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 23.60% per annum.
- NKE price at the close of May 9, 2025 was $58.30 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 85.54% per annum.
- NKE price at the close of May 9, 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 4, 2023
End date: May 9, 2025
a = 5.5465
b = -0.0007
s = 0.0791
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0007) – 1
= -23.60%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0791) – 1
= 37.19%
January 4, 2023 calculations
Top border of price channel:
Exp(Y668)
= Exp(a + b × X668 + 2 × s)
= Exp(a + b × 968 + 2 × s)
= Exp(5.5465 + -0.0007 × 968 + 2 × 0.0791)
= Exp(4.9906)
= $147.02
Bottom border of price channel:
Exp(Y668)
= Exp(a + b × X668 – 2 × s)
= Exp(a + b × 968 – 2 × s)
= Exp(5.5465 + -0.0007 × 968 – 2 × 0.0791)
= Exp(4.6744)
= $107.17
May 9, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(5.5465 + -0.0007 × 1,824 + 2 × 0.0791)
= Exp(4.3592)
= $78.20
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(5.5465 + -0.0007 × 1,824 – 2 × 0.0791)
= Exp(4.0430)
= $57.00
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 23.60% per annum.
- NKE price at the close of May 9, 2025 was $58.30 and was inside the primary price channel.
Secondary Trend
Start date: February 18, 2025
End date: May 9, 2025
a = 13.6301
b = -0.0053
s = 0.0625
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0053) – 1
= -85.54%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0625) – 1
= 28.41%
February 18, 2025 calculations
Top border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 + 2 × s)
= Exp(a + b × 1,744 + 2 × s)
= Exp(13.6301 + -0.0053 × 1,744 + 2 × 0.0625)
= Exp(4.5139)
= $91.28
Bottom border of price channel:
Exp(Y1,199)
= Exp(a + b × X1,199 – 2 × s)
= Exp(a + b × 1,744 – 2 × s)
= Exp(13.6301 + -0.0053 × 1,744 – 2 × 0.0625)
= Exp(4.2638)
= $71.08
May 9, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(13.6301 + -0.0053 × 1,824 + 2 × 0.0625)
= Exp(4.0900)
= $59.74
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(13.6301 + -0.0053 × 1,824 – 2 × 0.0625)
= Exp(3.8399)
= $46.52
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 85.54% per annum.
- NKE price at the close of May 9, 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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