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 49.79% per annum.
- AMZN price at the close of October 29, 2026 was $243.79 and was lower than the bottom border of the primary price channel by $154.45 (38.78%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.52% per annum.
- AMZN price at the close of October 29, 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 21, 2025
a = 4.1268
b = 0.0011
s = 0.0789
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 49.79%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0789) – 1
= 37.13%
October 7, 2022 calculations
Top border of price channel:
Exp(Y235)
= Exp(a + b × X235 + 2 × s)
= Exp(a + b × 340 + 2 × s)
= Exp(4.1268 + 0.0011 × 340 + 2 × 0.0789)
= Exp(4.6611)
= $105.75
Bottom border of price channel:
Exp(Y235)
= Exp(a + b × X235 – 2 × s)
= Exp(a + b × 340 – 2 × s)
= Exp(4.1268 + 0.0011 × 340 – 2 × 0.0789)
= Exp(4.3454)
= $77.12
February 21, 2025 calculations
Top border of price channel:
Exp(Y829)
= Exp(a + b × X829 + 2 × s)
= Exp(a + b × 1,208 + 2 × s)
= Exp(4.1268 + 0.0011 × 1,208 + 2 × 0.0789)
= Exp(5.6220)
= $276.43
Bottom border of price channel:
Exp(Y829)
= Exp(a + b × X829 – 2 × s)
= Exp(a + b × 1,208 – 2 × s)
= Exp(4.1268 + 0.0011 × 1,208 – 2 × 0.0789)
= Exp(5.3062)
= $201.59
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 49.79% per annum.
- AMZN price at the close of October 29, 2026 was $243.79 and was lower than the bottom border of the primary price channel by $154.45 (38.78%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 25, 2024
End date: October 29, 2026
a = 4.8392
b = 0.0004
s = 0.0697
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 15.52%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0697) – 1
= 32.17%
January 25, 2024 calculations
Top border of price channel:
Exp(Y560)
= Exp(a + b × X560 + 2 × s)
= Exp(a + b × 815 + 2 × s)
= Exp(4.8392 + 0.0004 × 815 + 2 × 0.0697)
= Exp(5.3008)
= $200.50
Bottom border of price channel:
Exp(Y560)
= Exp(a + b × X560 – 2 × s)
= Exp(a + b × 815 – 2 × s)
= Exp(4.8392 + 0.0004 × 815 – 2 × 0.0697)
= Exp(5.0219)
= $151.70
October 29, 2026 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.8392 + 0.0004 × 1,823 + 2 × 0.0697)
= Exp(5.6993)
= $298.67
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.8392 + 0.0004 × 1,823 – 2 × 0.0697)
= Exp(5.4204)
= $225.97
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 15.52% per annum.
- AMZN price at the close of October 29, 2026 was inside the secondary price channel.