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 50.43% per annum.
- CTAS price at the close of February 20, 2025 was $205.93 and was lower than the bottom border of the primary price channel by $10.87 (5.01%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 7.09% per annum.
- CTAS price at the close of February 20, 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 CTAS 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: January 18, 2023
End date: December 17, 2024
a = 3.4106
b = 0.0011
s = 0.0373
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 50.43%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0373) – 1
= 16.07%
January 18, 2023 calculations
Top border of price channel:
Exp(Y732)
= Exp(a + b × X732 + 2 × s)
= Exp(a + b × 1,062 + 2 × s)
= Exp(3.4106 + 0.0011 × 1,062 + 2 × 0.0373)
= Exp(4.6733)
= $107.05
Bottom border of price channel:
Exp(Y732)
= Exp(a + b × X732 – 2 × s)
= Exp(a + b × 1,062 – 2 × s)
= Exp(3.4106 + 0.0011 × 1,062 – 2 × 0.0373)
= Exp(4.5242)
= $92.23
December 17, 2024 calculations
Top border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 + 2 × s)
= Exp(a + b × 1,761 + 2 × s)
= Exp(3.4106 + 0.0011 × 1,761 + 2 × 0.0373)
= Exp(5.4553)
= $233.99
Bottom border of price channel:
Exp(Y1,214)
= Exp(a + b × X1,214 – 2 × s)
= Exp(a + b × 1,761 – 2 × s)
= Exp(3.4106 + 0.0011 × 1,761 – 2 × 0.0373)
= Exp(5.3062)
= $201.59
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 50.43% per annum.
- CTAS price at the close of February 20, 2025 was $205.93 and was lower than the bottom border of the primary price channel by $10.87 (5.01%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: August 26, 2024
End date: February 20, 2025
a = 5.6712
b = -0.0002
s = 0.0507
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0002) – 1
= -7.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0507) – 1
= 22.50%
August 26, 2024 calculations
Top border of price channel:
Exp(Y1,135)
= Exp(a + b × X1,135 + 2 × s)
= Exp(a + b × 1,648 + 2 × s)
= Exp(5.6712 + -0.0002 × 1,648 + 2 × 0.0507)
= Exp(5.4406)
= $230.59
Bottom border of price channel:
Exp(Y1,135)
= Exp(a + b × X1,135 – 2 × s)
= Exp(a + b × 1,648 – 2 × s)
= Exp(5.6712 + -0.0002 × 1,648 – 2 × 0.0507)
= Exp(5.2377)
= $188.23
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(5.6712 + -0.0002 × 1,826 + 2 × 0.0507)
= Exp(5.4048)
= $222.47
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.6712 + -0.0002 × 1,826 – 2 × 0.0507)
= Exp(5.2018)
= $181.60
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 7.09% per annum.
- CTAS 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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