Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 49.59% per annum.
- AMZN price at the close of October 2, 2026 was $251.52 and was lower than the bottom border of the primary price channel by $133.23 (34.63%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.62% per annum.
- AMZN price at the close of October 2, 2026 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of AMZN price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: October 7, 2022
End date: February 26, 2025
a = 4.0983
b = 0.0011
s = 0.0791
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 49.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0791) – 1
= 37.21%
October 7, 2022 calculations
Top border of price channel:
Exp(Y255)
= Exp(a + b × X255 + 2 × s)
= Exp(a + b × 368 + 2 × s)
= Exp(4.0983 + 0.0011 × 368 + 2 × 0.0791)
= Exp(4.6625)
= $105.90
Bottom border of price channel:
Exp(Y255)
= Exp(a + b × X255 – 2 × s)
= Exp(a + b × 368 – 2 × s)
= Exp(4.0983 + 0.0011 × 368 – 2 × 0.0791)
= Exp(4.3461)
= $77.18
February 26, 2025 calculations
Top border of price channel:
Exp(Y852)
= Exp(a + b × X852 + 2 × s)
= Exp(a + b × 1,241 + 2 × s)
= Exp(4.0983 + 0.0011 × 1,241 + 2 × 0.0791)
= Exp(5.6257)
= $277.46
Bottom border of price channel:
Exp(Y852)
= Exp(a + b × X852 – 2 × s)
= Exp(a + b × 1,241 – 2 × s)
= Exp(4.0983 + 0.0011 × 1,241 – 2 × 0.0791)
= Exp(5.3093)
= $202.22
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 49.59% per annum.
- AMZN price at the close of October 2, 2026 was $251.52 and was lower than the bottom border of the primary price channel by $133.23 (34.63%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 25, 2024
End date: October 2, 2026
a = 4.8253
b = 0.0004
s = 0.0706
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 15.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0706) – 1
= 32.62%
January 25, 2024 calculations
Top border of price channel:
Exp(Y580)
= Exp(a + b × X580 + 2 × s)
= Exp(a + b × 843 + 2 × s)
= Exp(4.8253 + 0.0004 × 843 + 2 × 0.0706)
= Exp(5.3017)
= $200.68
Bottom border of price channel:
Exp(Y580)
= Exp(a + b × X580 – 2 × s)
= Exp(a + b × 843 – 2 × s)
= Exp(4.8253 + 0.0004 × 843 – 2 × 0.0706)
= Exp(5.0194)
= $151.32
October 2, 2026 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.8253 + 0.0004 × 1,824 + 2 × 0.0706)
= Exp(5.6919)
= $296.45
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.8253 + 0.0004 × 1,824 – 2 × 0.0706)
= Exp(5.4096)
= $223.54
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.62% per annum.
- AMZN price at the close of October 2, 2026 was inside the secondary price channel.