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 0.49% per annum.
- UNH price at the close of May 17, 2024 was $524.63 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 417.30% per annum.
- UNH price at the close of May 17, 2024 was inside the secondary price channel.
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 8, 2021
End date: May 17, 2024
a = 6.2022
b = 0.0000
s = 0.0495
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0000) – 1
= 0.49%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0495) – 1
= 21.89%
December 8, 2021 calculations
Top border of price channel:
Exp(Y645)
= Exp(a + b × X645 + 2 × s)
= Exp(a + b × 933 + 2 × s)
= Exp(6.2022 + 0.0000 × 933 + 2 × 0.0495)
= Exp(6.3135)
= $552.00
Bottom border of price channel:
Exp(Y645)
= Exp(a + b × X645 – 2 × s)
= Exp(a + b × 933 – 2 × s)
= Exp(6.2022 + 0.0000 × 933 – 2 × 0.0495)
= Exp(6.1156)
= $452.87
May 17, 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(6.2022 + 0.0000 × 1,824 + 2 × 0.0495)
= Exp(6.3254)
= $558.59
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(6.2022 + 0.0000 × 1,824 – 2 × 0.0495)
= Exp(6.1275)
= $458.28
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 0.49% per annum.
- UNH price at the close of May 17, 2024 was $524.63 and was inside the primary price channel.
Secondary Trend
Start date: April 30, 2024
End date: May 17, 2024
a = -1.9523
b = 0.0045
s = 0.0055
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0045) – 1
= 417.30%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0055) – 1
= 2.21%
April 30, 2024 calculations
Top border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 + 2 × s)
= Exp(a + b × 1,807 + 2 × s)
= Exp(-1.9523 + 0.0045 × 1,807 + 2 × 0.0055)
= Exp(6.1949)
= $490.26
Bottom border of price channel:
Exp(Y1,245)
= Exp(a + b × X1,245 – 2 × s)
= Exp(a + b × 1,807 – 2 × s)
= Exp(-1.9523 + 0.0045 × 1,807 – 2 × 0.0055)
= Exp(6.1731)
= $479.66
May 17, 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(-1.9523 + 0.0045 × 1,824 + 2 × 0.0055)
= Exp(6.2715)
= $529.26
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-1.9523 + 0.0045 × 1,824 – 2 × 0.0055)
= Exp(6.2496)
= $517.81
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 417.30% per annum.
- UNH price at the close of May 17, 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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