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 109.97% per annum.
- UAL price at the close of April 29, 2025 was $68.93 and was lower than the bottom border of the primary price channel by $4.65 (6.31%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 90.17% per annum.
- UAL price at the close of April 29, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 UAL 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 2, 2023
End date: March 10, 2025
a = 0.9374
b = 0.0020
s = 0.1740
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0020) – 1
= 109.97%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1740) – 1
= 100.56%
October 2, 2023 calculations
Top border of price channel:
Exp(Y861)
= Exp(a + b × X861 + 2 × s)
= Exp(a + b × 1,250 + 2 × s)
= Exp(0.9374 + 0.0020 × 1,250 + 2 × 0.1740)
= Exp(3.8257)
= $45.86
Bottom border of price channel:
Exp(Y861)
= Exp(a + b × X861 – 2 × s)
= Exp(a + b × 1,250 – 2 × s)
= Exp(0.9374 + 0.0020 × 1,250 – 2 × 0.1740)
= Exp(3.1297)
= $22.87
March 10, 2025 calculations
Top border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 + 2 × s)
= Exp(a + b × 1,775 + 2 × s)
= Exp(0.9374 + 0.0020 × 1,775 + 2 × 0.1740)
= Exp(4.8926)
= $133.30
Bottom border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 – 2 × s)
= Exp(a + b × 1,775 – 2 × s)
= Exp(0.9374 + 0.0020 × 1,775 – 2 × 0.1740)
= Exp(4.1967)
= $66.47
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 109.97% per annum.
- UAL price at the close of April 29, 2025 was $68.93 and was lower than the bottom border of the primary price channel by $4.65 (6.31%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 10, 2025
End date: April 25, 2025
a = 15.6894
b = -0.0064
s = 0.0790
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0064) – 1
= -90.17%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0790) – 1
= 37.14%
January 10, 2025 calculations
Top border of price channel:
Exp(Y1,181)
= Exp(a + b × X1,181 + 2 × s)
= Exp(a + b × 1,716 + 2 × s)
= Exp(15.6894 + -0.0064 × 1,716 + 2 × 0.0790)
= Exp(4.9417)
= $140.01
Bottom border of price channel:
Exp(Y1,181)
= Exp(a + b × X1,181 – 2 × s)
= Exp(a + b × 1,716 – 2 × s)
= Exp(15.6894 + -0.0064 × 1,716 – 2 × 0.0790)
= Exp(4.6259)
= $102.10
April 25, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(15.6894 + -0.0064 × 1,821 + 2 × 0.0790)
= Exp(4.2744)
= $71.84
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(15.6894 + -0.0064 × 1,821 – 2 × 0.0790)
= Exp(3.9586)
= $52.38
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 90.17% per annum.
- UAL price at the close of April 29, 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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