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 10.02% per annum.
- DHR price at the close of January 17, 2025 was $238.36 and was higher than the top border of the primary price channel by $32.00 (15.51%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.75% per annum.
- DHR price at the close of January 17, 2025 was lower than the bottom border of the secondary price channel by $13.68 (5.43%). 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 17, 2021
End date: December 12, 2023
a = 5.7348
b = -0.0003
s = 0.0611
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.02%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0611) – 1
= 27.66%
June 17, 2021 calculations
Top border of price channel:
Exp(Y355)
= Exp(a + b × X355 + 2 × s)
= Exp(a + b × 513 + 2 × s)
= Exp(5.7348 + -0.0003 × 513 + 2 × 0.0611)
= Exp(5.7085)
= $301.43
Bottom border of price channel:
Exp(Y355)
= Exp(a + b × X355 – 2 × s)
= Exp(a + b × 513 – 2 × s)
= Exp(5.7348 + -0.0003 × 513 – 2 × 0.0611)
= Exp(5.4643)
= $236.12
December 12, 2023 calculations
Top border of price channel:
Exp(Y981)
= Exp(a + b × X981 + 2 × s)
= Exp(a + b × 1,421 + 2 × s)
= Exp(5.7348 + -0.0003 × 1,421 + 2 × 0.0611)
= Exp(5.4459)
= $231.80
Bottom border of price channel:
Exp(Y981)
= Exp(a + b × X981 – 2 × s)
= Exp(a + b × 1,421 – 2 × s)
= Exp(5.7348 + -0.0003 × 1,421 – 2 × 0.0611)
= Exp(5.2017)
= $181.58
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.02% per annum.
- DHR price at the close of January 17, 2025 was $238.36 and was higher than the top border of the primary price channel by $32.00 (15.51%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 14, 2023
End date: October 23, 2024
a = 4.7765
b = 0.0005
s = 0.0526
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 18.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0526) – 1
= 23.41%
February 14, 2023 calculations
Top border of price channel:
Exp(Y773)
= Exp(a + b × X773 + 2 × s)
= Exp(a + b × 1,120 + 2 × s)
= Exp(4.7765 + 0.0005 × 1,120 + 2 × 0.0526)
= Exp(5.4090)
= $223.41
Bottom border of price channel:
Exp(Y773)
= Exp(a + b × X773 – 2 × s)
= Exp(a + b × 1,120 – 2 × s)
= Exp(4.7765 + 0.0005 × 1,120 – 2 × 0.0526)
= Exp(5.1986)
= $181.02
October 23, 2024 calculations
Top border of price channel:
Exp(Y1,198)
= Exp(a + b × X1,198 + 2 × s)
= Exp(a + b × 1,737 + 2 × s)
= Exp(4.7765 + 0.0005 × 1,737 + 2 × 0.0526)
= Exp(5.6995)
= $298.71
Bottom border of price channel:
Exp(Y1,198)
= Exp(a + b × X1,198 – 2 × s)
= Exp(a + b × 1,737 – 2 × s)
= Exp(4.7765 + 0.0005 × 1,737 – 2 × 0.0526)
= Exp(5.4891)
= $242.04
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 18.75% per annum.
- DHR price at the close of January 17, 2025 was lower than the bottom border of the secondary price channel by $13.68 (5.43%). 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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