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 113.03% per annum.
- UAL price at the close of April 10, 2025 was $62.75 and was lower than the bottom border of the primary price channel by $8.80 (12.30%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 95.61% per annum.
- UAL price at the close of April 10, 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 9, 2023
End date: March 10, 2025
a = 0.8387
b = 0.0021
s = 0.1727
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 113.03%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1727) – 1
= 99.55%
October 9, 2023 calculations
Top border of price channel:
Exp(Y879)
= Exp(a + b × X879 + 2 × s)
= Exp(a + b × 1,274 + 2 × s)
= Exp(0.8387 + 0.0021 × 1,274 + 2 × 0.1727)
= Exp(3.8238)
= $45.78
Bottom border of price channel:
Exp(Y879)
= Exp(a + b × X879 – 2 × s)
= Exp(a + b × 1,274 – 2 × s)
= Exp(0.8387 + 0.0021 × 1,274 – 2 × 0.1727)
= Exp(3.1329)
= $22.94
March 10, 2025 calculations
Top border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 + 2 × s)
= Exp(a + b × 1,792 + 2 × s)
= Exp(0.8387 + 0.0021 × 1,792 + 2 × 0.1727)
= Exp(4.8971)
= $133.90
Bottom border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 – 2 × s)
= Exp(a + b × 1,792 – 2 × s)
= Exp(0.8387 + 0.0021 × 1,792 – 2 × 0.1727)
= Exp(4.2062)
= $67.10
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 113.03% per annum.
- UAL price at the close of April 10, 2025 was $62.75 and was lower than the bottom border of the primary price channel by $8.80 (12.30%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: January 27, 2025
End date: April 10, 2025
a = 19.7489
b = -0.0086
s = 0.0654
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0086) – 1
= -95.61%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0654) – 1
= 29.92%
January 27, 2025 calculations
Top border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 + 2 × s)
= Exp(a + b × 1,750 + 2 × s)
= Exp(19.7489 + -0.0086 × 1,750 + 2 × 0.0654)
= Exp(4.8916)
= $133.16
Bottom border of price channel:
Exp(Y1,204)
= Exp(a + b × X1,204 – 2 × s)
= Exp(a + b × 1,750 – 2 × s)
= Exp(19.7489 + -0.0086 × 1,750 – 2 × 0.0654)
= Exp(4.6298)
= $102.50
April 10, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(19.7489 + -0.0086 × 1,823 + 2 × 0.0654)
= Exp(4.2664)
= $71.26
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(19.7489 + -0.0086 × 1,823 – 2 × 0.0654)
= Exp(4.0046)
= $54.85
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 95.61% per annum.
- UAL price at the close of April 10, 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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