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 44.74% per annum.
- AAPL price at the close of April 22, 2025 was $199.74 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 77.64% per annum.
- AAPL price at the close of April 22, 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 AAPL 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: December 3, 2024
End date: April 22, 2025
a = 8.2876
b = -0.0016
s = 0.0522
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0016) – 1
= -44.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0522) – 1
= 23.23%
December 3, 2024 calculations
Top border of price channel:
Exp(Y1,161)
= Exp(a + b × X1,161 + 2 × s)
= Exp(a + b × 1,685 + 2 × s)
= Exp(8.2876 + -0.0016 × 1,685 + 2 × 0.0522)
= Exp(5.6535)
= $285.30
Bottom border of price channel:
Exp(Y1,161)
= Exp(a + b × X1,161 – 2 × s)
= Exp(a + b × 1,685 – 2 × s)
= Exp(8.2876 + -0.0016 × 1,685 – 2 × 0.0522)
= Exp(5.4447)
= $231.52
April 22, 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(8.2876 + -0.0016 × 1,825 + 2 × 0.0522)
= Exp(5.4260)
= $227.24
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(8.2876 + -0.0016 × 1,825 – 2 × 0.0522)
= Exp(5.2171)
= $184.41
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 44.74% per annum.
- AAPL price at the close of April 22, 2025 was $199.74 and was inside the primary price channel.
Secondary Trend
Start date: February 13, 2025
End date: April 22, 2025
a = 12.7374
b = -0.0041
s = 0.0457
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0041) – 1
= -77.64%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0457) – 1
= 20.05%
February 13, 2025 calculations
Top border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 + 2 × s)
= Exp(a + b × 1,757 + 2 × s)
= Exp(12.7374 + -0.0041 × 1,757 + 2 × 0.0457)
= Exp(5.6191)
= $275.64
Bottom border of price channel:
Exp(Y1,209)
= Exp(a + b × X1,209 – 2 × s)
= Exp(a + b × 1,757 – 2 × s)
= Exp(12.7374 + -0.0041 × 1,757 – 2 × 0.0457)
= Exp(5.4364)
= $229.60
April 22, 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(12.7374 + -0.0041 × 1,825 + 2 × 0.0457)
= Exp(5.3401)
= $208.53
Bottom border of price channel:
Exp(Y1,255)
= Exp(a + b × X1,255 – 2 × s)
= Exp(a + b × 1,825 – 2 × s)
= Exp(12.7374 + -0.0041 × 1,825 – 2 × 0.0457)
= Exp(5.1573)
= $173.70
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 77.64% per annum.
- AAPL price at the close of April 22, 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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