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 21.99% per annum.
- NKE price at the close of January 17, 2025 was $70.84 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.62% per annum.
- NKE price at the close of January 17, 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: January 17, 2025
a = 5.5554
b = -0.0007
s = 0.0697
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -21.99%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0697) – 1
= 32.17%
January 3, 2023 calculations
Top border of price channel:
Exp(Y744)
= Exp(a + b × X744 + 2 × s)
= Exp(a + b × 1,078 + 2 × s)
= Exp(5.5554 + -0.0007 × 1,078 + 2 × 0.0697)
= Exp(4.9614)
= $142.79
Bottom border of price channel:
Exp(Y744)
= Exp(a + b × X744 – 2 × s)
= Exp(a + b × 1,078 – 2 × s)
= Exp(5.5554 + -0.0007 × 1,078 – 2 × 0.0697)
= Exp(4.6824)
= $108.03
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.5554 + -0.0007 × 1,823 + 2 × 0.0697)
= Exp(4.4544)
= $86.01
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.5554 + -0.0007 × 1,823 – 2 × 0.0697)
= Exp(4.1755)
= $65.07
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 21.99% per annum.
- NKE price at the close of January 17, 2025 was $70.84 and was inside the primary price channel.
Secondary Trend
Start date: December 11, 2024
End date: January 17, 2025
a = 9.7378
b = -0.0030
s = 0.0104
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0030) – 1
= -66.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0104) – 1
= 4.25%
December 11, 2024 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,786 + 2 × s)
= Exp(9.7378 + -0.0030 × 1,786 + 2 × 0.0104)
= Exp(4.3893)
= $80.58
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,786 – 2 × s)
= Exp(9.7378 + -0.0030 × 1,786 – 2 × 0.0104)
= Exp(4.3477)
= $77.30
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(9.7378 + -0.0030 × 1,823 + 2 × 0.0104)
= Exp(4.2780)
= $72.10
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(9.7378 + -0.0030 × 1,823 – 2 × 0.0104)
= Exp(4.2365)
= $69.16
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.62% per annum.
- NKE price at the close of January 17, 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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