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 9.98% per annum.
- UPS price at the close of February 20, 2025 was $116.60 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 15.94% per annum.
- UPS 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 UPS 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: April 29, 2021
End date: February 20, 2025
a = 5.3686
b = -0.0003
s = 0.0649
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -9.98%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0649) – 1
= 29.64%
April 29, 2021 calculations
Top border of price channel:
Exp(Y299)
= Exp(a + b × X299 + 2 × s)
= Exp(a + b × 433 + 2 × s)
= Exp(5.3686 + -0.0003 × 433 + 2 × 0.0649)
= Exp(5.3736)
= $215.65
Bottom border of price channel:
Exp(Y299)
= Exp(a + b × X299 – 2 × s)
= Exp(a + b × 433 – 2 × s)
= Exp(5.3686 + -0.0003 × 433 – 2 × 0.0649)
= Exp(5.1140)
= $166.34
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(5.3686 + -0.0003 × 1,826 + 2 × 0.0649)
= Exp(4.9723)
= $144.36
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.3686 + -0.0003 × 1,826 – 2 × 0.0649)
= Exp(4.7127)
= $111.35
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 9.98% per annum.
- UPS price at the close of February 20, 2025 was $116.60 and was inside the primary price channel.
Secondary Trend
Start date: January 31, 2023
End date: February 20, 2025
a = 5.6503
b = -0.0005
s = 0.0482
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -15.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0482) – 1
= 21.25%
January 31, 2023 calculations
Top border of price channel:
Exp(Y741)
= Exp(a + b × X741 + 2 × s)
= Exp(a + b × 1,075 + 2 × s)
= Exp(5.6503 + -0.0005 × 1,075 + 2 × 0.0482)
= Exp(5.2351)
= $187.75
Bottom border of price channel:
Exp(Y741)
= Exp(a + b × X741 – 2 × s)
= Exp(a + b × 1,075 – 2 × s)
= Exp(5.6503 + -0.0005 × 1,075 – 2 × 0.0482)
= Exp(5.0425)
= $154.85
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(5.6503 + -0.0005 × 1,826 + 2 × 0.0482)
= Exp(4.8777)
= $131.33
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.6503 + -0.0005 × 1,826 – 2 × 0.0482)
= Exp(4.6851)
= $108.32
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 15.94% per annum.
- UPS 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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