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 4.33% per annum.
- ABBV price at the close of March 28, 2025 was $205.29 and was higher than the top border of the primary price channel by $37.02 (22.00%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 32.31% per annum.
- ABBV price at the close of March 28, 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 ABBV 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 15, 2021
End date: December 29, 2023
a = 4.7972
b = 0.0001
s = 0.0584
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0584) – 1
= 26.29%
December 15, 2021 calculations
Top border of price channel:
Exp(Y433)
= Exp(a + b × X433 + 2 × s)
= Exp(a + b × 625 + 2 × s)
= Exp(4.7972 + 0.0001 × 625 + 2 × 0.0584)
= Exp(4.9864)
= $146.41
Bottom border of price channel:
Exp(Y433)
= Exp(a + b × X433 – 2 × s)
= Exp(a + b × 625 – 2 × s)
= Exp(4.7972 + 0.0001 × 625 – 2 × 0.0584)
= Exp(4.7530)
= $115.93
December 29, 2023 calculations
Top border of price channel:
Exp(Y945)
= Exp(a + b × X945 + 2 × s)
= Exp(a + b × 1,369 + 2 × s)
= Exp(4.7972 + 0.0001 × 1,369 + 2 × 0.0584)
= Exp(5.0728)
= $159.61
Bottom border of price channel:
Exp(Y945)
= Exp(a + b × X945 – 2 × s)
= Exp(a + b × 1,369 – 2 × s)
= Exp(4.7972 + 0.0001 × 1,369 – 2 × 0.0584)
= Exp(4.8394)
= $126.39
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 4.33% per annum.
- ABBV price at the close of March 28, 2025 was $205.29 and was higher than the top border of the primary price channel by $37.02 (22.00%).
Secondary Trend
Start date: May 4, 2023
End date: November 8, 2024
a = 3.9695
b = 0.0008
s = 0.0515
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 32.31%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0515) – 1
= 22.85%
May 4, 2023 calculations
Top border of price channel:
Exp(Y780)
= Exp(a + b × X780 + 2 × s)
= Exp(a + b × 1,130 + 2 × s)
= Exp(3.9695 + 0.0008 × 1,130 + 2 × 0.0515)
= Exp(4.9393)
= $139.67
Bottom border of price channel:
Exp(Y780)
= Exp(a + b × X780 – 2 × s)
= Exp(a + b × 1,130 – 2 × s)
= Exp(3.9695 + 0.0008 × 1,130 – 2 × 0.0515)
= Exp(4.7334)
= $113.68
November 8, 2024 calculations
Top border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 + 2 × s)
= Exp(a + b × 1,684 + 2 × s)
= Exp(3.9695 + 0.0008 × 1,684 + 2 × 0.0515)
= Exp(5.3642)
= $213.62
Bottom border of price channel:
Exp(Y1,162)
= Exp(a + b × X1,162 – 2 × s)
= Exp(a + b × 1,684 – 2 × s)
= Exp(3.9695 + 0.0008 × 1,684 – 2 × 0.0515)
= Exp(5.1584)
= $173.89
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 32.31% per annum.
- ABBV price at the close of March 28, 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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