Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.74% per annum.
- PFE price at the close of February 20, 2025 was $25.90 and was higher than the top border of the primary price channel by $1.65 (6.82%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.33% per annum.
- PFE price at the close of February 20, 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 PFE 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 17, 2021
End date: July 11, 2024
a = 4.4021
b = -0.0007
s = 0.0710
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0710) – 1
= 32.86%
November 17, 2021 calculations
Top border of price channel:
Exp(Y440)
= Exp(a + b × X440 + 2 × s)
= Exp(a + b × 635 + 2 × s)
= Exp(4.4021 + -0.0007 × 635 + 2 × 0.0710)
= Exp(4.0726)
= $58.71
Bottom border of price channel:
Exp(Y440)
= Exp(a + b × X440 – 2 × s)
= Exp(a + b × 635 – 2 × s)
= Exp(4.4021 + -0.0007 × 635 – 2 × 0.0710)
= Exp(3.7885)
= $44.19
July 11, 2024 calculations
Top border of price channel:
Exp(Y1,103)
= Exp(a + b × X1,103 + 2 × s)
= Exp(a + b × 1,602 + 2 × s)
= Exp(4.4021 + -0.0007 × 1,602 + 2 × 0.0710)
= Exp(3.3546)
= $28.63
Bottom border of price channel:
Exp(Y1,103)
= Exp(a + b × X1,103 – 2 × s)
= Exp(a + b × 1,602 – 2 × s)
= Exp(4.4021 + -0.0007 × 1,602 – 2 × 0.0710)
= Exp(3.0704)
= $21.55
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.74% per annum.
- PFE price at the close of February 20, 2025 was $25.90 and was higher than the top border of the primary price channel by $1.65 (6.82%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 19, 2023
End date: February 20, 2025
a = 3.2991
b = 0.0000
s = 0.0480
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= -0.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0480) – 1
= 21.17%
October 19, 2023 calculations
Top border of price channel:
Exp(Y922)
= Exp(a + b × X922 + 2 × s)
= Exp(a + b × 1,336 + 2 × s)
= Exp(3.2991 + 0.0000 × 1,336 + 2 × 0.0480)
= Exp(3.3828)
= $29.45
Bottom border of price channel:
Exp(Y922)
= Exp(a + b × X922 – 2 × s)
= Exp(a + b × 1,336 – 2 × s)
= Exp(3.2991 + 0.0000 × 1,336 – 2 × 0.0480)
= Exp(3.1908)
= $24.31
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(3.2991 + 0.0000 × 1,826 + 2 × 0.0480)
= Exp(3.3783)
= $29.32
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.2991 + 0.0000 × 1,826 – 2 × 0.0480)
= Exp(3.1863)
= $24.20
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 0.33% per annum.
- PFE price at the close of February 20, 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.
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