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 12.59% per annum.
- AAPL price at the close of January 29, 2025 was $239.36 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 25.90% per annum.
- AAPL price at the close of January 29, 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: August 12, 2020
End date: June 10, 2024
a = 4.7297
b = 0.0003
s = 0.0868
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 12.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0868) – 1
= 41.53%
August 12, 2020 calculations
Top border of price channel:
Exp(Y135)
= Exp(a + b × X135 + 2 × s)
= Exp(a + b × 195 + 2 × s)
= Exp(4.7297 + 0.0003 × 195 + 2 × 0.0868)
= Exp(4.9668)
= $143.56
Bottom border of price channel:
Exp(Y135)
= Exp(a + b × X135 – 2 × s)
= Exp(a + b × 195 – 2 × s)
= Exp(4.7297 + 0.0003 × 195 – 2 × 0.0868)
= Exp(4.6195)
= $101.44
June 10, 2024 calculations
Top border of price channel:
Exp(Y1,097)
= Exp(a + b × X1,097 + 2 × s)
= Exp(a + b × 1,593 + 2 × s)
= Exp(4.7297 + 0.0003 × 1,593 + 2 × 0.0868)
= Exp(5.4211)
= $226.14
Bottom border of price channel:
Exp(Y1,097)
= Exp(a + b × X1,097 – 2 × s)
= Exp(a + b × 1,593 – 2 × s)
= Exp(4.7297 + 0.0003 × 1,593 – 2 × 0.0868)
= Exp(5.0738)
= $159.78
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 12.59% per annum.
- AAPL price at the close of January 29, 2025 was $239.36 and was inside the primary price channel.
Secondary Trend
Start date: September 28, 2022
End date: January 29, 2025
a = 4.3245
b = 0.0006
s = 0.0707
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 25.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0707) – 1
= 32.70%
September 28, 2022 calculations
Top border of price channel:
Exp(Y671)
= Exp(a + b × X671 + 2 × s)
= Exp(a + b × 972 + 2 × s)
= Exp(4.3245 + 0.0006 × 972 + 2 × 0.0707)
= Exp(5.0793)
= $160.66
Bottom border of price channel:
Exp(Y671)
= Exp(a + b × X671 – 2 × s)
= Exp(a + b × 972 – 2 × s)
= Exp(4.3245 + 0.0006 × 972 – 2 × 0.0707)
= Exp(4.7963)
= $121.07
January 29, 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(4.3245 + 0.0006 × 1,826 + 2 × 0.0707)
= Exp(5.6181)
= $275.37
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.3245 + 0.0006 × 1,826 – 2 × 0.0707)
= Exp(5.3352)
= $207.50
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 25.90% per annum.
- AAPL price at the close of January 29, 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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