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 1.75% per annum.
- UNH price at the close of May 19, 2025 was $315.89 and was lower than the bottom border of the primary price channel by $142.64 (31.11%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.77% per annum.
- UNH price at the close of May 19, 2025 was lower than the bottom border of the secondary price channel by $111.89 (26.16%).
- 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 UNH 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: December 6, 2021
End date: July 15, 2024
a = 6.1385
b = 0.0000
s = 0.0486
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 1.75%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0486) – 1
= 21.46%
December 6, 2021 calculations
Top border of price channel:
Exp(Y390)
= Exp(a + b × X390 + 2 × s)
= Exp(a + b × 565 + 2 × s)
= Exp(6.1385 + 0.0000 × 565 + 2 × 0.0486)
= Exp(6.2626)
= $524.58
Bottom border of price channel:
Exp(Y390)
= Exp(a + b × X390 – 2 × s)
= Exp(a + b × 565 – 2 × s)
= Exp(6.1385 + 0.0000 × 565 – 2 × 0.0486)
= Exp(6.0682)
= $431.89
July 15, 2024 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,517 + 2 × s)
= Exp(6.1385 + 0.0000 × 1,517 + 2 × 0.0486)
= Exp(6.3078)
= $548.85
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,517 – 2 × s)
= Exp(6.1385 + 0.0000 × 1,517 – 2 × 0.0486)
= Exp(6.1134)
= $451.87
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 1.75% per annum.
- UNH price at the close of May 19, 2025 was $315.89 and was lower than the bottom border of the primary price channel by $142.64 (31.11%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: August 14, 2024
End date: March 28, 2025
a = 7.7802
b = -0.0009
s = 0.0474
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -27.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0474) – 1
= 20.89%
August 14, 2024 calculations
Top border of price channel:
Exp(Y1,065)
= Exp(a + b × X1,065 + 2 × s)
= Exp(a + b × 1,547 + 2 × s)
= Exp(7.7802 + -0.0009 × 1,547 + 2 × 0.0474)
= Exp(6.4961)
= $662.58
Bottom border of price channel:
Exp(Y1,065)
= Exp(a + b × X1,065 – 2 × s)
= Exp(a + b × 1,547 – 2 × s)
= Exp(7.7802 + -0.0009 × 1,547 – 2 × 0.0474)
= Exp(6.3064)
= $548.07
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 + 2 × s)
= Exp(a + b × 1,773 + 2 × s)
= Exp(7.7802 + -0.0009 × 1,773 + 2 × 0.0474)
= Exp(6.2947)
= $541.69
Bottom border of price channel:
Exp(Y1,220)
= Exp(a + b × X1,220 – 2 × s)
= Exp(a + b × 1,773 – 2 × s)
= Exp(7.7802 + -0.0009 × 1,773 – 2 × 0.0474)
= Exp(6.1050)
= $448.07
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 27.77% per annum.
- UNH price at the close of May 19, 2025 was lower than the bottom border of the secondary price channel by $111.89 (26.16%).
- 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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