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 31.60% per annum.
- LOW price at the close of April 21, 2025 was $212.77 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 57.54% per annum.
- LOW price at the close of April 21, 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 LOW 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: September 30, 2024
End date: April 21, 2025
a = 7.3211
b = -0.0010
s = 0.0345
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0010) – 1
= -31.60%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0345) – 1
= 14.78%
September 30, 2024 calculations
Top border of price channel:
Exp(Y1,117)
= Exp(a + b × X1,117 + 2 × s)
= Exp(a + b × 1,622 + 2 × s)
= Exp(7.3211 + -0.0010 × 1,622 + 2 × 0.0345)
= Exp(5.7025)
= $299.62
Bottom border of price channel:
Exp(Y1,117)
= Exp(a + b × X1,117 – 2 × s)
= Exp(a + b × 1,622 – 2 × s)
= Exp(7.3211 + -0.0010 × 1,622 – 2 × 0.0345)
= Exp(5.5646)
= $261.03
April 21, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(7.3211 + -0.0010 × 1,825 + 2 × 0.0345)
= Exp(5.4913)
= $242.58
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(7.3211 + -0.0010 × 1,825 – 2 × 0.0345)
= Exp(5.3534)
= $211.33
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 31.60% per annum.
- LOW price at the close of April 21, 2025 was $212.77 and was inside the primary price channel.
Secondary Trend
Start date: January 21, 2025
End date: April 21, 2025
a = 9.6525
b = -0.0023
s = 0.0215
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0023) – 1
= -57.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0215) – 1
= 8.97%
January 21, 2025 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,735 + 2 × s)
= Exp(9.6525 + -0.0023 × 1,735 + 2 × 0.0215)
= Exp(5.6233)
= $276.81
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,735 – 2 × s)
= Exp(9.6525 + -0.0023 × 1,735 – 2 × 0.0215)
= Exp(5.5374)
= $254.02
April 21, 2025 calculations
Top border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 + 2 × s)
= Exp(a + b × 1,825 + 2 × s)
= Exp(9.6525 + -0.0023 × 1,825 + 2 × 0.0215)
= Exp(5.4121)
= $224.11
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(9.6525 + -0.0023 × 1,825 – 2 × 0.0215)
= Exp(5.3262)
= $205.65
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 57.54% per annum.
- LOW price at the close of April 21, 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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