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 115.83% per annum.
- UAL price at the close of March 7, 2025 was $82.88 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 444.81% per annum.
- UAL price at the close of March 7, 2025 was lower than the bottom border of the secondary price channel by $11.27 (11.97%). This indicates a possible reversal in the secondary trend direction.
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 13, 2023
End date: March 7, 2025
a = 0.7082
b = 0.0021
s = 0.1720
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 115.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1720) – 1
= 98.99%
October 13, 2023 calculations
Top border of price channel:
Exp(Y907)
= Exp(a + b × X907 + 2 × s)
= Exp(a + b × 1,313 + 2 × s)
= Exp(0.7082 + 0.0021 × 1,313 + 2 × 0.1720)
= Exp(3.8197)
= $45.59
Bottom border of price channel:
Exp(Y907)
= Exp(a + b × X907 – 2 × s)
= Exp(a + b × 1,313 – 2 × s)
= Exp(0.7082 + 0.0021 × 1,313 – 2 × 0.1720)
= Exp(3.1316)
= $22.91
March 7, 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(0.7082 + 0.0021 × 1,824 + 2 × 0.1720)
= Exp(4.8967)
= $133.85
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(0.7082 + 0.0021 × 1,824 – 2 × 0.1720)
= Exp(4.2086)
= $67.26
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 115.83% per annum.
- UAL price at the close of March 7, 2025 was $82.88 and was inside the primary price channel.
Secondary Trend
Start date: July 8, 2024
End date: March 7, 2025
a = -3.6400
b = 0.0046
s = 0.1434
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0046) – 1
= 444.81%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1434) – 1
= 77.44%
July 8, 2024 calculations
Top border of price channel:
Exp(Y1,089)
= Exp(a + b × X1,089 + 2 × s)
= Exp(a + b × 1,582 + 2 × s)
= Exp(-3.6400 + 0.0046 × 1,582 + 2 × 0.1434)
= Exp(3.9944)
= $54.29
Bottom border of price channel:
Exp(Y1,089)
= Exp(a + b × X1,089 – 2 × s)
= Exp(a + b × 1,582 – 2 × s)
= Exp(-3.6400 + 0.0046 × 1,582 – 2 × 0.1434)
= Exp(3.4210)
= $30.60
March 7, 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(-3.6400 + 0.0046 × 1,824 + 2 × 0.1434)
= Exp(5.1184)
= $167.06
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-3.6400 + 0.0046 × 1,824 – 2 × 0.1434)
= Exp(4.5449)
= $94.15
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 444.81% per annum.
- UAL price at the close of March 7, 2025 was lower than the bottom border of the secondary price channel by $11.27 (11.97%). This indicates a possible reversal in the secondary trend direction.
- 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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