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 52.39% per annum.
- AMZN price at the close of February 20, 2025 was $222.88 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 94.91% per annum.
- AMZN price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $4.18 (1.84%). This indicates a possible reversal in the secondary trend direction.
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: February 20, 2025
a = 3.3693
b = 0.0012
s = 0.0696
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 52.39%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0696) – 1
= 32.11%
November 1, 2022 calculations
Top border of price channel:
Exp(Y680)
= Exp(a + b × X680 + 2 × s)
= Exp(a + b × 984 + 2 × s)
= Exp(3.3693 + 0.0012 × 984 + 2 × 0.0696)
= Exp(4.6442)
= $103.98
Bottom border of price channel:
Exp(Y680)
= Exp(a + b × X680 – 2 × s)
= Exp(a + b × 984 – 2 × s)
= Exp(3.3693 + 0.0012 × 984 – 2 × 0.0696)
= Exp(4.3657)
= $78.71
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.3693 + 0.0012 × 1,826 + 2 × 0.0696)
= Exp(5.6160)
= $274.80
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.3693 + 0.0012 × 1,826 – 2 × 0.0696)
= Exp(5.3375)
= $208.00
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 52.39% per annum.
- AMZN price at the close of February 20, 2025 was $222.88 and was inside the primary price channel.
Secondary Trend
Start date: August 2, 2024
End date: February 20, 2025
a = 2.1540
b = 0.0018
s = 0.0337
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0018) – 1
= 94.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0337) – 1
= 14.42%
August 2, 2024 calculations
Top border of price channel:
Exp(Y1,119)
= Exp(a + b × X1,119 + 2 × s)
= Exp(a + b × 1,624 + 2 × s)
= Exp(2.1540 + 0.0018 × 1,624 + 2 × 0.0337)
= Exp(5.1906)
= $179.58
Bottom border of price channel:
Exp(Y1,119)
= Exp(a + b × X1,119 – 2 × s)
= Exp(a + b × 1,624 – 2 × s)
= Exp(2.1540 + 0.0018 × 1,624 – 2 × 0.0337)
= Exp(5.0559)
= $156.95
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.1540 + 0.0018 × 1,826 + 2 × 0.0337)
= Exp(5.5600)
= $259.82
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.1540 + 0.0018 × 1,826 – 2 × 0.0337)
= Exp(5.4252)
= $227.06
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 94.91% per annum.
- AMZN price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $4.18 (1.84%). This indicates a possible reversal in the secondary trend direction.
- 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