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 11.91% per annum.
- UPS price at the close of April 25, 2025 was $97.91 and was lower than the bottom border of the primary price channel by $8.63 (8.10%).
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 17.28% per annum.
- UPS price at the close of April 25, 2025 was lower than the bottom border of the secondary price channel by $3.30 (3.26%).
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: April 3, 2025
a = 5.4246
b = -0.0003
s = 0.0612
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -11.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0612) – 1
= 27.74%
October 22, 2021 calculations
Top border of price channel:
Exp(Y377)
= Exp(a + b × X377 + 2 × s)
= Exp(a + b × 543 + 2 × s)
= Exp(5.4246 + -0.0003 × 543 + 2 × 0.0612)
= Exp(5.3583)
= $212.37
Bottom border of price channel:
Exp(Y377)
= Exp(a + b × X377 – 2 × s)
= Exp(a + b × 543 – 2 × s)
= Exp(5.4246 + -0.0003 × 543 – 2 × 0.0612)
= Exp(5.1135)
= $166.25
April 3, 2025 calculations
Top border of price channel:
Exp(Y1,241)
= Exp(a + b × X1,241 + 2 × s)
= Exp(a + b × 1,802 + 2 × s)
= Exp(5.4246 + -0.0003 × 1,802 + 2 × 0.0612)
= Exp(4.9209)
= $137.13
Bottom border of price channel:
Exp(Y1,241)
= Exp(a + b × X1,241 – 2 × s)
= Exp(a + b × 1,802 – 2 × s)
= Exp(5.4246 + -0.0003 × 1,802 – 2 × 0.0612)
= Exp(4.6761)
= $107.35
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 11.91% per annum.
- UPS price at the close of April 25, 2025 was $97.91 and was lower than the bottom border of the primary price channel by $8.63 (8.10%).
Secondary Trend
Start date: January 31, 2023
End date: April 25, 2025
a = 5.6749
b = -0.0005
s = 0.0548
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0005) – 1
= -17.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0548) – 1
= 24.51%
January 31, 2023 calculations
Top border of price channel:
Exp(Y696)
= Exp(a + b × X696 + 2 × s)
= Exp(a + b × 1,009 + 2 × s)
= Exp(5.6749 + -0.0005 × 1,009 + 2 × 0.0548)
= Exp(5.2600)
= $192.49
Bottom border of price channel:
Exp(Y696)
= Exp(a + b × X696 – 2 × s)
= Exp(a + b × 1,009 – 2 × s)
= Exp(5.6749 + -0.0005 × 1,009 – 2 × 0.0548)
= Exp(5.0408)
= $154.60
April 25, 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(5.6749 + -0.0005 × 1,824 + 2 × 0.0548)
= Exp(4.8364)
= $126.02
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.6749 + -0.0005 × 1,824 – 2 × 0.0548)
= Exp(4.6172)
= $101.21
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 17.28% per annum.
- UPS price at the close of April 25, 2025 was lower than the bottom border of the secondary price channel by $3.30 (3.26%).
- 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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