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 33.50% per annum.
- ABT price at the close of February 20, 2025 was $133.17 and was higher than the top border of the primary price channel by $1.13 (0.86%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 346.74% per annum.
- ABT price at the close of February 20, 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 ABT 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: May 2, 2024
End date: December 4, 2024
a = 3.3923
b = 0.0008
s = 0.0227
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 33.50%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0227) – 1
= 9.52%
May 2, 2024 calculations
Top border of price channel:
Exp(Y1,056)
= Exp(a + b × X1,056 + 2 × s)
= Exp(a + b × 1,532 + 2 × s)
= Exp(3.3923 + 0.0008 × 1,532 + 2 × 0.0227)
= Exp(4.6504)
= $104.62
Bottom border of price channel:
Exp(Y1,056)
= Exp(a + b × X1,056 – 2 × s)
= Exp(a + b × 1,532 – 2 × s)
= Exp(3.3923 + 0.0008 × 1,532 – 2 × 0.0227)
= Exp(4.5594)
= $95.53
December 4, 2024 calculations
Top border of price channel:
Exp(Y1,205)
= Exp(a + b × X1,205 + 2 × s)
= Exp(a + b × 1,748 + 2 × s)
= Exp(3.3923 + 0.0008 × 1,748 + 2 × 0.0227)
= Exp(4.8213)
= $124.13
Bottom border of price channel:
Exp(Y1,205)
= Exp(a + b × X1,205 – 2 × s)
= Exp(a + b × 1,748 – 2 × s)
= Exp(3.3923 + 0.0008 × 1,748 – 2 × 0.0227)
= Exp(4.7304)
= $113.34
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 33.50% per annum.
- ABT price at the close of February 20, 2025 was $133.17 and was higher than the top border of the primary price channel by $1.13 (0.86%).
Secondary Trend
Start date: December 30, 2024
End date: February 20, 2025
a = -2.5775
b = 0.0041
s = 0.0261
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0041) – 1
= 346.74%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0261) – 1
= 10.98%
December 30, 2024 calculations
Top border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 + 2 × s)
= Exp(a + b × 1,774 + 2 × s)
= Exp(-2.5775 + 0.0041 × 1,774 + 2 × 0.0261)
= Exp(4.7495)
= $115.52
Bottom border of price channel:
Exp(Y1,222)
= Exp(a + b × X1,222 – 2 × s)
= Exp(a + b × 1,774 – 2 × s)
= Exp(-2.5775 + 0.0041 × 1,774 – 2 × 0.0261)
= Exp(4.6453)
= $104.09
February 20, 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(-2.5775 + 0.0041 × 1,826 + 2 × 0.0261)
= Exp(4.9627)
= $142.98
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-2.5775 + 0.0041 × 1,826 – 2 × 0.0261)
= Exp(4.8585)
= $128.83
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 346.74% per annum.
- ABT price at the close of February 20, 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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