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 November 4, 2024 was $247.18 and was higher than the top border of the primary price channel by $36.11 (17.11%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 23.45% per annum.
- DHR price at the close of November 4, 2024 was lower than the bottom border of the secondary price channel by $5.04 (2.00%). 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 = 5.7582
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(Y406)
= Exp(a + b × X406 + 2 × s)
= Exp(a + b × 590 + 2 × s)
= Exp(5.7582 + -0.0003 × 590 + 2 × 0.0611)
= Exp(5.7097)
= $301.78
Bottom border of price channel:
Exp(Y406)
= Exp(a + b × X406 – 2 × s)
= Exp(a + b × 590 – 2 × s)
= Exp(5.7582 + -0.0003 × 590 – 2 × 0.0611)
= Exp(5.4655)
= $236.39
December 12, 2023 calculations
Top border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 + 2 × s)
= Exp(a + b × 1,498 + 2 × s)
= Exp(5.7582 + -0.0003 × 1,498 + 2 × 0.0611)
= Exp(5.4471)
= $232.07
Bottom border of price channel:
Exp(Y1,032)
= Exp(a + b × X1,032 – 2 × s)
= Exp(a + b × 1,498 – 2 × s)
= Exp(5.7582 + -0.0003 × 1,498 – 2 × 0.0611)
= Exp(5.2029)
= $181.79
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.02% per annum.
- DHR price at the close of November 4, 2024 was $247.18 and was higher than the top border of the primary price channel by $36.11 (17.11%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 25, 2023
End date: October 22, 2024
a = 4.5694
b = 0.0006
s = 0.0464
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0006) – 1
= 23.45%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0464) – 1
= 20.41%
April 25, 2023 calculations
Top border of price channel:
Exp(Y872)
= Exp(a + b × X872 + 2 × s)
= Exp(a + b × 1,267 + 2 × s)
= Exp(4.5694 + 0.0006 × 1,267 + 2 × 0.0464)
= Exp(5.3935)
= $219.96
Bottom border of price channel:
Exp(Y872)
= Exp(a + b × X872 – 2 × s)
= Exp(a + b × 1,267 – 2 × s)
= Exp(4.5694 + 0.0006 × 1,267 – 2 × 0.0464)
= Exp(5.2077)
= $182.68
October 22, 2024 calculations
Top border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 + 2 × s)
= Exp(a + b × 1,813 + 2 × s)
= Exp(4.5694 + 0.0006 × 1,813 + 2 × 0.0464)
= Exp(5.7085)
= $301.43
Bottom border of price channel:
Exp(Y1,248)
= Exp(a + b × X1,248 – 2 × s)
= Exp(a + b × 1,813 – 2 × s)
= Exp(4.5694 + 0.0006 × 1,813 – 2 × 0.0464)
= Exp(5.5228)
= $250.34
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 23.45% per annum.
- DHR price at the close of November 4, 2024 was lower than the bottom border of the secondary price channel by $5.04 (2.00%). 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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