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 21.93% per annum.
- NKE price at the close of February 20, 2025 was $77.23 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 28.84% per annum.
- NKE price at the close of February 20, 2025 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 NKE 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: January 3, 2023
End date: February 20, 2025
a = 5.5315
b = -0.0007
s = 0.0686
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.93%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0686) – 1
= 31.59%
January 3, 2023 calculations
Top border of price channel:
Exp(Y722)
= Exp(a + b × X722 + 2 × s)
= Exp(a + b × 1,047 + 2 × s)
= Exp(5.5315 + -0.0007 × 1,047 + 2 × 0.0686)
= Exp(4.9586)
= $142.40
Bottom border of price channel:
Exp(Y722)
= Exp(a + b × X722 – 2 × s)
= Exp(a + b × 1,047 – 2 × s)
= Exp(5.5315 + -0.0007 × 1,047 – 2 × 0.0686)
= Exp(4.6841)
= $108.21
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.5315 + -0.0007 × 1,826 + 2 × 0.0686)
= Exp(4.4302)
= $83.95
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.5315 + -0.0007 × 1,826 – 2 × 0.0686)
= Exp(4.1557)
= $63.80
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.93% per annum.
- NKE price at the close of February 20, 2025 was $77.23 and was inside the primary price channel.
Secondary Trend
Start date: November 6, 2023
End date: February 20, 2025
a = 5.9507
b = -0.0009
s = 0.0657
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0009) – 1
= -28.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0657) – 1
= 30.08%
November 6, 2023 calculations
Top border of price channel:
Exp(Y934)
= Exp(a + b × X934 + 2 × s)
= Exp(a + b × 1,354 + 2 × s)
= Exp(5.9507 + -0.0009 × 1,354 + 2 × 0.0657)
= Exp(4.8199)
= $123.96
Bottom border of price channel:
Exp(Y934)
= Exp(a + b × X934 – 2 × s)
= Exp(a + b × 1,354 – 2 × s)
= Exp(5.9507 + -0.0009 × 1,354 – 2 × 0.0657)
= Exp(4.5570)
= $95.30
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(5.9507 + -0.0009 × 1,826 + 2 × 0.0657)
= Exp(4.3799)
= $79.83
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(5.9507 + -0.0009 × 1,826 – 2 × 0.0657)
= Exp(4.1170)
= $61.37
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 28.84% per annum.
- NKE price at the close of February 20, 2025 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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