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 10.20% per annum.
- DHR price at the close of April 26, 2024 was $246.58 and was higher than the top border of the primary price channel by $23.97 (10.77%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.75% per annum.
- DHR price at the close of April 26, 2024 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 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 22, 2021
End date: December 12, 2023
a = 5.8227
b = -0.0003
s = 0.0600
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0003) – 1
= -10.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0600) – 1
= 27.15%
June 22, 2021 calculations
Top border of price channel:
Exp(Y542)
= Exp(a + b × X542 + 2 × s)
= Exp(a + b × 785 + 2 × s)
= Exp(5.8227 + -0.0003 × 785 + 2 × 0.0600)
= Exp(5.7115)
= $302.33
Bottom border of price channel:
Exp(Y542)
= Exp(a + b × X542 – 2 × s)
= Exp(a + b × 785 – 2 × s)
= Exp(5.8227 + -0.0003 × 785 – 2 × 0.0600)
= Exp(5.4713)
= $237.78
December 12, 2023 calculations
Top border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 + 2 × s)
= Exp(a + b × 1,688 + 2 × s)
= Exp(5.8227 + -0.0003 × 1,688 + 2 × 0.0600)
= Exp(5.4455)
= $231.71
Bottom border of price channel:
Exp(Y1,165)
= Exp(a + b × X1,165 – 2 × s)
= Exp(a + b × 1,688 – 2 × s)
= Exp(5.8227 + -0.0003 × 1,688 – 2 × 0.0600)
= Exp(5.2053)
= $182.24
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 10.20% per annum.
- DHR price at the close of April 26, 2024 was $246.58 and was higher than the top border of the primary price channel by $23.97 (10.77%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: April 25, 2023
End date: April 26, 2024
a = 4.5223
b = 0.0005
s = 0.0519
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0005) – 1
= 21.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0519) – 1
= 23.05%
April 25, 2023 calculations
Top border of price channel:
Exp(Y1,005)
= Exp(a + b × X1,005 + 2 × s)
= Exp(a + b × 1,457 + 2 × s)
= Exp(4.5223 + 0.0005 × 1,457 + 2 × 0.0519)
= Exp(5.4114)
= $223.95
Bottom border of price channel:
Exp(Y1,005)
= Exp(a + b × X1,005 – 2 × s)
= Exp(a + b × 1,457 – 2 × s)
= Exp(4.5223 + 0.0005 × 1,457 – 2 × 0.0519)
= Exp(5.2040)
= $182.00
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.5223 + 0.0005 × 1,824 + 2 × 0.0519)
= Exp(5.6093)
= $272.95
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.5223 + 0.0005 × 1,824 – 2 × 0.0519)
= Exp(5.4019)
= $221.82
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 21.75% per annum.
- DHR price at the close of April 26, 2024 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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