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 43.91% per annum.
- VLO price at the close of May 7, 2024 was $156.67 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.08% per annum.
- VLO price at the close of May 7, 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 VLO 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: March 11, 2020
End date: April 20, 2023
a = 3.5080
b = 0.0010
s = 0.1423
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.91%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1423) – 1
= 76.71%
March 11, 2020 calculations
Top border of price channel:
Exp(Y212)
= Exp(a + b × X212 + 2 × s)
= Exp(a + b × 308 + 2 × s)
= Exp(3.5080 + 0.0010 × 308 + 2 × 0.1423)
= Exp(4.0998)
= $60.33
Bottom border of price channel:
Exp(Y212)
= Exp(a + b × X212 – 2 × s)
= Exp(a + b × 308 – 2 × s)
= Exp(3.5080 + 0.0010 × 308 – 2 × 0.1423)
= Exp(3.5305)
= $34.14
April 20, 2023 calculations
Top border of price channel:
Exp(Y995)
= Exp(a + b × X995 + 2 × s)
= Exp(a + b × 1,443 + 2 × s)
= Exp(3.5080 + 0.0010 × 1,443 + 2 × 0.1423)
= Exp(5.2317)
= $187.11
Bottom border of price channel:
Exp(Y995)
= Exp(a + b × X995 – 2 × s)
= Exp(a + b × 1,443 – 2 × s)
= Exp(3.5080 + 0.0010 × 1,443 – 2 × 0.1423)
= Exp(4.6624)
= $105.89
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 43.91% per annum.
- VLO price at the close of May 7, 2024 was $156.67 and was inside the primary price channel.
Secondary Trend
Start date: March 30, 2022
End date: March 8, 2024
a = 4.4830
b = 0.0002
s = 0.0847
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 9.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0847) – 1
= 40.34%
March 30, 2022 calculations
Top border of price channel:
Exp(Y730)
= Exp(a + b × X730 + 2 × s)
= Exp(a + b × 1,057 + 2 × s)
= Exp(4.4830 + 0.0002 × 1,057 + 2 × 0.0847)
= Exp(4.9042)
= $134.86
Bottom border of price channel:
Exp(Y730)
= Exp(a + b × X730 – 2 × s)
= Exp(a + b × 1,057 – 2 × s)
= Exp(4.4830 + 0.0002 × 1,057 – 2 × 0.0847)
= Exp(4.5653)
= $96.10
March 8, 2024 calculations
Top border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 + 2 × s)
= Exp(a + b × 1,766 + 2 × s)
= Exp(4.4830 + 0.0002 × 1,766 + 2 × 0.0847)
= Exp(5.0731)
= $159.67
Bottom border of price channel:
Exp(Y1,217)
= Exp(a + b × X1,217 – 2 × s)
= Exp(a + b × 1,766 – 2 × s)
= Exp(4.4830 + 0.0002 × 1,766 – 2 × 0.0847)
= Exp(4.7342)
= $113.77
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 9.08% per annum.
- VLO price at the close of May 7, 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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