}476,190$ and $K=\mathrm{\$}23,809,524$. Entries 2 and 8 apply for both methods when $K=\mathrm{\$}476,190$. Entries 3 and 9 apply for the least squares method when $K=\mathrm{\$}476,190$. Entries 4 and 10 apply for the weighted least squares method when $K=\mathrm{\$}476,190$. Entries 5 and 11 apply for both methods when $K=\mathrm{\$}23,809,524$. Entries 6 and 12 apply for the least squares method when $K=\mathrm{\$}23,809,524$. Entries 7 and 13 apply for the weighted least squares method when $K=\mathrm{\$}23,809,524$.

Table 2. Dates and magnitudes of bear market local minima 4,5,6,7,8 when $K=\mathrm{\$}476,190$ and $K=\mathrm{\$}23,809,524$, predicted until year 2050

Bear market local minima	4	5	6	7	8
Logistic growth $p_L$	Asymptotic. 04/09/25; 428,795. Asymptotic. 05/01/25; 2,898,043.	Asymptotic. 12/07/30; 476,150. Asymptotic. 01/01/31; 23,669,932.	Asymptotic. Asymptotic. Asymptotic. 05/05/37; 23,809,475.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.
Gompertz growth $p_G$	03/05/24; 45,736. Asymptotic. 12/28/23; 73,350. Asymptotic.	09/10/29; 174,196. Asymptotic. 06/24/29; 802,142. Asymptotic.	11/22/35; 323,674. Asymptotic. 08/27/35; 3,725,750. Asymptotic.	09/22/42; 416,631. Asymptotic. 06/19/42; 9,196,504. Asymptotic.	02/27/50; 456,629. Asymptotic. 11/16/49; 15,043,891. Asymptotic.
Charged capacitor growth $p_C$	10/24/23; 9,710. Asymptotic. 11/01/23; 9,743. Asymptotic.	04/12/29; 15,198. Asymptotic. 04/21/29; 15,342. Asymptotic.	06/07/35; 21,449. Asymptotic. 06/16/35; 21,799. Asymptotic.	03/21/42; 28,365. Asymptotic. 04/01/42; 29,046. Asymptotic.	08/11/49; 35,866. Asymptotic. 08/22/49; 37,031. Asymptotic.
Combined logistic and charged capacitor growth $p_{LC}$	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.	Asymptotic. Asymptotic. Asymptotic. Asymptotic.
Combined logistic and charged capacitor growth $p_{LC\lambda }$	03/17/24; 78,327. Asymptotic. 03/09/24; 95,424. Asymptotic.	09/24/29; 355,689. Asymptotic. 09/14/29; 1,139,873. Asymptotic.	12/07/35; 466,389. Asymptotic. 11/27/35; 7,376,641. Asymptotic.	10/08/42; 475,712. Asymptotic. 09/27/42; 18,476,294. Asymptotic.	03/16/50; 476,173. Asymptotic. 03/04/50; 22,992,469. Asymptotic.
Combined Gompertz and charged capacitor growth $p_{GC}$	Asymptotic. Asymptotic. 03/11/24; 57,377. 05/03/24; 62,860.	Asymptotic. Asymptotic. 09/17/29; 360,351. 11/16/29; 358,295.	Asymptotic. Asymptotic. 11/29/35; 1,334,243. 02/04/36; 1,263,066.	Asymptotic. Asymptotic. 09/30/42; 3,371,727. 12/12/42; 3,128,527.	Asymptotic. Asymptotic. 03/07/50; 6,458,819. 05/25/50; 5,975,591.
Combined Gompertz and charged capacitor growth $p_{GC\lambda }$	01/17/24; 27,008. Asymptotic. 01/14/24; 45,585. Asymptotic.	07/18/29; 77,314. Asymptotic. 07/13/29; 196,739. Asymptotic.	09/22/35; 152,541. Asymptotic. 09/18/35; 587,238. Asymptotic.	07/17/42; 236,548. Asymptotic. 07/12/42; 1,354,016. Asymptotic.	12/16/49; 312,871. Asymptotic. 12/11/49; 2,585,103. Asymptotic.
Date and local minima expected value $\pm$ standard deviation	05/17/24 $\pm 182$. 06/04/24 $\pm 208$. 02/22/24 $\pm$ 32. 04/09/25 $\pm 0$. 05/06/24 $\pm$ 182. 02/06/24 $\pm 38$. 10/31/24 $\pm$ 257. 144,966 $\pm$ 190,403. 50,357 $\pm 25,970$. 428,795 $\pm 0$. 538,773 $\pm 1,155,924$. 67,934 $\pm 21,571$. 1,480,452 $\pm 2,004,777$.	12/02/29 $\pm 206$. 12/22/29 $\pm 235$. 08/27/29 $\pm 36$. 12/07/30 $\pm 0$. 11/18/29 $\pm$ 207. 08/09/29 $\pm 43$. 06/09/30 $\pm$ 291. 270,837 $\pm$ 179,019. 202,400 $\pm 141,314$. 476,150 $\pm 0$. 4,421,222 $\pm 9,436,336$. 624,776 $\pm 428,143$. 12,014,113 $\pm 16,483,817$.	01/07/36 $\pm 188$. 11/06/35 $\pm 40$. 11/06/35 $\pm 40$. Asymptotic. 02/07/36 $\pm 229$. 10/18/35 $\pm 48$. 09/19/36 $\pm 322$. 314,201 $\pm 157,138$. 314,201 $\pm 157,138$. Asymptotic. 6,349,402 $\pm 8,910,871$. 3,255,968 $\pm 3,055,912$. 12,536,271 $\pm 15,942,719$.	09/06/42 $\pm 58$. 09/05/42 $\pm 44$. 09/05/42 $\pm 44$. Asymptotic. 09/07/42 $\pm 70$. 08/14/42 $\pm 53$. 12/12/42 $\pm 0$. 376,297 $\pm 124,579$. 376,297 $\pm 124,579$. Asymptotic. 7,105,414 $\pm 7,008,998$. 8,099,635 $\pm 7,675,386$. 3,128,527 $\pm 0$.	02/09/50 $\pm 63$. 02/08/50 $\pm 48$. 02/08/50 $\pm 48$. Asymptotic. 02/10/50 $\pm 76$. 01/16/50 $\pm 57$. 05/25/50 $\pm 0$. 415,224 $\pm 89,177$. 415,224 $\pm 89,177$. Asymptotic. 10,611,175 $\pm 8,308,037$. 11,770,071 $\pm 9,114,698$. 5,975,591 $\pm 0$.

The structure is the same as for Table 1, but applies for local minima instead of local maxima.

Data availability statement

The article contains no associated data. All data generated or analyzed during this study is included in this published article.