Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.14% per annum.
- DHR price at the close of February 20, 2025 was $207.95 and was higher than the top border of the primary price channel by $4.47 (2.20%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.91% per annum.
- DHR price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $6.97 (3.24%). This indicates a possible reversal in the secondary trend direction.
- 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 DHR 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: June 21, 2021
End date: December 12, 2023
a = 5.7299
b = -0.0003
s = 0.0603
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0603) – 1
= 27.29%
June 21, 2021 calculations
Top border of price channel:
Exp(Y335)
= Exp(a + b × X335 + 2 × s)
= Exp(a + b × 486 + 2 × s)
= Exp(5.7299 + -0.0003 × 486 + 2 × 0.0603)
= Exp(5.7082)
= $301.31
Bottom border of price channel:
Exp(Y335)
= Exp(a + b × X335 – 2 × s)
= Exp(a + b × 486 – 2 × s)
= Exp(5.7299 + -0.0003 × 486 – 2 × 0.0603)
= Exp(5.4669)
= $236.72
December 12, 2023 calculations
Top border of price channel:
Exp(Y959)
= Exp(a + b × X959 + 2 × s)
= Exp(a + b × 1,390 + 2 × s)
= Exp(5.7299 + -0.0003 × 1,390 + 2 × 0.0603)
= Exp(5.4433)
= $231.21
Bottom border of price channel:
Exp(Y959)
= Exp(a + b × X959 – 2 × s)
= Exp(a + b × 1,390 – 2 × s)
= Exp(5.7299 + -0.0003 × 1,390 – 2 × 0.0603)
= Exp(5.2020)
= $181.64
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.14% per annum.
- DHR price at the close of February 20, 2025 was $207.95 and was higher than the top border of the primary price channel by $4.47 (2.20%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 22, 2022
End date: January 28, 2025
a = 5.2790
b = 0.0001
s = 0.0744
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 4.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0744) – 1
= 34.65%
April 22, 2022 calculations
Top border of price channel:
Exp(Y547)
= Exp(a + b × X547 + 2 × s)
= Exp(a + b × 791 + 2 × s)
= Exp(5.2790 + 0.0001 × 791 + 2 × 0.0744)
= Exp(5.5317)
= $252.57
Bottom border of price channel:
Exp(Y547)
= Exp(a + b × X547 – 2 × s)
= Exp(a + b × 791 – 2 × s)
= Exp(5.2790 + 0.0001 × 791 – 2 × 0.0744)
= Exp(5.2342)
= $187.58
January 28, 2025 calculations
Top border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 + 2 × s)
= Exp(a + b × 1,803 + 2 × s)
= Exp(5.2790 + 0.0001 × 1,803 + 2 × 0.0744)
= Exp(5.6647)
= $288.51
Bottom border of price channel:
Exp(Y1,240)
= Exp(a + b × X1,240 – 2 × s)
= Exp(a + b × 1,803 – 2 × s)
= Exp(5.2790 + 0.0001 × 1,803 – 2 × 0.0744)
= Exp(5.3672)
= $214.27
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 4.91% per annum.
- DHR price at the close of February 20, 2025 was lower than the bottom border of the secondary price channel by $6.97 (3.24%). 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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