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 12.82% per annum.
- UPS price at the close of May 9, 2025 was $95.89 and was lower than the bottom border of the primary price channel by $5.72 (5.63%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 45.76% per annum.
- UPS price at the close of May 9, 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: October 22, 2021
End date: May 9, 2025
a = 5.4468
b = -0.0004
s = 0.0701
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -12.82%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0701) – 1
= 32.36%
October 22, 2021 calculations
Top border of price channel:
Exp(Y367)
= Exp(a + b × X367 + 2 × s)
= Exp(a + b × 529 + 2 × s)
= Exp(5.4468 + -0.0004 × 529 + 2 × 0.0701)
= Exp(5.3882)
= $218.81
Bottom border of price channel:
Exp(Y367)
= Exp(a + b × X367 – 2 × s)
= Exp(a + b × 529 – 2 × s)
= Exp(5.4468 + -0.0004 × 529 – 2 × 0.0701)
= Exp(5.1078)
= $165.31
May 9, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.4468 + -0.0004 × 1,824 + 2 × 0.0701)
= Exp(4.9015)
= $134.49
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.4468 + -0.0004 × 1,824 – 2 × 0.0701)
= Exp(4.6212)
= $101.61
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 12.82% per annum.
- UPS price at the close of May 9, 2025 was $95.89 and was lower than the bottom border of the primary price channel by $5.72 (5.63%).
Secondary Trend
Start date: October 24, 2024
End date: May 9, 2025
a = 7.6564
b = -0.0017
s = 0.0524
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0017) – 1
= -45.76%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0524) – 1
= 23.31%
October 24, 2024 calculations
Top border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 + 2 × s)
= Exp(a + b × 1,627 + 2 × s)
= Exp(7.6564 + -0.0017 × 1,627 + 2 × 0.0524)
= Exp(5.0345)
= $153.63
Bottom border of price channel:
Exp(Y1,122)
= Exp(a + b × X1,122 – 2 × s)
= Exp(a + b × 1,627 – 2 × s)
= Exp(7.6564 + -0.0017 × 1,627 – 2 × 0.0524)
= Exp(4.8250)
= $124.59
May 9, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(7.6564 + -0.0017 × 1,824 + 2 × 0.0524)
= Exp(4.7044)
= $110.43
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(7.6564 + -0.0017 × 1,824 – 2 × 0.0524)
= Exp(4.4949)
= $89.56
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 45.76% per annum.
- UPS price at the close of May 9, 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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