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 November 19, 2024 was $166.57 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 33.28% per annum.
- ABBV price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $11.53 (6.47%). This indicates a possible reversal in the secondary trend direction.
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 = 4.7915
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(Y521)
= Exp(a + b × X521 + 2 × s)
= Exp(a + b × 756 + 2 × s)
= Exp(4.7915 + 0.0001 × 756 + 2 × 0.0584)
= Exp(4.9960)
= $147.81
Bottom border of price channel:
Exp(Y521)
= Exp(a + b × X521 – 2 × s)
= Exp(a + b × 756 – 2 × s)
= Exp(4.7915 + 0.0001 × 756 – 2 × 0.0584)
= Exp(4.7626)
= $117.04
December 29, 2023 calculations
Top border of price channel:
Exp(Y1,033)
= Exp(a + b × X1,033 + 2 × s)
= Exp(a + b × 1,500 + 2 × s)
= Exp(4.7915 + 0.0001 × 1,500 + 2 × 0.0584)
= Exp(5.0823)
= $161.14
Bottom border of price channel:
Exp(Y1,033)
= Exp(a + b × X1,033 – 2 × s)
= Exp(a + b × 1,500 – 2 × s)
= Exp(4.7915 + 0.0001 × 1,500 – 2 × 0.0584)
= Exp(4.8489)
= $127.60
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 4.33% per annum.
- ABBV price at the close of November 19, 2024 was $166.57 and was inside the primary price channel.
Secondary Trend
Start date: May 16, 2023
End date: November 8, 2024
a = 3.8458
b = 0.0008
s = 0.0504
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 33.28%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0504) – 1
= 22.33%
May 16, 2023 calculations
Top border of price channel:
Exp(Y876)
= Exp(a + b × X876 + 2 × s)
= Exp(a + b × 1,273 + 2 × s)
= Exp(3.8458 + 0.0008 × 1,273 + 2 × 0.0504)
= Exp(4.9486)
= $140.98
Bottom border of price channel:
Exp(Y876)
= Exp(a + b × X876 – 2 × s)
= Exp(a + b × 1,273 – 2 × s)
= Exp(3.8458 + 0.0008 × 1,273 – 2 × 0.0504)
= Exp(4.7470)
= $115.24
November 8, 2024 calculations
Top border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 + 2 × s)
= Exp(a + b × 1,815 + 2 × s)
= Exp(3.8458 + 0.0008 × 1,815 + 2 × 0.0504)
= Exp(5.3753)
= $215.99
Bottom border of price channel:
Exp(Y1,250)
= Exp(a + b × X1,250 – 2 × s)
= Exp(a + b × 1,815 – 2 × s)
= Exp(3.8458 + 0.0008 × 1,815 – 2 × 0.0504)
= Exp(5.1737)
= $176.56
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 33.28% per annum.
- ABBV price at the close of November 19, 2024 was lower than the bottom border of the secondary price channel by $11.53 (6.47%). This indicates a possible reversal in the secondary trend direction.
- 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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