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 78.84% per annum.
- WMT price at the close of February 20, 2025 was $97.21 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 91.20% per annum.
- WMT 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 WMT 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: November 29, 2023
End date: February 20, 2025
a = 1.6976
b = 0.0016
s = 0.0305
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 78.84%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0305) – 1
= 13.00%
November 29, 2023 calculations
Top border of price channel:
Exp(Y950)
= Exp(a + b × X950 + 2 × s)
= Exp(a + b × 1,377 + 2 × s)
= Exp(1.6976 + 0.0016 × 1,377 + 2 × 0.0305)
= Exp(3.9519)
= $52.03
Bottom border of price channel:
Exp(Y950)
= Exp(a + b × X950 – 2 × s)
= Exp(a + b × 1,377 – 2 × s)
= Exp(1.6976 + 0.0016 × 1,377 – 2 × 0.0305)
= Exp(3.8297)
= $46.05
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(1.6976 + 0.0016 × 1,826 + 2 × 0.0305)
= Exp(4.6670)
= $106.38
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.6976 + 0.0016 × 1,826 – 2 × 0.0305)
= Exp(4.5448)
= $94.14
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 78.84% per annum.
- WMT price at the close of February 20, 2025 was $97.21 and was inside the primary price channel.
Secondary Trend
Start date: April 15, 2024
End date: February 20, 2025
a = 1.3855
b = 0.0018
s = 0.0282
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0018) – 1
= 91.20%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0282) – 1
= 11.92%
April 15, 2024 calculations
Top border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 + 2 × s)
= Exp(a + b × 1,515 + 2 × s)
= Exp(1.3855 + 0.0018 × 1,515 + 2 × 0.0282)
= Exp(4.1321)
= $62.31
Bottom border of price channel:
Exp(Y1,043)
= Exp(a + b × X1,043 – 2 × s)
= Exp(a + b × 1,515 – 2 × s)
= Exp(1.3855 + 0.0018 × 1,515 – 2 × 0.0282)
= Exp(4.0195)
= $55.67
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(1.3855 + 0.0018 × 1,826 + 2 × 0.0282)
= Exp(4.6844)
= $108.24
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.3855 + 0.0018 × 1,826 – 2 × 0.0282)
= Exp(4.5718)
= $96.71
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 91.20% per annum.
- WMT 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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