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 64.50% per annum.
- AMZN price at the close of January 17, 2025 was $225.94 and was lower than the bottom border of the primary price channel by $6.77 (2.91%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 42.19% per annum.
- AMZN price at the close of January 17, 2025 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: November 1, 2022
End date: July 17, 2024
a = 3.0733
b = 0.0014
s = 0.0547
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 64.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0547) – 1
= 24.48%
November 1, 2022 calculations
Top border of price channel:
Exp(Y702)
= Exp(a + b × X702 + 2 × s)
= Exp(a + b × 1,015 + 2 × s)
= Exp(3.0733 + 0.0014 × 1,015 + 2 × 0.0547)
= Exp(4.5669)
= $96.24
Bottom border of price channel:
Exp(Y702)
= Exp(a + b × X702 – 2 × s)
= Exp(a + b × 1,015 – 2 × s)
= Exp(3.0733 + 0.0014 × 1,015 – 2 × 0.0547)
= Exp(4.3479)
= $77.32
July 17, 2024 calculations
Top border of price channel:
Exp(Y1,129)
= Exp(a + b × X1,129 + 2 × s)
= Exp(a + b × 1,639 + 2 × s)
= Exp(3.0733 + 0.0014 × 1,639 + 2 × 0.0547)
= Exp(5.4178)
= $225.39
Bottom border of price channel:
Exp(Y1,129)
= Exp(a + b × X1,129 – 2 × s)
= Exp(a + b × 1,639 – 2 × s)
= Exp(3.0733 + 0.0014 × 1,639 – 2 × 0.0547)
= Exp(5.1989)
= $181.07
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 64.50% per annum.
- AMZN price at the close of January 17, 2025 was $225.94 and was lower than the bottom border of the primary price channel by $6.77 (2.91%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: May 17, 2023
End date: January 17, 2025
a = 3.6377
b = 0.0010
s = 0.0591
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 42.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0591) – 1
= 26.69%
May 17, 2023 calculations
Top border of price channel:
Exp(Y837)
= Exp(a + b × X837 + 2 × s)
= Exp(a + b × 1,212 + 2 × s)
= Exp(3.6377 + 0.0010 × 1,212 + 2 × 0.0591)
= Exp(4.9247)
= $137.65
Bottom border of price channel:
Exp(Y837)
= Exp(a + b × X837 – 2 × s)
= Exp(a + b × 1,212 – 2 × s)
= Exp(3.6377 + 0.0010 × 1,212 – 2 × 0.0591)
= Exp(4.6881)
= $108.65
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(3.6377 + 0.0010 × 1,823 + 2 × 0.0591)
= Exp(5.5139)
= $248.11
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.6377 + 0.0010 × 1,823 – 2 × 0.0591)
= Exp(5.2773)
= $195.84
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 42.19% per annum.
- AMZN price at the close of January 17, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
Check out AMZN and 1,499 other stocks on our new website