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 34.80% per annum.
- ABT price at the close of March 28, 2025 was $130.82 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 64.41% per annum.
- ABT price at the close of March 28, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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 6, 2024
End date: March 28, 2025
a = 3.3759
b = 0.0008
s = 0.0370
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 34.80%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0370) – 1
= 15.94%
May 6, 2024 calculations
Top border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 + 2 × s)
= Exp(a + b × 1,498 + 2 × s)
= Exp(3.3759 + 0.0008 × 1,498 + 2 × 0.0370)
= Exp(4.6753)
= $107.26
Bottom border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 – 2 × s)
= Exp(a + b × 1,498 – 2 × s)
= Exp(3.3759 + 0.0008 × 1,498 – 2 × 0.0370)
= Exp(4.5274)
= $92.52
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.3759 + 0.0008 × 1,824 + 2 × 0.0370)
= Exp(4.9420)
= $140.05
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.3759 + 0.0008 × 1,824 – 2 × 0.0370)
= Exp(4.7941)
= $120.79
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 34.80% per annum.
- ABT price at the close of March 28, 2025 was $130.82 and was inside the primary price channel.
Secondary Trend
Start date: February 24, 2025
End date: March 28, 2025
a = 10.0005
b = -0.0028
s = 0.0222
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0028) – 1
= -64.41%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0222) – 1
= 9.30%
February 24, 2025 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,792 + 2 × s)
= Exp(10.0005 + -0.0028 × 1,792 + 2 × 0.0222)
= Exp(4.9723)
= $144.36
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,792 – 2 × s)
= Exp(10.0005 + -0.0028 × 1,792 – 2 × 0.0222)
= Exp(4.8834)
= $132.08
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(10.0005 + -0.0028 × 1,824 + 2 × 0.0222)
= Exp(4.8818)
= $131.86
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(10.0005 + -0.0028 × 1,824 – 2 × 0.0222)
= Exp(4.7928)
= $120.64
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 64.41% per annum.
- ABT 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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