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 1,880.91% per annum.
- UAL price at the close of February 4, 2025 was $108.67 and was lower than the bottom border of the primary price channel by $40.55 (27.17%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 115.43% per annum.
- UAL price at the close of February 4, 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 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: July 31, 2024
End date: December 11, 2024
a = -9.8179
b = 0.0082
s = 0.0578
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0082) – 1
= 1,880.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0578) – 1
= 26.01%
July 31, 2024 calculations
Top border of price channel:
Exp(Y1,128)
= Exp(a + b × X1,128 + 2 × s)
= Exp(a + b × 1,638 + 2 × s)
= Exp(-9.8179 + 0.0082 × 1,638 + 2 × 0.0578)
= Exp(3.6985)
= $40.39
Bottom border of price channel:
Exp(Y1,128)
= Exp(a + b × X1,128 – 2 × s)
= Exp(a + b × 1,638 – 2 × s)
= Exp(-9.8179 + 0.0082 × 1,638 – 2 × 0.0578)
= Exp(3.4673)
= $32.05
December 11, 2024 calculations
Top border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 + 2 × s)
= Exp(a + b × 1,771 + 2 × s)
= Exp(-9.8179 + 0.0082 × 1,771 + 2 × 0.0578)
= Exp(4.7866)
= $119.90
Bottom border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 – 2 × s)
= Exp(a + b × 1,771 – 2 × s)
= Exp(-9.8179 + 0.0082 × 1,771 – 2 × 0.0578)
= Exp(4.5554)
= $95.15
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1,880.91% per annum.
- UAL price at the close of February 4, 2025 was $108.67 and was lower than the bottom border of the primary price channel by $40.55 (27.17%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 6, 2024
End date: February 4, 2025
a = 0.8478
b = 0.0021
s = 0.0292
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 115.43%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0292) – 1
= 12.38%
November 6, 2024 calculations
Top border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 + 2 × s)
= Exp(a + b × 1,736 + 2 × s)
= Exp(0.8478 + 0.0021 × 1,736 + 2 × 0.0292)
= Exp(4.5562)
= $95.22
Bottom border of price channel:
Exp(Y1,197)
= Exp(a + b × X1,197 – 2 × s)
= Exp(a + b × 1,736 – 2 × s)
= Exp(0.8478 + 0.0021 × 1,736 – 2 × 0.0292)
= Exp(4.4395)
= $84.73
February 4, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(0.8478 + 0.0021 × 1,826 + 2 × 0.0292)
= Exp(4.7455)
= $115.06
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(0.8478 + 0.0021 × 1,826 – 2 × 0.0292)
= Exp(4.6287)
= $102.38
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 115.43% per annum.
- UAL price at the close of February 4, 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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